PATTERN -R ECOGN IT ION AND SEA RCH 291T H IN K I N G A N D R E A S O N I N G 1 9 9 7 3 ( 4 ) 2 9 1 ndash 3 1 3

copy 1 9 9 7 P sy c h o lo g y P r e ss L td

A P attern -recogn ition T heory o f S earch in E xpert

P rob lem So lv ing

F e rna n d G obet

U n iv e rs ity o f N o ttin g h a m U K

U n d e rs ta n d in g h o w lo o k -a h e a d s e a rc h a n d p a tte rn re c o g n it io n in te ra c t is o n e o f

th e im p o rta n t r e s e a rc h q u e s t io n s in th e s tu d y o f e x p e r t p ro b le m s o lv in g T h is p a p e r

e x a m in e s th e im p lic a t io n s o f th e te m p la te th e o ry (G o b e t amp S im o n 1 9 9 6 a ) a r e c e n t

th e o ry o f e x p e r t m e m o ry o n th e th e o ry o f p ro b le m so lv in g in c h e s s T e m p la te s a re

ldquo c h u n k s rdquo (C h a s e amp S im o n 1 9 7 3 ) th a t h a v e e v o lv e d in to m o re c o m p le x d a ta

s t ru c tu re s a n d th a t p o ss e s s s lo ts a l lo w in g v a lu e s to b e e n c o d e d ra p id ly T e m p la te s

m a y fa c i li ta te s e a rc h in th re e w a y s (a ) b y a llo w in g in fo rm a t io n to b e s to re d in to

L T M ra p id ly (b ) b y a l lo w in g a s e a rc h in th e te m p la te s p a c e in a d d i t io n to a s e a rc h

in th e m o v e s p a c e a n d (c ) b y c o m p e n s a t in g lo s s in th e ldquo m in d rsquos e y e rdquo d u e to

in ter fe re n c e a n d d e c a y A c o m p u te r m o d e l im p le m e n t in g th e m a in id e a s o f th e

th e o ry is p re s e n te d a n d s im u la t io n s o f i ts s e a rc h b e h a v io u r a re d is c u s s e d T h e

te m p la te th e o ry a c c o u n ts fo r th e s lig h t s k i l l d if fe re n c e in a v e ra g e d e p th o f s e a rc h

fo u n d in c h e s s p la y e rs a s w e l l a s fo r o th e r e m p ir ic a l d a ta

IN TRO DU CT ION

H o w m u c h o f e x p er t p ro b le m -so lv in g b e h a v io u r is ex p la in e d b y rea l-tim e se a rc h

th ro u g h th e ta sk p ro b le m s p a ce an d h o w m u c h is ex p la in e d b y p a tte rn

re c o g n itio n E v e r s in c e th e s em in a l w o rk o f D e G ro o t (1 9 4 6 1 9 7 8 ) th is q u e stio n

h a s b e e n a re cu rrin g th em e in th e stu d y o f e x p e rtise (s ee C h a rn e ss 1 9 9 1

H o ld in g 1 9 8 5 )

T h e s tu d y o f c h e ss p la y e rs o rig in ate d in its m o d ern fo rm b y D e G ro o t (1 9 4 6 )

h a s b e e n a p ro d u ctiv e su b fie ld o f th e p s y ch o lo g y o f e x p e rtise C h e s s is a ta s k

w h e re p e rc ep tio n m e m o ry k n o w le d g e o rg an isa tio n a n d se a rch in te ra ct in a

c o m p le x d y n a m ic w a y T h e a d v a n tag e s it o ffe rs in c lu d e a q u a n tita tiv e sc a le fo r

m ea s u rin g sk ill a la rg e d ata b a se o f g a m es a n d e c o lo g ica l v a lid ity (N eis se r

1 9 7 6 ) o f th e d o m a in In ad d itio n n u m ero u s e m p ir ic a l d a ta h a v e b e en c o lle cte d

a n d s ev e ra l p s y ch o lo g ic a l th eo rie s o f c h e ss sk ill h a v e b e e n p ro p o s e d

R e q u e s ts fo r r e p rin ts sh o u ld b e se n t to F e rn a n d G o b e t D e p a rtm e n t o f P sy c h o lo gy U n iv e r s i ty o f

N o t t in g h a m N o tt in g h a m N G 7 2 R D U K E m a i l f rg p sy c n o t ta c u k

I a m g ra te fu l to F r a n k R it te r a n d to a n a n o n y m o u s r e v ie w e r fo r h e lp fu l c o m m e n ts o n th is p a p e r

292 GOBET

T h e g o al o f th is p a p e r is to ex te n d th e te m p late th eo ry (G o b e t amp S im o n

1 9 9 6 a ) w h ich w a s o rig in a lly in ten d e d a s a th eo ry o f c h es s p lay ers rsquo p erc e p tio n

a n d m em o ry to th e re a lm o f p ro b le m s o lv in g In th e firs t p a rt I b rie fly re v iew

p re v io u s th eo r ie s o f p ro b le m s o lv in g in c h e ss T h e n I p ro p o se e lem e n ts o f a

c o m p re h e n siv e th e o ry o f c h es s p ro b le m s o lv in g th at is c o m p atib le w ith e m p iric a l

d a ta o n m e m o ry a n d p e rce p tio n res e arc h A sp e c ts o f th is th e o ry a re im p le m e n te d

in a c o m p u te r p ro g ram S E A R C H w h ic h is d es c rib ed in th e th ird p a rt o f th e

p a p e r in co n ju n c tio n w ith re s u lts o f s im u la tio n s F in ally I c o n s id e r h o w th e

p ro p o s e d th eo ry g e n e ralis es to o th e r d o m a in s o f ex p e rtise

CHESS PROB LEM SO LV ING TH EO R IES AN D D ATA

D e G roo t rsquos C la ss ic R e su lts

T h e b a sic f in d in g o f D e G ro o trsquos s tu d y (1 9 4 6 1 9 7 8 ) w as th a t th e re w ere n o

im p o rtan t d if fer en c e s in th e m a c ro s tru ctu re o f se a rc h b e tw e e n w o rld -c la ss

g ra n d m a ste rs a n d s tro n g a m ate u rs e x c e p t th at th e b e s t p la y e rs fo u n d b e tte r

m o v e s a n d w e re s o m e w h a t f as ter to re a c h a d e c isio n O n a v e rag e p la y e rs fro m

b o th s k ill lev els se a rc h e d e q u a lly d e ep v isited th e sa m e n u m b e r o f p o sitio n s in

th e ir s ea rc h a n d p ro p o se d th e sa m e n u m b e r o f c a n d id a te m o v es D e G ro o t

c o n clu d e d th a t th e k e y to e x p e rtise is n o t a s u p e rio rity in ldquo sp e ed o f th in k in g rdquo o r in

a m o re ra tio n a l w a y o f o rg an is in g o n e rsquos th o u g h t b u t s p e cific k n o w le d g e a b o u t

v a rio u s a sp e c ts o f th e ta s k d o m a in D e G ro o t n o ted th a t th e se arch b e h a v io u r

sh o w n b y h is p la y ers w a s c o m p a tib le w ith S e lzrsquos (1 9 2 2 ) th eo ry o f p ro d u ctiv e

th in k in g b u t h e d id n o t o ffe r a d e ta ile d m o d e l o f c h e ss th in k in g

S im on rsquos Theo ry and Com pu te r P rog ram so f Che ss P la y ing

A d e ta ile d a c c o u n t o f c h es s th in k in g w as la te r o f fere d b y C h as e an d S im o n

(1 9 7 3 ) T h e ir th e o ry k n o w n a s th e c h u n k in g th e o ry (C T ) p ro p o s ed th a t a t th e

c o re o f ex p ertis e lie s th e a b ility to re c o g n ise im p o rta n t p ro b le m fe a tu res ra p id ly

T h es e fe a tu res in te rn a lly s to re d as ch u n k s a c t a s a cc e ss p o in ts to se m an tic lo n g -

te rm m em o ry (L T M ) a n d a s th e c o n d itio n s o f p ro d u c tio n s w h o se a c tio n s m a y b e

c ar ried o u t in tern ally o r e x tern ally T h is p ro d u c tio n - sy s te m ac c o u n t w a s lin k e d

to a ss u m p tio n s ab o u t in fo rm a tio n -p ro c e ss in g m e c h a n ism s d e sc rib in g fo r

e x a m p le h o w a n o b jec t is so rte d th ro u g h a d isc rim in atio n n e t in o rd e r to re a ch a

n o d e in L T M I t a lso in c lu d e d p a ra m e te rs s p e cify in g le a rn in g a n d a cc e ss in g

tim e s (e g a b o u t e ig h t s ec o n d s to le a rn a n e w c h u n k ) a s w e ll a s s tr ic t c ap ac ity

lim its (e g S T M lim ite d to se v e n c h u n k s) In th e ca s e o f ch e s s ex p e rtise

p e rc ep tio n m ec h a n ism s in C T a llo w rec o g n itio n o f p atte rn s o f p ie ce s o n th e

b o a rd T h es e p a tte rn s su g g e s t m o v e s w h ich ar e u se d to u p d a te th e in te rn a l

re p re se n ta tio n o f th e b o a rd in w h a t th e y c a ll th e m in d rsquos ey e (T h e m in d rsquos ey e is a

re la tio n al s y ste m th a t c a n b e s u b jec te d to v is u o -sp a tia l m e n tal o p e ra tio n s an d th a t

PATTERN -R ECOGN IT ION AND SEA RCH 293

sto re s p e rc ep tu a l s tru c tu res b o th fro m ex te rn a l in p u ts a n d fro m m e m o ry s to res )

P a tte rn -re c o g n itio n m e c h an is m s a p p ly re cu rs iv e ly in th e in tern al re p re se n ta tio n

o f p o s itio n s in th e m in d rsquos ey e T e rm in a tio n o f se a rch in a b ra n c h is o b ta in e d b y

e v a lu a tin g w h e th e r c erta in g o a ls a re a b o v e o r b e lo w a th res h o ld w h o s e v a lu e

m ay ch a n g e a s a fu n ctio n o f p lay e rs rsquo e x p e cta tio n lev el o f th e p o sitio n

V a rio u s c o m p u te r p ro g ra m s o f p ro b lem s o lv in g in c h e ss w e re d e v e lo p e d b y

S im o n a n d h is co lle a g u es b u t n o n e o f th em d ire ctly in co rp o ra te d th e

re c o g n itio n ndash as so c ia tio n m ec h a n ism o f th e c h u n k in g th eo ry T h e p ro g ra m s

w ritte n b y N ew ell S h a w a n d S im o n (1 9 6 3 ) an d B a y lo r a n d S im o n (1 9 6 6 )

im p le m e n te d th e id ea o f s e le c tiv e se a rc h m a d e p o ss ib le b y th e u se o f h e u ristic s

N e w e ll a n d S im o n rsquos m o d e l (1 9 6 5 se e a lso W a g n e r amp S c u rra h 1 9 7 1 ) fo rm u la te d

six p rin c ip les th a t d ic ta te th e g e n e ra tio n o f m o v es o r e p iso d es u s in g m a in ly th e

e v a lu a tio n o b ta in ed at th e e n d o f a b ra n c h

Ho ld ing rsquos S EEK Theo ry

H o ld in g (1 9 8 5 1 9 9 2 ) critic is e d C T an d p ro p o s ed in ste ad th e S E E K (S E a rc h

E v alu a tio n a n d K n o w led g e ) th e o ry a th eo ry th a t w a s h o w e v e r o n ly lo o se ly

fra m ed an d d id n o t re a ch th e th e o re tica l d e ta il o f C T T h e m a in th ru st o f S E E K

w a s to su g g es t th at m a ste ry in ch e s s d e p e n d s p rim a rily in th in k in g a h e a d an d n o t

in p a tte rn re c o g n itio n N o te th a t a ll th re e c o m p o n e n ts o f th e S E E K th e o ry a re

p re se n t in C T a n d th at i t is re ally th e w eig h t g iv en to e ac h o f th es e c o m p o n en ts

th a t d iff ere n tia te th e tw o th eo r ie s

S aa rilu om arsquos A ppe rcep tio n andR es tru c tu ra tio n Theo ry

R e ce n tly S a a rilu o m a (1 9 9 0 1 9 9 2 ) p ro p o se d th a t p la y e rs w h ile try in g to fin d a

m o v e in a p o sitio n a cc e ss g o a l p o s itio n s b y p a ttern re co g n itio n (S a ar ilu o m a u s es

th e o ld te rm ldquoa p p e rc e p tio n rdquo ) T h e y th e n try to c lo se th e p a th fro m th e p ro b le m

p o sitio n to th e g o al p o sitio n W h en it is n o t p o ss ib le to c lo se th e p a th th e p ro b le m

sp a c e is re stru c tu red T h u s p ro c e sse s le a d in g to a M as terrsquos c h o o sin g a m o v e m a y

b e d e sc rib e d a s a s eq u e n c e o f a p p e rc ep tio n ndash res tru ctu ratio n c y c les w h ic h m a k e it

p o s sib le to f in d so lu tio n s w ith o n ly a lim ite d s ea rc h in th e p ro b le m s p a ce

S a a rilu o m arsquos th e o ry a d m itte d ly s till a t i ts e arly s ta g e o f d ev e lo p m e n t is n o t

q u ite sa tisfa c to ry i t is u n c lea r w h a t d iffe ren tia te s it fro m N e w e ll a n d S im o n rsquos

(1 9 7 2 ) m e a n sndash e n d s a n a ly s is a n d it d o e s n o t m a k e p ro v is io n fo r w h at h ap p e n s

w h e n p la y e rs d o n o t h av e a g o a l p o sitio n in m in d

E ricsson and K in tsch rsquos Long -te rm W o rk ingM em o ry Theo ry

E rics so n a n d K in tsc h (1 9 9 5 ) p ro p o s e w ith in th e fr am e w o rk o f th e ir lo n g -term

w o rk in g m e m o ry th eo ry (L T W M T ) th a t sk ille d p lay e rs h av e c o n s tru cte d a n

h ie ra rch ic a l re tr ie v a l s tru c tu re n o t u n lik e th e stru c tu re c rea te d b y S F a n d D D

294 GOBET

tw o m n em o n is ts sp e c ia lise d in th e d ig it- sp a n ta s k (C h as e amp E ric s so n 1 9 8 2 )

T h is p o w e rfu l m e m o ry stru c tu re iso m o rp h ic to th e 6 4 s q u ares o f th e c h e ss b o a rd

a llo w s p la y e rs to u p d a te in fo rm a tio n ra p id ly d u rin g se a rc h T h e th eo ry a ls o

p ro p o s e s th a t c h e ss p lay e rs ca n c re ate n e w L T M as so c ia tio n s ra p id ly a lth o u g h

n o p ara m e te r is g iv e n to s p e cify th is s p ee d o f e n co d in g

I h av e sh o w n els ew h ere (G o b e t 1 9 9 6 ) th a t L T W M T in a d d itio n to b e in g

v a g u e a n d le a v in g m a n y d e ta ils u n s p e cifie d g e n e ra te s p re d ic tio n s th a t d o n o t

a g re e w ith th e e x p e rim en ta l d a ta o n c h es s p e rc ep tio n a n d m e m o ry In ad d itio n

th e m e m o ry m e ch a n ism s p ro p o s ed b y L T W M T (re tr ie v a l s tru c tu re a n d ra p id

e lab o ratio n o f L T M stru c tu re s) s ee m a t o d d s w ith th e fo llo w in g a sp e c t o f c h e ss

p la y er srsquo se arch b e h av io u r I t is co m m o n fo r c h e ss p la y er s to re v is it a n o d e d u rin g

th e ir a n aly s is o f th e p o sitio n H o w ev e r in ste a d o f ac c e ssin g th is n o d e d ire c tly as

su g g es ted b y L T W M T rsquos v e ry p o w erfu l m e ch a n is m s fo r s to rin g p o sitio n s ra p id ly

a n d a c c u rate ly p la y er s a c c es s th e targ e t p o sitio n b y g en era tin g a s e q u e n ce o f

in d iv id u a l m o v e s fro m th e g iv en p ro b le m p o s itio n (c f D e G ro o t 1 9 4 6 ) T h is

b e h a v io u r su g g e sts th a t p lay e rs m a y n o t s to re p o sitio n s a s q u ic k ly a s p ro p o s e d b y

L T W M T

TH E TEM P LA TE TH EO RY AN D ITS A PPL IC A T IO NTO PRO BLEM SO LV ING

In itia lly th e tem p la te th e o ry (T T ) w a s d e v elo p e d to re m o v e so m e w e a k n e ss es in

th e c h u n k in g th e o ry w ith r es p e ct to d ata fro m m e m o ry re se a rch (G o b e t amp S im o n

1 9 9 6 a ) C o n tra ry to C T rsquos p re d ic tio n s b a s ed o n a lim ited S T M ca p a c ity c h e ss

p la y er srsquo m e m o ry is res is ta n t to re tro a ctiv e in te rfe re n ce (C h arn es s 1 9 7 6 ) a n d

c h e ss p la y e rs c a n re c a ll s ev e ra l b rief ly p re s en te d p o sitio n s w ith re a so n a b le

a cc u ra c y (C o o k e A tla s L a n e amp B erg e r 1 9 9 3 G o b e t amp S im o n 1 9 9 6 a )

L ik e C T T T p ro p o s es th a t c h u n k s a re ac c e ss ed b y tra v e rsin g a d isc rim in a tio n

n e t C h u n k s a re lin k e d to o th e r in fo rm a tio n s to red in L T M s u ch a s m o v es p la n s

ta ctic al m o tiv es a n d s o o n In a d d itio n c h u n k s th a t o fte n o cc u r in a p lay e rrsquos

e x p er ie n c e c a n e v o lv e in to m o re c o m p le x d a ta s tru ctu re s ( te m p la tes ) w h ich h a v e

slo ts a llo w in g v a ria b les to b e e n c o d ed fo r e x a m p le to sp e c ify th e sq u a re

o c c u p ie d b y a p iec e A c c o rd in g to T T th is en c o d in g o cc u rs ra p id ly (a b o u t o n e

se c o n d p e r s lo t) In a d d itio n to s lo ts tem p la te s co n ta in a co r e w h ic h is m ad e u p

o f (v a ria b le -fre e ) c h u n k s A lto g e th er te m p late s a re as su m e d to s to re a t le as t

a b o u t 1 0 p iec e s F in ally te m p la te s m a y b e lin k e d to o th er te m p la tes T T als o

p ro p o s e s th a t in fo rm a tio n sto re d in th e m in d rsquos e y e a s tru ctu re s im ilar to th a t

p ro p o s e d b y C T d e ca y s ra p id ly a n d th at i t n e e d s to b e u p d a te d e ith e r b y in p u ts

fro m th e e x te rn a l w o rld o r b y in p u ts fro m m e m o ry s tru ctu re s

T T re m o v e s th e d iffic u lty o f C T w ith in te rfe ren c e p h e n o m en a f ir s t b e ca u s e it

h y p o th e sis es s o m e fa st L T M e n c o d in g (th ro u g h te m p late s lo ts) a n d se c o n d

b e c au s e te m p la te s co n ta in m o re in fo rm a tio n th a n th e ch u n k s p ro p o s ed b y C T

(C T a ssu m e d th a t c h u n k s co n ta in a t m o s t f iv e o r s ix p iec e s) F in a lly T T k ee p s

PATTERN -R ECOGN IT ION AND SEA RCH 295

th e p o w e r o f C T to e x p lain th e r ap id rec o g n itio n o f p o sitio n s sh o w n b y m a ste rs

a s th e s am e d isc rim in a tio n m e ch a n ism s are p res e n t (G o b e t 1 9 9 6 )

S ea rch M echan ism s

T T a n d C T p ro p o se th a t se a rc h is ca rrie d o u t in a fo rw ard fa sh io n b y re cu rsiv e

a p p lica tio n o f p a tte rn re co g n itio n p ro ce s se s in th e in te rn a l rep res e n ta tio n In th e

re m ain d e r o f th is se c tio n I w ill f le sh o u t th is m e c h an ism w ith ad d itio n a l sp e c ifi-

c atio n s I w ill a lso sh o w h o w c h u n k s an d te m p late s m a y b e u se d to te rm in a te

se a rc h a n d h o w te m p la te s m a y b e u se d to ca rry o u t s ea rc h a t a le v e l m o re

a b stra c t th a n th e m o v e le v e l

M o v e G e n e ra tio n A s m en tio n e d e arlie r p a ttern r ec o g n itio n is a p p lie d

re c u rsiv e ly in T T If a c h u n k mdash o r a te m p la te a s tem p la te s ar e a s p e cia l c as e o f

c h u n k smdash is rec o g n is ed i t m a y g iv e a c c es s to a m o v e (o r a se q u e n c e o f m o v e s ) o r

to a n h e u ris tic fo r se le ctin g th e n ex t m o v e E x a m p le s o f s u ch h e u ristic s a re

ldquo O c c u p y o p e n lin e s rdquo o r ldquo C o u n te r-a tta c k in th e ce n tre w h e n a ttac k e d o n th e

K in g rsquos s id e rdquo In th is ca s e th e m o v e(s ) is (a re ) c a rried o u t in th e m in d rsquos e y e If n o

m o v e re su lts fro m p a tte rn re co g n itio n o n e o f tw o o p era tio n s m a y b e ap p lie d

E ith e r th ere is a n e w atte m p t to g e n e rate a m o v e b y a cc e ss in g a d iffe re n t c h u n k

o r w ea k e r h e u ristic s a re a p p lie d

U p d a te o f In te rn a l R ep re se n ta tio n a n d S to r a g e o f In fo rm a tio n in to

T e m p la te W h en a m o v e o r a se q u e n c e o f m o v e s is c a rrie d o u t in th e m in d rsquos

e y e th e in te rn a l rep res e n ta tio n is u p d a te d a n d w h e n a te m p la te h as b e e n

a cc e ss e d s lo ts a re u p d ate d a s w e ll S lo ts m a y sto re in fo rm a tio n a b o u t th e

lo c atio n o f p ie ce s s tra teg ic in fo rm a tio n e v alu a tio n o f th e p o sitio n o r p a rt o f i t

a n d s o o n N o te th a t th is in fo rm a tio n fa c ilita te s s ea rc h b e c au se p o s sib le fo r -

g e ttin g th ro u g h d ec a y in th e m in d rsquos e y e m a y b e b ac k e d -u p b y in fo rm a tio n s to re d

in s lo ts

E va lu a tio n o f N o d e s E v a lu a tio n o f a p o sitio n is n o t c ar ried o u t af te r e ac h

m o v e b u t o n ly a t th e term in a l p o sitio n s E v a lu atio n is e ith e r r e trie v e d w h e n

p o s sib le fro m ch u n k s th a t h a v e b e en re c o g n ise d o r co m p u te d w h e n th e p la y e r

d e c id e s to te rm in a te s e arc h (s ee n e x t p a ra g ra p h ) D e G ro o trsquos (1 9 4 6 ) p ro to co ls

in d ic ate th a t p la y e rs e v a lu a te o n ly te rm in a l p o s itio n s a n d th a t th e ir e v a lu atio n s

a re ra th e r s im p le ta k in g in to a c co u n t a s in g le fe a tu re su c h as m o b ility o r c o n tro l

o f th e c e n tre a n d stro n g ly su g g e s t th a t e v a lu a tio n s are n o t co m p u te d b y

c o n jo in in g s e v eral fe atu re s

E n d in g S ea r c h o f a n E p iso d e A c ritic a l q u es tio n g iv e n a lim ite d

in fo rm a tio n -p ro c es sin g c a p a city is w h e n to s to p se a rc h in g a n e p iso d e (i e a

se q u e n c e o f m o v es g e n e ra ted fro m a b as e m o v e ) I p ro p o se th a t th e fo llo w in g

296 GOBET

c o n d itio n s ca n h alt th e se a rc h o f a n e p iso d e T o b e g in w ith th e p ro b a b ility o f

m ak in g a n e rro r is to o h ig h P s y ch o lo g ic a lly th is p ro b a b ility is a fu n ctio n o f th e

fo rg e ttin g a n d in ter fer en c e r a te s in th e m in d rsquo s ey e P h e n o m e n o lo g ic a lly p lay e rs

p ro b a b ly a s se ss th is p ro b a b ility b y ta k in g in to a c c o u n t th e d e p th o f se a rc h

re a ch e d a n d b y e s tim a tin g th e ir fa m ilia rity w ith th e p o s itio n

A n o th e r re a so n to h a lt s ea rc h o c cu r s w h e n th e le v e l o f e x p e c tatio n fo r th e

p o s itio n is m et o r w h e n a f ea tu re o f th e p o s itio n (e g sa fe ty o f th e K in g ) w as

e v a lu a te d to b e lo w e r th a n its a d m iss ib le v a lu e (N e w e ll amp S im o n 1 9 7 2 ) T h is

le v el o f e x p e c ta tio n is p ro v id e d b y a c h u n k en c o u n te re d d u rin g e arlie r s ea rc h o r

b y e x p lic it ev a lu a tio n o f th e p o s itio n a n d w a s s to re d e ith e r in S T M o r w h e n

a v a ila b le in a te m p late s lo t A fin a l h a ltin g c o n d itio n is th a t a d e c isiv e e v e n t

o c c u rre d s u ch a s m a te im p o rta n t m a teria l g a in o r lo ss o r fu lfilm e n t o f a k e y

g o al

S e lec tin g th e N e x t B a s e -m o v e N o w co n s id er th e q u e stio n o f w h ic h b a se -

m o v e to se a rch n ex t w h en a le a f n o d e h a s b e e n re a ch ed A n y o f s ix m e c h an is m s

m ay b e e n g a g e d F irst if th e le a f w a s e v a lu ate d w ith a h ig h risk o f er ro r th e s am e

se q u e n c e o f m o v e s is se a rc h ed a g ain in o rd e r to o b ta in a m o re re lia b le e stim a te

S e c o n d th e sa m e s eq u en c e o f m o v e s m a y b e se a rch e d a g a in to m a k e s u re th a t i t

h a s b e e n sto re d in L T M T h ird if a tem p la te h a s b e e n re co g n ise d a m e ta -se a rc h

(s ee la te r) is c arr ie d o u t F o u rth th e re is a b ia s to g iv e p re fe ren ce to n o rm a l b as e -

m o v e s ea rly in se a rch a n d to u n u su a l b a s e-m o v e s la ter (N ew ell amp S im o n 1 9 7 2

p 7 2 3) F ifth a m ov e re ac h e d at a n y le v e l o f d e p th in s ea rch in g a lin e m a y b e trie d

a s a ca n d id a te m o v e in th e n ex t lin e S ix th if th e e v alu a tio n o f an e p iso d e g iv e s a

fa v o u ra b le re su lt its an aly s is is c o n tin u e d if th e ev a lu a tio n is u n fa v o u rab le a

d iffe re n t b a se -m o v e is ta k e n u p (N e w e ll amp S im o n 1 9 7 2 )

M e ta -s e a rc h w ith T e m p la te s (A b stra c t P la n n in g ) S e arc h m ay b e c arrie d o u t

n o t o n ly a t th e m o v e le v e l b u t a lso a t th e te m p la te le v el P lay e rs s o m e tim es

d e v e lo p a tre e se a rc h b y g e n eratin g k ey p o sitio n s (te m p la tes ) in s tea d o f

d e v e lo p in g a tree se arch b y g e n e ra tin g m o v e s (e g D e G ro o t 1 9 7 8 p 1 5 3 ) P ath s

b e tw e en k e y p o sitio n s c o n s is t o f m a cro -o p e ra to r s o r in u n s p ec ifie d o p e ra to r s

w h ic h w ill b e fil le d in a t a la te r s ta g e o f se a rch if th e le a f p o sitio n s a re ju d g e d

fa v o u ra b le T h is ty p e o f se arch is c o n tin g en t to th e p res e n ce in p la y ers rsquo L T M o f

te m p la tes su ffic ie n tly c lo se to th e p o s itio n a t h a n d K o ed in g e r a n d A n d e rs o n

(1 9 9 0 ) h a v e p ro p o se d a s im ilar id e a w ith re sp e c t to g eo m e try T h is m e ta -se a rc h

m ec h a n ism is a ls o sim ilar to th e ldquoa p p e rc e p tio n rdquo m e c h a n ism su g g es ted b y

S a a rilu o m a (1 9 9 0 1 9 9 2 )

Theo re t ica l Im po rta n ce o f Tem p la te s

O b v io u s ly m an y o f th e p ro ce s se s ju st d es c rib ed c a n b e im p le m e n te d w ith in th e

e ar lie r C T w ith o u t h y p o th e sisin g th e p re se n c e o f te m p la tes T e m p la tes a re

h o w e v e r im p o rta n t fo r s o m e o f th e k ey c o g n itiv e p ro c es se s in c h e ss b e c au se

PATTERN -R ECOGN IT ION AND SEA RCH 297

(a ) s lo ts a llo w in fo rm a tio n ab o u t s tra te g ic o r tac tica l th e m e s a s w e ll a s a b o u t

e v a lu a tio n o f th e p o sitio n to b e en co d e d in L T M rap id ly (b ) lin k s b e tw e e n

te m p la tes a llo w fo r ldquo m e ta -se a rc h rdquo (c ) in fo rm a tio n s to re d b o th in th e c o re a n d in

th e slo ts o f th e te m p late c o m p en sa tes fo r d e c a y an d in te rfe re n c e in th e m in d rsquos

e y e as it m a y b e u se d to re in sta te fa d in g in fo rm a tio n T h is c o m p e n sa tio n

m ec h a n ism is p ar tic u la rly u se fu l w h e n p e rce p tu a l in fo rm a tio n fro m th e ex te rn a l

b o a rd is u n re liab le fo r ex a m p le b e ca u s e se v e ra l m o v e s h a v e b e en c arr ie d o u t in

th e m in d rsquos e y e

Em p ir ica l D a ta Sup po rtin g th e TT A ccoun t o f Sea rchand Pa tte rn R e cogn itio n

In th is se c tio n T T is q u alita tiv e ly ap p lie d to s o m e o f th e k ey d a ta f ro m e m p ir ic a l

stu d ie s o f ch e s s p ro b le m s o lv in g Q u a n tita tiv e a s se ss m e n t w ill b e th e to p ic o f

th e fo llo w in g se c tio n I h a v e sh o w n e lse w h e re (G o b e t 1 9 9 6 ) th at th e p re d ic tio n s

o f T T a re w e ll su p p o rted b y e m p ir ic a l d a ta fro m re se a rch o n m e m o ry a n d

p e rce p tio n

In c re a sin g th e n u m b e r o f c h u n k s a n d te m p la te s h a s tw o o p p o site ef fec ts w ith

re sp e c t to se a rch (G o b e t in p res s) O n th e o n e h a n d d e ep s e arc h is fac ilita te d as

c o m p are d w ith th e m o re co m p u ta tio n a lly e x p e n s iv e w e a k m e th o d s b e c au se

p a tte rn re c o g n itio n is a ra p id p ro c es s a n d b e ca u s e se q u e n c e s o f m o v es m a y b e

le arn e d an d su g g e ste d b y c h u n k s O n th e o th er h a n d th e n ee d fo r d e e p se a rc h

o fte n d isa p p e ar s b e ca u s e e v a lu atio n s su g g e ste d b y p a tte rn re c o g n itio n m a y b e

m o re re lia b le th a n e v a lu atio n s co m p u te d b y w e a k m eth o d s T h e s e tw o o p p o site

e ffe cts c a n e x p la in w h y th e sk ill d iffe re n c e s in a v e rag e d e p th o f se a rc h a re sm all

P a tte rn re co g n itio n a llo w s stro n g p la y e rs to b e h ig h ly s e le c tiv e in th e ir s ea rc h

T h is c a n b e s e en b o th in th e ra p id w a y M a s te rs ze ro in to th e k e y as p e cts o f a

p o s itio n (D e G ro o t 1 9 4 6 ) an d in th e w ay e y e m o v e m e n ts d iffe r a s a fu n c tio n o f

sk ill d u rin g th e firs t s ec o n d s o f th e p e rc ep tio n o f a p o sitio n (D e G ro o t amp G o b et

1 9 9 6 ) A d d itio n a l e v id e n ce is p ro v id e d b y S a a rilu o m a (1 9 9 0 ) w h o h a s sh o w n

th a t p la y e rs ch o o se ste re o ty p e d so lu tio n s in p ro b le m s w h e re fa ste r ( in th e

n u m b e r o f m o v es to r ea c h m a te) b u t u n c o m m o n so lu tio n s a re p re s en t T h e se d a ta

a d d s u p p o rt to T T b e c a u se p a ttern re co g n itio n lie s a t i ts c o re

F u r th er s tro n g e v id e n ce fo r th e ro le o f p atte rn re c o g n itio n is th a t M as te rs c a n

p la y s ev e ra l o p p o n en ts s im u lta n eo u sly a t a s tre n g th c lo se to th at in o n e -a g ain s t-

o n e p lay I t is in te re stin g th at in s im u lta n eo u s g a m e s th ey te n d to p la y ldquon o rm a lrdquo

m o v e s a n d re ly o n o p p o n e n ts rsquo e rro rs (G o b e t amp S im o n 1 9 9 6 c ) N o rm a l m o v es

m ay c o rre sp o n d to th e ty p e o f m o v e s su g g e ste d b y c h u n k s an d tem p la te s

A fea tu re o f c h es s ex p e rtise c a p tu re d u n iq u e ly b y T T is th e h ig h le v e ls a t

w h ic h ch e s s p lay e rs o rg a n is e th e ir k n o w le d g e D e G ro o t (1 9 4 6 ) p ro p o s e d th a t

p la y er s o rg an is e p o sitio n s a ro u n d la rg e ldquo c o m p le x e srdquo b ig g e r th a n th e c h u n k s th a t

w e re la te r p ro p o se d b y C h a se a n d S im o n (1 9 7 3 ) D e G ro o t a lso su g g es ted a s d id

C o o k e e t a l (1 9 9 3 ) th a t p la y e rs re p re s en t in fo rm a tio n a t a c o n c e p tu a l lev el In

p a rticu la r D e G ro o t (1 9 4 6 ) p ro p o se d th a t M a ste rsrsquo d e sc rip tio n s o f g am e s a re

298 GOBET

c en tred a ro u n d k ey p o sitio n s o f th e g a m e T T o ffe rs th eo retic al s tru c tu res

(te m p la te s) th a t co u ld a c c o u n t fo r p lay ers rsquo larg e c o m p le x es h ig h - le v e l re p re -

se n ta tio n s a n d k e y p o sitio n s T T a lso o ff ers m e ch a n ism s b as e d o n f req u en c y o f

o c c u rre n ce s e x p la in in g h o w th e s e h ig h - le v e l re p re se n ta tio n s a re d ev elo p e d a n d

m ec h a n ism s b a se d o n d isc rim in a tio n p ro c e sse s e x p la in in g h o w th ey c o u ld b e

a c ce ss e d ra p id ly

T T is a lso co m p a tib le w ith re su lts fro m e x p er im e n ts u s in g p o s itio n s fo r w h ic h

a cc e ss to k n o w le d g e is d iffic u lt In H o ld in g a n d R e y n o ld s rsquo (1 9 8 2 ) e x p e rim e n t

c h e ss s k ill d id n o t c o rr ela te w ith th e re c a ll o f s e m i-ra n d o m p o s itio n s sh o w n fo r a

fe w se co n d s b u t eff ec tiv en es s o f th e s ea rc h fo r th e b e st m o v e in th es e p o s itio n s

d id c o rr ela te w ith s k ill T T o f fer s a n ex p la n a tio n fo r th e fa c t th a t th e re w a s a

stro n g c o rre la tio n b e tw e en sk ill le v e l a n d q u a lity o f m o v e p ro p o se d P lay e rs

re c u rsiv e ly g e n e ra te a m o v e th ro u g h w ea k m e th o d s w h en n o c h u n k is

re c o g n ise d u n til o n e o f th e h a ltin g co n d itio n s (m en tio n e d e a rlier ) a p p lie s T h e n

g iv e n th eir la rg e r d ata b a se o f c h u n k s s tro n g p la y e rs a re m o re lik e ly th a n w e a k

p la y er s to f in d a u s efu l p a tte rn in p o sitio n s th a t h a v e b ee n n e w ly u p d ate d in th e

m in d rsquos e y e a n d th e re fo re a re m o re lik e ly to f in d g o o d m o v e s in th eir se a rch

I m en tio n e d e a rlier th at E ric ss o n a n d K in tsc h (1 9 9 5 ) p ro p o s ed m ec h a n ism s

(re trie v al s tru c tu re a n d ela b o ra tio n s o f L T M sc h e m a s ) th a t e n c o d e in fo rm a tio n

q u ic k ly a n d re lia b ly B y c o n tra st th e e n c o d in g c a p a c ity o f te m p la te s is r e la tiv ely

w e a k In p a rtic u la r T T p re d icts th at th e sa m e te m p la te m a y s o m e tim e s b e u se d to

e n c o d e s e v era l s im ilar p o sitio n s th u s in c re as in g th e ris k o f in terf ere n c e as se a rc h

p ro g re s se s A s a co n se q u e n ce a n d c o n trary to L T W M T rsquos p re d ic tio n s p lay e rs

sh o u ld o fte n re v isit p o sitio n s b y g e n era tin g m o v es in s tea d o f a cc e ss in g th e m

d ire ctly fro m m em o ry T h is is w h at p la y e rsmdash e v e n m a ste rs mdash d o (D e G ro o t

1 9 4 6 ) F in a lly T T m a y h a v e s o m e th in g to sa y a b o u t e rro rs in c h e ss K ro g iu s

(1 9 7 6 ) m e n tio n s th a t er ro rs o f te n o c c u r w h e n a m o v e h a s ca u s ed im p o rta n t

c h a n g es in th e p o s itio n T h is m a y b e d u e to p la y e rsrsquo in a b ility to re c o g n ise th a t a

p re v io u sly a d eq u ate te m p late h as b ec o m e in a d e q u a te

In s u m m a ry T T o ffe rs a g o o d q u alita tiv e a c co u n t o f s e v eral im p o rtan t c h e ss

p h e n o m en a I t is n o w tim e to tu rn to m o re o b je c tiv e q u an tita tiv e te sts o f th e

th eo ry

A COM PUTER M ODE L O F S EARCH IN CH ESS

In th e re m a in d e r o f th is p a p e r I p re s en t a c o m p u te r m o d e l c a lled S E A R C H

w h ic h im p le m e n ts T T in so m e d e ta il I f irs t d e s crib e th e im p le m en ta tio n o f

S E A R C H m a k in g cle a r w h a t a s p ec ts o f T T h a v e b e e n in c lu d ed a n d th en d isc u ss

its b e h a v io u r w ith r es p e ct to h u m a n d a ta

O ve rv iew o f M ode l

F u ll im p le m e n ta tio n o f T T a s a c h e ss-p la y in g c o m p u ter p ro g ram w o u ld b e a

m ajo r ta sk mdash th is d iffic u lty is d e m o n stra te d b y th e fa c t th a t n o c o m p le te co m p u te r

m o d e l o f ch e s s c o g n itio n in c lu d in g p e rc e p tio n m em o ry a n d p ro b le m so lv in g

PATTERN -R ECOGN IT ION AND SEA RCH 299

h a s e v e r b e e n d e v elo p e d I p u rs u e d a lim ited a im a co m p u te r m o d el th a t c o n tain s

so m e o f th e im p o rta n t p aram e te rs o f T T a n d th a t co m p u te s k e y b e h a v io u ra l

v a ria b le s T h is m o d el d o e s n o t c o n stitu te a co m p le te im p le m e n ta tio n o f th e

th e o ry (it d o e s n o t s ea rc h o r e v a lu a te c h e ss p o sitio n s) b u t is d e ta ile d en o u g h to

o ffe r a g o o d te st o f so m e a s p ec ts o f T T I t is s o b e rin g to n o tic e th a t e v e n th is

p a rtia l im p lem e n tatio n o f th e th e o ry is q u ite c o m p le x a n d re q u ire s m a n y

p a ra m e te rs T h is is th e p rice o f a v o id in g th e v ag u en e s s o f v e rb al th e o ris in g

The M a in P rob lem -so lv in g Loop

T h e m ain in te re st o f th e m o d el is in th e in te ra c tio n b etw ee n p atte rn re c o g n itio n

a n d s ea rc h T h e m o d e l g e n e ra tes in d e p en d en t ep is o d es fo llo w in g se v e ral ru les

fo r g e n eratin g m o v e s a n d ch o o sin g sto p co n d itio n s C o m p atib le w ith m o s t

h u m an p ro to co ls th e p ro g ra m c o n sid e rs o n ly o n e b ra n c h w ith in a n ep is o d e (th u s

th e re is n o b ra n c h in g p o in t w ith in a n e p iso d e) A s illu stra te d in F ig 1 th e m o d e l

is c lo se to th e d es crip tio n o f T T g iv en e a rlie r in th is p a p e r T h e v ario u s c o n d itio n s

a n d o p e ra tio n s in S E A R C H a re re p re se n te d as p ro b a b ilit ie s o r p ro b ab ility

d istr ib u tio n s an d n o t a s a ctu a l c h e ss m o v e s e v a lu atio n s o r s y m b o lic s tru c tu res

in S T M o r in th e m in d rsquos e y e

A tra c e o f S E A R C H is sh o w n in F ig 2 T h e an aly s is w ill c e n tre o n th e

fo llo w in g v a ria b les a s a fu n c tio n o f th e n u m b e r o f c h u n k s ra te o f g en e ra tin g a

m o v e le v el o f fu z zin e ss in th e m in d rsquos e y e w h en a n e p is o d e is e n d e d m e an d e p th

o f s ea rc h m eth o d s u se d fo r g en e ra tin g a m o v e a n d m eth o d s u se d fo r s to p p in g a n

e p iso d e

T h e c o n c ep t o f te m p la te is im p le m e n te d in tw o w a y s (a ) b y h ig h e r

p ro b a b ilitie s o f f in d in g (s eq u en c e s o f) m o v e s a n d ev a lu a tio n s th an w ith p la in

c h u n k s a n d (b ) b y a d e cre a se in th e le v e l o f fu zz in e ss m ad e p o s sib le b y th e L T M

re p re se n ta tio n o f th e c o re o f th e p o sitio n a n d o f s lo ts

T h e le v e l o f re lia b ility o f th e in fo rm a tio n in th e m in d rsquos ey e is c a p tu re d b y a

ldquo fu z zin e s srdquo p a ra m e te r e x p re ss ed in a rb itr ary u n its T h re e m a in c o g n itiv e

fe a tu res ar e c a p tu red b y th is p a ra m ete r w o rk in g m e m o ry c a p a c ity a b ility to

m ain ta in a v isu o -s p atia l im ag e a n d su b je ctiv e e s tim a te o f th e r isk o f m ak in g a n

e rro r T h e fu z z in es s p a ram e ter is th e n as su m e d to o rig in ate b o th fro m th e

h a rd w a re a n d th e so ftw a re o f th e sy s tem It m a y v a ry d u r in g th e life tim e o f a

p la y er b e c a u se o f b io lo g ic a l m a tu ra tio n o r a g e in g an d m a y b e a ffe c ted b y

e x p e rim e n ta l m a n ip u latio n s T h e re a re th ree re a so n s w h y S E A R C H en d s a

se a rc h th e lev el o f fu z z in e s s is to o h ig h a n e v a lu atio n is p ro p o se d o r n o m o v e is

p ro p o s e d T h e id e a o f ex p ec ta tio n le v e l is n o t e x p lic itly p re se n t in th e m o d el b u t

it is im p lic it in th e p ro b a b ility v alu e s o f f in d in g fe atu re s e n d in g th e s ea rc h o f a n

e p iso d e e ith er b y p a tte rn re c o g n itio n o r b y th e a p p lica tio n o f h e u ristic s

S e le ctio n o f th e n ex t b a se -m o v e (a k e y c o n c ern o f N ew e ll amp S im o n 1 9 6 5 a n d

W ag n e r amp S c u rra h 1 9 7 1 ) is n o t ad d res se d b y S E A R C H w h ic h in g e n e ra l lac k s

th e s em a n tic in fo rm a tio n n e c es sa ry fo r su c h a se le c tio n F in a lly m e ta -se a rc h

w ith te m p la te s is n o t d ire c tly im p le m e n te d in S E A R C H b u t it is im p lic itly

300 GOBET

300

FIG 1 F lo w c h a rt o f S E A R C H

PATTERN -R ECOGN IT ION AND SEA RCH 301

301

F IG 2 E x a m p le s o f e p is o d e s g e n e ra te d b y S E A R C H

302 GOBET

re p re se n te d b y th e re la tiv e ly h ig h p ro b ab ility o f f in d in g (s eq u e n c e s o f) m o v es

a n d e v a lu atio n s w ith tem p la tes as c o m p are d w ith ch u n k s

The M ode lrsquos P aram e te rs

S E A R C H h as m a n y p a ra m ete rs a n d it is o f c o u rs e n e c es sa ry to se t u p a f ew o f

th e m w ith in d e p e n d e n t d a ta in o rd er to re d u c e th e n u m b e r o f d e g re e s o f fre e d o m

in th e m o d e l W h e n p o ss ib le I h a v e u s e d sim u la tio n s w ith th e C H R E S T (D e

G ro o t amp G o b e t 1 9 9 6 G o b e t 1 9 9 3 ) an d C H U M P (G o b e t amp Ja n s en 1 9 9 4 )

p ro g ram s to se t p a ra m e te r v a lu es C H R E S T is a p ro g ra m im p le m e n tin g as p e cts

o f T T a n d s im u la tin g n u m e ro u s e x p er im e n ts o n p e rc ep tio n an d m e m o ry in ch e s s

a n d C H U M P is a p ro g ra m p la y in g (w e ak ) c h e ss b y p u re p a tte rn re co g n itio n

N u m b e r o f C h u n k s a n d T e m p la te s T ab le 1 sh o w s th e v a lu es th at w ill b e

u s ed w ith th e S E A R C H m o d e l fo r th e se p a ra m ete rs T o c h o o se th e v a lu e s re la te d

to th e n u m b e r o f ch u n k s a n d te m p la tes th e c u rre n t v e rsio n o f C H R E S T h a s b e e n

e m p lo y e d T h e p ro b a b ility o f f in d in g a tem p la te w a s e stim ate d b y ru n n in g

C H R E S T o n 5 0 p o s itio n s ran d o m ly tak e n fro m M as ters rsquo g am e s T h e firs t lin e (0

c h u n k ) w a s ad d e d to g e t p re d ic tio n s a t th e n o v ic e lev e l W ith n e ts o f 1 0 0 0 0 0

1 2 0 0 0 0 a n d 1 5 0 0 0 0 c h u n k s th e p ara m ete rs w ere e stim ate d w ith th e b e s t-fit t in g

fu n c tio n s av a ilab le ( th e ldquo n o v ice rdquo v alu e s w ere n o t u se d ) T h e n u m b er o f te m p la tes

is ro u g h ly a lin e ar fu n c tio n o f th e n u m b er o f c h u n k s (r 2 = 9 7 ) T h e p ro b a b ility

o f f in d in g a tem p la te is a p p ro x im a tely a lo g -fu n c tio n o f th e n u m b e r o f c h u n k s

(r 2 = 9 4 )

H e u r is tic s C h u n k s T e m p la tes a n d T h e ir R e la tio n to th e P ro b a b ility o f

F in d in g M o v e s a n d E v a lu a tio n s T ab le 2 g iv e s th e v a lu e s u s ed in th e

sim u la tio n s fo r th e p a ra m ete rs re la te d to h e u ristic s c h u n k s a n d te m p la te s

H e u ris tic s in c lu d e sim p le se a rc h te c h n iq u e s (e g ldquo ta k e a p ie c e b a c k rdquo o r ldquoc h e c k

th e K in g rdquo ) a s w ell a s m o re a b stra c t ru le s (e g ldquoo c c u p y th e c en tre rdquo ) T h eir m a in

c h a rac te ris tic in co m p a riso n w ith c h u n k s an d tem p la te s is th a t th ey are g e n e ra l

a n d re q u ire so m e co n sc io u s c o m p u tatio n in o rd e r to p ro d u ce a m o v e T h e

a ss u m p tio n u n d e rly in g T a b le 2 is th at th e p aram e ters re la ted to h e u ristic s s ta y

ro u g h ly c o n sta n t w h ile th e o th e r p aram e te rs v a ry as a lo g arith m ic fu n c tio n o f th e

n u m b e r o f c h u n k s in th e n e t (A lo g arith m ic fu n ctio n h a s b e e n c h o se n to in d ica te

th a t ch u n k s y ie ld a d im in ish in g re tu rn as th e ir n u m b e r in c re a se s) T h e

a ss u m p tio n th a t th e n u m b e r o f h e u ristic s is c o n sta n t ac ro s s s k ill le v e ls se e m s

re a so n a b le (p e rh a p s w ith th e e x ce p tio n o f th e n o v ic e le v e l) a s m o s t c h e ss

M a ste rs rsquo k n o w le d g e is v e ry sp ec ific to c erta in a sp e c ts o f th e g a m e (D e G ro o t

1 9 4 6 )

T h e fo llo w in g c o n s id era tio n s w e re m ad e in se ttin g th e v alu e s g iv e n in

T ab le 2 I t w a s d ee m e d p lau sib le th a t th e p ro b a b ility o f f in d in g so m e h e u ristic in

a p o s itio n b e h ig h ( 9 5 ) a s w e ll a s th e p ro b a b ility o f f in d in g s o m e c h u n k F in ally

PATTERN -R ECOGN IT ION AND SEA RCH 303

TA BLE 1

The V a lu es o f th e 14 N e ts U sed in th e S im u la tio ns

P ro b a b i li ty o f

re c o g n is in g a t le as t

P ro p o r t io n o f o n e te m p la te g iv e n a

N u m b e r o f c h u n k s N u m b e r o f te m p la te s te m p la te s p o s i t io n

0 0 0 0 0 0 0 0

1 0 0 2 0 0 0 0 0 0 0

2 6 8 0 5 0 0 2 1 8 0

5 0 0 3 3 6 0 0 7 1 4 0

1 0 0 1 1 1 0 0 0 1 0 2 4 0

2 0 0 0 3 2 6 5 0 1 3 3 0 0

3 0 0 0 1 4 9 3 0 1 6 3 6 0

4 0 0 0 5 7 7 4 0 1 9 4 6 0

5 0 0 0 6 1 1 4 2 0 2 3 4 0 0

7 2 0 4 4 2 1 3 6 0 3 0 4 8 0

8 0 0 1 0 2 2 8 5 0 2 9 5 4 0

1 0 0 0 0 0 2 7 6 5 0 2 8 5 1 0

1 2 0 0 0 0 3 3 5 7 0 2 8 5 4 0

1 5 0 0 0 0 4 2 4 5 0 2 8 5 6 0

T h e v a lu e s b e lo w 1 0 0 0 0 0 c h u n k s w e r e ta k e n f ro m s im u la t io n s w ith C H R E S T th e o the rs

e x t ra p o la te d S e e te x t f o r d e ta ils

TA BLE 2

H eur is t ic s C hun ks Tem pla tes and Their Re la tion to th e P ro bab ility of Fin d in g

M oves and Evalu ta tio ns

T y p e H e u r is tic s C h u n k s T e m p la te s

P ro b a b i li ty o f e v o k in g a n 9 5 g (n _ c h u n k s 9 5 )a se e T a b le 1

h e u ri s t ic a c h u n k o r a te m p la te

P ro b a b i li ty o f f in d in g a m o v e 5 0 g (n _ c h u n k s 5 0 ) g (n _ c h u n k s 9 0 )

g ive n th a t a n h e u r is tic a c h u n k

o r a te m p la te h a s b e e n e v o k e d

P ro b a b i li ty o f f in d in g a n e v a lu a tio n 1 5 g (n _ c h u n k s 0 5 ) g (n _ c h u n k s 5 0 )

g iv e n th a t a n h e u ri s t ic a c h u n k o r

a te m p la te h a s b e e n e v o k e d

aT h e fu n c tio n g i s d e f in e d a s

g (n _ c h un k s p ro b ) = p ro b 0 2 lo g1 0

(n _ c h un k s ) i f n _ c h u n k s gt 0

a n d

g (n _ c h u n k s p ro b ) = 0 i f n _ c h u n k s = 0

w h e re n _ c h u n k s i s th e n u m b e r o f c h u n k s in a g iv e n n e t a n d p ro b i s a c o n s ta n t

303

304 GOBET

th e p ro b a b ility o f re c o g n isin g a te m p la te in a p o sitio n is sm a lle r a n d is g iv e n in

T ab le 1

T h e p ro b a b ility o f f in d in g a m o v e g iv e n a h e u ristic is s e t to 5 0 in d ic atin g th a t

h e u ristic s m a y fa il to p ro d u ce a m o v e h a lf o f th e tim e T h is is b e c a u se so m e

h e u ristic s m ay n o t y ie ld a m o v e a n d b ec a u se so m e p ro p o se d m o v es m a y b e

ille g a l T h e p ro b a b ility o f f in d in g a m o v e g iv en a tem p la te is h ig h p a rtly

re fle ctin g th e ric h s em a n tic k n o w le d g e an d th e in te r-te m p la te lin k s a s su m e d to

c h a rac te rise te m p la te s F o r th e p ro b a b ility o f f in d in g a m o v e g iv e n th a t a ch u n k

h a s b e en re co g n ise d I u se d th e p ara m e te r p ro b in th e fu n ctio n g (s ee T a b le 2 ) so

th a t i t a p p ro x im a te s th e d ata p ro d u c ed b y th e C H U M P p ro g ram (G o b et amp Ja n se n

1 9 9 4 ) E v a lu a tio n s a re su p p o s ed to b e h a rd er to le arn a n d th e re fo re h a rd e r to u se

th a n m o v es H e n ce th e ir p ro b a b ilit ie s a re lo w e r th a n th e co r res p o n d in g p ro b -

a b ilit ie s w ith m o v es A g a in fo llo w in g d irec tly fro m th e th e o ry te m p la te s o ffe r

th e b e st so u rce o f ev alu a tio n s

W ith re sp e c t to th e n u m b e r o f se q u e n tia l m o v e s p ro p o s ed c o u n ted in p lie s

(i e m o v e s fo r W h ite o r B la ck ) i t is as su m e d th a t h e u ristic s g iv e a cc e ss to o n ly

o n e m o v e w h ile c h u n k s a n d te m p late s y ie ld se q u e n c es o f m o v e s w h o se n u m b e r

fo llo w s a g e o m e tric p ro b a b ility d is tr ib u tio n (th e c h o ice o f th is d is tr ib u tio n w as

in sp ire d b y sta tis tic s ta k e n fro m C H U M P ) T h e lo n g e s t s eq u e n c e ( ca ll i t k ) h as a

fre q u e n c y o f 1 th e s e co n d -lo n g e st a fre q u en cy o f 2 th e th ird -lo n g e st a fre q u e n c y

o f 4 a n d so o n u n til th e sh o rte st se q u e n c e w h o s e len g th is 1 m o v e an d w h o se

fre q u e n c y is 2 (k ndash 1 ) T h e m a x im u m se q u e n ce o f m o v es w a s se t to 1 8 F in a lly

S E A R C H atte m p ts to g e n e ra te a m o v e b y p a ttern re c o g n itio n ( ch u n k o r te m p la te )

fo u r tim e s b e fo re u sin g a n h e u ristic

T im e a n d F u zzin e ss P a ra m ete rs T h e tim e p a ram e ter s fo r th e re sp e c tiv e

o p e ra tio n s w e re s et u sin g p la u sib le v a lu e s (se e T a b le 3 ) M o v e g en era tio n b y

p a tte rn re c o g n itio n (c h u n k o r te m p late ) is as su m e d to b e v e ry sh o rt (a few

h u n d re d m illis e co n d s) n o tim e c o st is u se d in th e m o d e l T h e tim e fo r c o m p u tin g

a m o v e-g en e ra tin g h e u ristic w a s s et to th e ra th e r lo n g 2 0 s ec o n d s mdash g en era tin g a

m o v e w ith o u t u sin g p a tte rn r ec o g n itio n re q u ires p u ttin g to g eth e r v a rio u s ty p e s o f

in fo rm a tio n a n d a s k s fo r m a n y ch e c k in g p ro c ed u res T h e tim e fo r c a rry in g o u t

o n e m o v e (o n c e g e n erate d ) in th e m in d rsquos e y e w a s s et to tw o s ec o n d s T h is is

c o m p atib le w ith S a a rilu o m a rsquos (1 9 8 9 ) d ata w h ic h sh o w th a t a b lin d fo ld ed M a ste r

c an fo llo w a g a m e d icta ted a t tw o se c o n d s a m o v e F in ally th e tim e fo r ca rry in g

o u t a n ev a lu a tio n b y h eu ris tic is s e t to 1 0 s e co n d s T h is ra th e r s h o rt tim e m a y b e

ju stif ie d b y th e fa c t th a t p la y e rs ty p ic a lly co n s id e r o n ly o n e (s u b jec tiv e ) a sp e c t o f

th e p o sitio n (D e G ro o t 1 9 4 6 ) a n d th at m an y e v a lu atio n s c a n b e g ro u n d ed o n th e

b a sis o f c lea r m a teria l lo ss e s

T h e fu z zin e ss lev el o f th e s y ste m is e x p re ss ed in a rb itra ry u n its I t s ta rts w ith

th e v a lu e z e ro a n d it is in c re a se d w h e n a m o v e is c a rrie d o u t in th e m in d rsquos e y e

a n d w h e n tim e is s p e n t a p p ly in g a n h e u ris tic W h e n a te m p la te is fo u n d th e

PATTERN -R ECOGN IT ION AND SEA RCH 305

fu z z in es s lev el is d e cre a se d a s p a rt o f th e in fo rm atio n m ay b e sto re d in L T M

d ire c tly fre e in g c ap ac ity in w o rk in g m e m o ry a n d in th e m in d rsquos ey e

S im u la t io n s w ith th e ldquo C anon ica l M ode lrdquo

T h e sim u latio n s d e sc rib ed in th is s ec tio n a re s tra ig h tfo rw a rd U s in g th e

p a ra m e te r v alu e s d is cu sse d e a rlie r I le t th e p ro g ra m s ea rc h 1 0 0 0 ep iso d e s fo r

e ac h n e t s iz e S u m m a ry v alu e s fo r m e a n d ep th o f se a rc h t im e ra tio d e p th tim e

a n d fu z zin e s s a s w e ll a s fo r g e n e ra tio n an d s to p co n d itio n s w e re c o m p u ted fo r

e ac h n e t s iz e

M e a n D e p th o f S e a r ch R a te o f S e a rc h a n d F u z zin e ss A cc o rd in g to

S E A R C H m ea n d e p th o f s ea rc h fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f

c h u n k s (se e F ig 3 a) If w e as su m e a co n sta n t ra te o f le a rn in g n e w c h u n k s a s is

c o m m o n p ra ctic e in so m e c o g n itiv e a rch ite c tu res (c f N e w e ll 1 9 9 0 ) a n d if w e

a ss u m e th a t s k ille d p la y e rs h a v e sp e n t m o re p rac tice a n d stu d y tim e th a n

u n s k ille d p la y e rs th e n m e an d e p th fo llo w s a p o w e r fu n c tio n o f s k ill as w e ll T h is

p re d ic tio n w h ic h is a t v ar ia n c e w ith H o ld in g rsquos p re d ic tio n (1 9 8 5 p 1 8 2 ) o f a

lin ea r in c rea s e is p artly co n siste n t w ith C h a rn e ss rsquos (1 9 8 1 ) p ro p o s a l th a t d e p th o f

se a rc h is n o t l in e arly re la ted to s k ill b u t th at th e re is a ce ilin g a t h ig h s k ill le v e ls

T h e re su lt is a ls o c o m p atib le w ith th e w e a k lin e ar re la tio n fo u n d in e m p ir ic a l

stu d ie s (C h a rn e ss 1 9 8 1 G o b e t in p re ss ) b e tw e e n m e a n d e p th o f se a rch a n d sk ill

le v el b e c a u se re stric te d ra n g e s o f th e c u rv e c a n b e a p p ro x im a ted b y a lin e a r

fu n c tio n T h e a b so lu te v alu e s a re a lso q u ite r ea so n ab le th ey ris e f ro m lo w d ep th s

(le ss th a n 1 p ly ) w ith n o ch u n k s (co r res p o n d in g to th e n o v ic e le v el) to a ro u n d 2 5

p lies w ith a sm a ll n et (1 0 0 0 c h u n k s ) an d th e n to a ro u n d 4 p lie s w ith ex p ert le v e l

(a ro u n d 3 0 0 0 0 c h u n k s a s e s tim a te d b y s im u la tio n s o n th e re ca ll tas k ) T h e y th e n

slo w ly (s av e fo r a f ew ra n d o m v a ria tio n s ) in c re a se to m o re th an 5 p lie s w ith n e t

la rg er th an 1 0 0 0 0 0 c h u n k s w h ic h c o rre sp o n d s to G ran d m a ste r le v e l H o ld in g

(1 9 8 5 ) c o m p u te d m e a n d e p th o f se a rch fo r d e G ro o trsquos (1 9 4 6 ) d a ta a n d fo u n d th a t

TA BLE 3

T im e and ldquo Fuzz in ess rdquo Param e ters U sed in th e

S im ula t io n s

T im e fo r c a r ry in g o u t a m o v e 2 s

T im e fo r c o m p u t in g m o v e -g e n e r a tin g h e u r is tic 2 0 s

T im e fo r c o m p u t in g e v a lu a t io n 1 0 s

U p p e r l im it o f fu z z in e ss 5 0

In c r e a se o f fu z z in e s s p e r m o v e 1

In c re a se o f f u z z in e ss p e r s e c o n d 2

D e c re a s e in fu z z in e ss d u e to te m p la te 5

306 GOBET

E x p e rts a n d G ra n d m as ters h a d res p e ctiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 8 a n d

5 3 T h e reg res sio n e q u a tio n d e riv e d f ro m C h a rn e ss rsquos (1 9 8 1 ) d ata y ie ld a n

a v e rag e d e p th o f se a rc h o f a b o u t 2 3 p lies a t th e 1 3 0 0 E L O 1 le v e l o f 4 1 a t th e

E x p e rt le v e l (2 0 0 0 E L O ) a n d o f 5 7 a t th e G ra n d m a s te r le v el U n fo rtu n a tely n o

stu d y te ste d p la y e rs ra n g in g fro m n o v ic es to G ran d m a ste rs an d S E A R C H rsquos

p re d ic tio n o f a p o w e r la w o f p rac tic e c an n o t b e te ste d (y e t) I w ill re p o rt la te r

sim u la tio n s a d d re ssin g d a ta co lle c ted b y S a arilu o m a (1 9 9 0 ) w h e re In tern atio n a l

M a ste rs a n d G ra n d m a s te rs te n d e d to s e arc h le s s th a n M as te rs

T h e ra te o f s ea rc h a lso fo llo w s a p o w e r fu n ctio n o f th e n u m b e r o f c h u n k s (se e

F ig 3 b ) D e G ro o t (1 9 4 6 ) C h arn es s (1 9 8 1 ) a n d G o b e t ( in p res s) a ll f o u n d th a t

stro n g p la y er s te n d e d to s e arc h fa ste r F o r ex a m p le G o b e t ( in p re s s) fo u n d th a t

h is M a ste rs E x p e rts C la ss A a n d C la s s B p lay e rs re sp e c tiv ely se arch e d 4 8 4 1

3 2 an d 3 4 n o d e s p e r m in u te S E A R C H rsquos v a lu es a re h ig h e r b u t s til l p la u s ib le

F o r ex am p le W a g n e r a n d S c u rra h rsquos (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r

m in u te N o te a lso th a t a ll th e ex p erim e n ts m e n tio n e d e a rlier h a v e u se d v e rb a l

p ro to c o ls w h ic h m ay h av e s lo w e d d o w n th e ra te o f se a rc h (c f E ric ss o n amp

S im o n 1 9 8 0 ) F in a lly th e ra te o f se arch m a y h av e b e e n u n d e res tim a ted in th e

lite ra tu re b ec a u se th e r a te o f g e n e ratin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d

b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l t im e H o w e v e r to ta l t im e in c lu d es

tim e n o t sp e n t in s e arc h ( fo r e x a m p le w h a t D e G ro o t c a lls th e ldquo firs t p h a se rdquo)

T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a riab le th e le v e l o f fu zz in e ss a t

w h ic h a se a rc h is e n d e d is m o re d if fic u lt to ju d g e b ec a u se lit tle is k n o w n a b o u t

th e ro le o f fu z z in es s in c h es s th in k in g A g ain S E A R C H p ro p o se s th a t th is

v a riab le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s ee F ig 3 c ) W ith la rg e r

n e ts e p iso d es te n d to b e e n d e d w ith lo w er le v els o f fu z z in e s s T h is su g g es ts th at

in g e n e ra l s tro n g p la y ers s h o u ld b e m o re c o n fid e n t in th e ir c alc u la tio n s as th e y

a re n o t a t th e e d g e o f th eir p o s sib ilitie s N o te th a t th e ra te o f ch an g e is ra th e r h ig h

fo r th is p o w er law w h ic h s u g g e sts th at it sh o u ld b e p o ss ib le to d e te c t i t

e x p erim e n tally

G e n e ra tio n o f M o ve s H o w is m o v e g en e ra tio n af fec te d b y sk ill le v e l A s

sh o w n in F ig 4 a S E A R C H m a k es c le a r p re d ic tio n s W ith sm a ll n u m b e rs o f

c h u n k s th e tim e -c o n s u m in g p ro ce s s o f g en e ra tin g m o v es b y h e u ristic s is

e m p lo y e d T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y ch u n k s

w h ic h is in tu rn d o m in a te d b y te m p la te g e n eratio n

1 T h e E L O ra t in g i s a n in te r v a l sc a le th a t ra n k s c o m p e t it io n c h e ss p la y e rs I ts s ta n d a rd de v ia t io n

(2 0 0 p o in ts) is o f te n in te r p re te d a s a m e a su r e o f sk i ll c la s s in c h e ss G r a n d m a s te r s a re n o rm a lly ra te d

a b o v e 2 5 0 0 In te rn a t io n a l M a s te r s a b o v e 2 4 0 0 M a s te r s a b o v e 2 2 0 0 a n d E x p e rt s a b o v e 2 0 0 0

B e lo w c la sse s (A B e tc ) d iv id e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in ts

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

292 GOBET

T h e g o al o f th is p a p e r is to ex te n d th e te m p late th eo ry (G o b e t amp S im o n

1 9 9 6 a ) w h ich w a s o rig in a lly in ten d e d a s a th eo ry o f c h es s p lay ers rsquo p erc e p tio n

a n d m em o ry to th e re a lm o f p ro b le m s o lv in g In th e firs t p a rt I b rie fly re v iew

p re v io u s th eo r ie s o f p ro b le m s o lv in g in c h e ss T h e n I p ro p o se e lem e n ts o f a

c o m p re h e n siv e th e o ry o f c h es s p ro b le m s o lv in g th at is c o m p atib le w ith e m p iric a l

d a ta o n m e m o ry a n d p e rce p tio n res e arc h A sp e c ts o f th is th e o ry a re im p le m e n te d

in a c o m p u te r p ro g ram S E A R C H w h ic h is d es c rib ed in th e th ird p a rt o f th e

p a p e r in co n ju n c tio n w ith re s u lts o f s im u la tio n s F in ally I c o n s id e r h o w th e

p ro p o s e d th eo ry g e n e ralis es to o th e r d o m a in s o f ex p e rtise

CHESS PROB LEM SO LV ING TH EO R IES AN D D ATA

D e G roo t rsquos C la ss ic R e su lts

T h e b a sic f in d in g o f D e G ro o trsquos s tu d y (1 9 4 6 1 9 7 8 ) w as th a t th e re w ere n o

im p o rtan t d if fer en c e s in th e m a c ro s tru ctu re o f se a rc h b e tw e e n w o rld -c la ss

g ra n d m a ste rs a n d s tro n g a m ate u rs e x c e p t th at th e b e s t p la y e rs fo u n d b e tte r

m o v e s a n d w e re s o m e w h a t f as ter to re a c h a d e c isio n O n a v e rag e p la y e rs fro m

b o th s k ill lev els se a rc h e d e q u a lly d e ep v isited th e sa m e n u m b e r o f p o sitio n s in

th e ir s ea rc h a n d p ro p o se d th e sa m e n u m b e r o f c a n d id a te m o v es D e G ro o t

c o n clu d e d th a t th e k e y to e x p e rtise is n o t a s u p e rio rity in ldquo sp e ed o f th in k in g rdquo o r in

a m o re ra tio n a l w a y o f o rg an is in g o n e rsquos th o u g h t b u t s p e cific k n o w le d g e a b o u t

v a rio u s a sp e c ts o f th e ta s k d o m a in D e G ro o t n o ted th a t th e se arch b e h a v io u r

sh o w n b y h is p la y ers w a s c o m p a tib le w ith S e lzrsquos (1 9 2 2 ) th eo ry o f p ro d u ctiv e

th in k in g b u t h e d id n o t o ffe r a d e ta ile d m o d e l o f c h e ss th in k in g

S im on rsquos Theo ry and Com pu te r P rog ram so f Che ss P la y ing

A d e ta ile d a c c o u n t o f c h es s th in k in g w as la te r o f fere d b y C h as e an d S im o n

(1 9 7 3 ) T h e ir th e o ry k n o w n a s th e c h u n k in g th e o ry (C T ) p ro p o s ed th a t a t th e

c o re o f ex p ertis e lie s th e a b ility to re c o g n ise im p o rta n t p ro b le m fe a tu res ra p id ly

T h es e fe a tu res in te rn a lly s to re d as ch u n k s a c t a s a cc e ss p o in ts to se m an tic lo n g -

te rm m em o ry (L T M ) a n d a s th e c o n d itio n s o f p ro d u c tio n s w h o se a c tio n s m a y b e

c ar ried o u t in tern ally o r e x tern ally T h is p ro d u c tio n - sy s te m ac c o u n t w a s lin k e d

to a ss u m p tio n s ab o u t in fo rm a tio n -p ro c e ss in g m e c h a n ism s d e sc rib in g fo r

e x a m p le h o w a n o b jec t is so rte d th ro u g h a d isc rim in atio n n e t in o rd e r to re a ch a

n o d e in L T M I t a lso in c lu d e d p a ra m e te rs s p e cify in g le a rn in g a n d a cc e ss in g

tim e s (e g a b o u t e ig h t s ec o n d s to le a rn a n e w c h u n k ) a s w e ll a s s tr ic t c ap ac ity

lim its (e g S T M lim ite d to se v e n c h u n k s) In th e ca s e o f ch e s s ex p e rtise

p e rc ep tio n m ec h a n ism s in C T a llo w rec o g n itio n o f p atte rn s o f p ie ce s o n th e

b o a rd T h es e p a tte rn s su g g e s t m o v e s w h ich ar e u se d to u p d a te th e in te rn a l

re p re se n ta tio n o f th e b o a rd in w h a t th e y c a ll th e m in d rsquos ey e (T h e m in d rsquos ey e is a

re la tio n al s y ste m th a t c a n b e s u b jec te d to v is u o -sp a tia l m e n tal o p e ra tio n s an d th a t

PATTERN -R ECOGN IT ION AND SEA RCH 293

sto re s p e rc ep tu a l s tru c tu res b o th fro m ex te rn a l in p u ts a n d fro m m e m o ry s to res )

P a tte rn -re c o g n itio n m e c h an is m s a p p ly re cu rs iv e ly in th e in tern al re p re se n ta tio n

o f p o s itio n s in th e m in d rsquos ey e T e rm in a tio n o f se a rch in a b ra n c h is o b ta in e d b y

e v a lu a tin g w h e th e r c erta in g o a ls a re a b o v e o r b e lo w a th res h o ld w h o s e v a lu e

m ay ch a n g e a s a fu n ctio n o f p lay e rs rsquo e x p e cta tio n lev el o f th e p o sitio n

V a rio u s c o m p u te r p ro g ra m s o f p ro b lem s o lv in g in c h e ss w e re d e v e lo p e d b y

S im o n a n d h is co lle a g u es b u t n o n e o f th em d ire ctly in co rp o ra te d th e

re c o g n itio n ndash as so c ia tio n m ec h a n ism o f th e c h u n k in g th eo ry T h e p ro g ra m s

w ritte n b y N ew ell S h a w a n d S im o n (1 9 6 3 ) an d B a y lo r a n d S im o n (1 9 6 6 )

im p le m e n te d th e id ea o f s e le c tiv e se a rc h m a d e p o ss ib le b y th e u se o f h e u ristic s

N e w e ll a n d S im o n rsquos m o d e l (1 9 6 5 se e a lso W a g n e r amp S c u rra h 1 9 7 1 ) fo rm u la te d

six p rin c ip les th a t d ic ta te th e g e n e ra tio n o f m o v es o r e p iso d es u s in g m a in ly th e

e v a lu a tio n o b ta in ed at th e e n d o f a b ra n c h

Ho ld ing rsquos S EEK Theo ry

H o ld in g (1 9 8 5 1 9 9 2 ) critic is e d C T an d p ro p o s ed in ste ad th e S E E K (S E a rc h

E v alu a tio n a n d K n o w led g e ) th e o ry a th eo ry th a t w a s h o w e v e r o n ly lo o se ly

fra m ed an d d id n o t re a ch th e th e o re tica l d e ta il o f C T T h e m a in th ru st o f S E E K

w a s to su g g es t th at m a ste ry in ch e s s d e p e n d s p rim a rily in th in k in g a h e a d an d n o t

in p a tte rn re c o g n itio n N o te th a t a ll th re e c o m p o n e n ts o f th e S E E K th e o ry a re

p re se n t in C T a n d th at i t is re ally th e w eig h t g iv en to e ac h o f th es e c o m p o n en ts

th a t d iff ere n tia te th e tw o th eo r ie s

S aa rilu om arsquos A ppe rcep tio n andR es tru c tu ra tio n Theo ry

R e ce n tly S a a rilu o m a (1 9 9 0 1 9 9 2 ) p ro p o se d th a t p la y e rs w h ile try in g to fin d a

m o v e in a p o sitio n a cc e ss g o a l p o s itio n s b y p a ttern re co g n itio n (S a ar ilu o m a u s es

th e o ld te rm ldquoa p p e rc e p tio n rdquo ) T h e y th e n try to c lo se th e p a th fro m th e p ro b le m

p o sitio n to th e g o al p o sitio n W h en it is n o t p o ss ib le to c lo se th e p a th th e p ro b le m

sp a c e is re stru c tu red T h u s p ro c e sse s le a d in g to a M as terrsquos c h o o sin g a m o v e m a y

b e d e sc rib e d a s a s eq u e n c e o f a p p e rc ep tio n ndash res tru ctu ratio n c y c les w h ic h m a k e it

p o s sib le to f in d so lu tio n s w ith o n ly a lim ite d s ea rc h in th e p ro b le m s p a ce

S a a rilu o m arsquos th e o ry a d m itte d ly s till a t i ts e arly s ta g e o f d ev e lo p m e n t is n o t

q u ite sa tisfa c to ry i t is u n c lea r w h a t d iffe ren tia te s it fro m N e w e ll a n d S im o n rsquos

(1 9 7 2 ) m e a n sndash e n d s a n a ly s is a n d it d o e s n o t m a k e p ro v is io n fo r w h at h ap p e n s

w h e n p la y e rs d o n o t h av e a g o a l p o sitio n in m in d

E ricsson and K in tsch rsquos Long -te rm W o rk ingM em o ry Theo ry

E rics so n a n d K in tsc h (1 9 9 5 ) p ro p o s e w ith in th e fr am e w o rk o f th e ir lo n g -term

w o rk in g m e m o ry th eo ry (L T W M T ) th a t sk ille d p lay e rs h av e c o n s tru cte d a n

h ie ra rch ic a l re tr ie v a l s tru c tu re n o t u n lik e th e stru c tu re c rea te d b y S F a n d D D

294 GOBET

tw o m n em o n is ts sp e c ia lise d in th e d ig it- sp a n ta s k (C h as e amp E ric s so n 1 9 8 2 )

T h is p o w e rfu l m e m o ry stru c tu re iso m o rp h ic to th e 6 4 s q u ares o f th e c h e ss b o a rd

a llo w s p la y e rs to u p d a te in fo rm a tio n ra p id ly d u rin g se a rc h T h e th eo ry a ls o

p ro p o s e s th a t c h e ss p lay e rs ca n c re ate n e w L T M as so c ia tio n s ra p id ly a lth o u g h

n o p ara m e te r is g iv e n to s p e cify th is s p ee d o f e n co d in g

I h av e sh o w n els ew h ere (G o b e t 1 9 9 6 ) th a t L T W M T in a d d itio n to b e in g

v a g u e a n d le a v in g m a n y d e ta ils u n s p e cifie d g e n e ra te s p re d ic tio n s th a t d o n o t

a g re e w ith th e e x p e rim en ta l d a ta o n c h es s p e rc ep tio n a n d m e m o ry In ad d itio n

th e m e m o ry m e ch a n ism s p ro p o s ed b y L T W M T (re tr ie v a l s tru c tu re a n d ra p id

e lab o ratio n o f L T M stru c tu re s) s ee m a t o d d s w ith th e fo llo w in g a sp e c t o f c h e ss

p la y er srsquo se arch b e h av io u r I t is co m m o n fo r c h e ss p la y er s to re v is it a n o d e d u rin g

th e ir a n aly s is o f th e p o sitio n H o w ev e r in ste a d o f ac c e ssin g th is n o d e d ire c tly as

su g g es ted b y L T W M T rsquos v e ry p o w erfu l m e ch a n is m s fo r s to rin g p o sitio n s ra p id ly

a n d a c c u rate ly p la y er s a c c es s th e targ e t p o sitio n b y g en era tin g a s e q u e n ce o f

in d iv id u a l m o v e s fro m th e g iv en p ro b le m p o s itio n (c f D e G ro o t 1 9 4 6 ) T h is

b e h a v io u r su g g e sts th a t p lay e rs m a y n o t s to re p o sitio n s a s q u ic k ly a s p ro p o s e d b y

L T W M T

TH E TEM P LA TE TH EO RY AN D ITS A PPL IC A T IO NTO PRO BLEM SO LV ING

In itia lly th e tem p la te th e o ry (T T ) w a s d e v elo p e d to re m o v e so m e w e a k n e ss es in

th e c h u n k in g th e o ry w ith r es p e ct to d ata fro m m e m o ry re se a rch (G o b e t amp S im o n

1 9 9 6 a ) C o n tra ry to C T rsquos p re d ic tio n s b a s ed o n a lim ited S T M ca p a c ity c h e ss

p la y er srsquo m e m o ry is res is ta n t to re tro a ctiv e in te rfe re n ce (C h arn es s 1 9 7 6 ) a n d

c h e ss p la y e rs c a n re c a ll s ev e ra l b rief ly p re s en te d p o sitio n s w ith re a so n a b le

a cc u ra c y (C o o k e A tla s L a n e amp B erg e r 1 9 9 3 G o b e t amp S im o n 1 9 9 6 a )

L ik e C T T T p ro p o s es th a t c h u n k s a re ac c e ss ed b y tra v e rsin g a d isc rim in a tio n

n e t C h u n k s a re lin k e d to o th e r in fo rm a tio n s to red in L T M s u ch a s m o v es p la n s

ta ctic al m o tiv es a n d s o o n In a d d itio n c h u n k s th a t o fte n o cc u r in a p lay e rrsquos

e x p er ie n c e c a n e v o lv e in to m o re c o m p le x d a ta s tru ctu re s ( te m p la tes ) w h ich h a v e

slo ts a llo w in g v a ria b les to b e e n c o d ed fo r e x a m p le to sp e c ify th e sq u a re

o c c u p ie d b y a p iec e A c c o rd in g to T T th is en c o d in g o cc u rs ra p id ly (a b o u t o n e

se c o n d p e r s lo t) In a d d itio n to s lo ts tem p la te s co n ta in a co r e w h ic h is m ad e u p

o f (v a ria b le -fre e ) c h u n k s A lto g e th er te m p late s a re as su m e d to s to re a t le as t

a b o u t 1 0 p iec e s F in ally te m p la te s m a y b e lin k e d to o th er te m p la tes T T als o

p ro p o s e s th a t in fo rm a tio n sto re d in th e m in d rsquos e y e a s tru ctu re s im ilar to th a t

p ro p o s e d b y C T d e ca y s ra p id ly a n d th at i t n e e d s to b e u p d a te d e ith e r b y in p u ts

fro m th e e x te rn a l w o rld o r b y in p u ts fro m m e m o ry s tru ctu re s

T T re m o v e s th e d iffic u lty o f C T w ith in te rfe ren c e p h e n o m en a f ir s t b e ca u s e it

h y p o th e sis es s o m e fa st L T M e n c o d in g (th ro u g h te m p late s lo ts) a n d se c o n d

b e c au s e te m p la te s co n ta in m o re in fo rm a tio n th a n th e ch u n k s p ro p o s ed b y C T

(C T a ssu m e d th a t c h u n k s co n ta in a t m o s t f iv e o r s ix p iec e s) F in a lly T T k ee p s

PATTERN -R ECOGN IT ION AND SEA RCH 295

th e p o w e r o f C T to e x p lain th e r ap id rec o g n itio n o f p o sitio n s sh o w n b y m a ste rs

a s th e s am e d isc rim in a tio n m e ch a n ism s are p res e n t (G o b e t 1 9 9 6 )

S ea rch M echan ism s

T T a n d C T p ro p o se th a t se a rc h is ca rrie d o u t in a fo rw ard fa sh io n b y re cu rsiv e

a p p lica tio n o f p a tte rn re co g n itio n p ro ce s se s in th e in te rn a l rep res e n ta tio n In th e

re m ain d e r o f th is se c tio n I w ill f le sh o u t th is m e c h an ism w ith ad d itio n a l sp e c ifi-

c atio n s I w ill a lso sh o w h o w c h u n k s an d te m p late s m a y b e u se d to te rm in a te

se a rc h a n d h o w te m p la te s m a y b e u se d to ca rry o u t s ea rc h a t a le v e l m o re

a b stra c t th a n th e m o v e le v e l

M o v e G e n e ra tio n A s m en tio n e d e arlie r p a ttern r ec o g n itio n is a p p lie d

re c u rsiv e ly in T T If a c h u n k mdash o r a te m p la te a s tem p la te s ar e a s p e cia l c as e o f

c h u n k smdash is rec o g n is ed i t m a y g iv e a c c es s to a m o v e (o r a se q u e n c e o f m o v e s ) o r

to a n h e u ris tic fo r se le ctin g th e n ex t m o v e E x a m p le s o f s u ch h e u ristic s a re

ldquo O c c u p y o p e n lin e s rdquo o r ldquo C o u n te r-a tta c k in th e ce n tre w h e n a ttac k e d o n th e

K in g rsquos s id e rdquo In th is ca s e th e m o v e(s ) is (a re ) c a rried o u t in th e m in d rsquos e y e If n o

m o v e re su lts fro m p a tte rn re co g n itio n o n e o f tw o o p era tio n s m a y b e ap p lie d

E ith e r th ere is a n e w atte m p t to g e n e rate a m o v e b y a cc e ss in g a d iffe re n t c h u n k

o r w ea k e r h e u ristic s a re a p p lie d

U p d a te o f In te rn a l R ep re se n ta tio n a n d S to r a g e o f In fo rm a tio n in to

T e m p la te W h en a m o v e o r a se q u e n c e o f m o v e s is c a rrie d o u t in th e m in d rsquos

e y e th e in te rn a l rep res e n ta tio n is u p d a te d a n d w h e n a te m p la te h as b e e n

a cc e ss e d s lo ts a re u p d ate d a s w e ll S lo ts m a y sto re in fo rm a tio n a b o u t th e

lo c atio n o f p ie ce s s tra teg ic in fo rm a tio n e v alu a tio n o f th e p o sitio n o r p a rt o f i t

a n d s o o n N o te th a t th is in fo rm a tio n fa c ilita te s s ea rc h b e c au se p o s sib le fo r -

g e ttin g th ro u g h d ec a y in th e m in d rsquos e y e m a y b e b ac k e d -u p b y in fo rm a tio n s to re d

in s lo ts

E va lu a tio n o f N o d e s E v a lu a tio n o f a p o sitio n is n o t c ar ried o u t af te r e ac h

m o v e b u t o n ly a t th e term in a l p o sitio n s E v a lu atio n is e ith e r r e trie v e d w h e n

p o s sib le fro m ch u n k s th a t h a v e b e en re c o g n ise d o r co m p u te d w h e n th e p la y e r

d e c id e s to te rm in a te s e arc h (s ee n e x t p a ra g ra p h ) D e G ro o trsquos (1 9 4 6 ) p ro to co ls

in d ic ate th a t p la y e rs e v a lu a te o n ly te rm in a l p o s itio n s a n d th a t th e ir e v a lu atio n s

a re ra th e r s im p le ta k in g in to a c co u n t a s in g le fe a tu re su c h as m o b ility o r c o n tro l

o f th e c e n tre a n d stro n g ly su g g e s t th a t e v a lu a tio n s are n o t co m p u te d b y

c o n jo in in g s e v eral fe atu re s

E n d in g S ea r c h o f a n E p iso d e A c ritic a l q u es tio n g iv e n a lim ite d

in fo rm a tio n -p ro c es sin g c a p a city is w h e n to s to p se a rc h in g a n e p iso d e (i e a

se q u e n c e o f m o v es g e n e ra ted fro m a b as e m o v e ) I p ro p o se th a t th e fo llo w in g

296 GOBET

c o n d itio n s ca n h alt th e se a rc h o f a n e p iso d e T o b e g in w ith th e p ro b a b ility o f

m ak in g a n e rro r is to o h ig h P s y ch o lo g ic a lly th is p ro b a b ility is a fu n ctio n o f th e

fo rg e ttin g a n d in ter fer en c e r a te s in th e m in d rsquo s ey e P h e n o m e n o lo g ic a lly p lay e rs

p ro b a b ly a s se ss th is p ro b a b ility b y ta k in g in to a c c o u n t th e d e p th o f se a rc h

re a ch e d a n d b y e s tim a tin g th e ir fa m ilia rity w ith th e p o s itio n

A n o th e r re a so n to h a lt s ea rc h o c cu r s w h e n th e le v e l o f e x p e c tatio n fo r th e

p o s itio n is m et o r w h e n a f ea tu re o f th e p o s itio n (e g sa fe ty o f th e K in g ) w as

e v a lu a te d to b e lo w e r th a n its a d m iss ib le v a lu e (N e w e ll amp S im o n 1 9 7 2 ) T h is

le v el o f e x p e c ta tio n is p ro v id e d b y a c h u n k en c o u n te re d d u rin g e arlie r s ea rc h o r

b y e x p lic it ev a lu a tio n o f th e p o s itio n a n d w a s s to re d e ith e r in S T M o r w h e n

a v a ila b le in a te m p late s lo t A fin a l h a ltin g c o n d itio n is th a t a d e c isiv e e v e n t

o c c u rre d s u ch a s m a te im p o rta n t m a teria l g a in o r lo ss o r fu lfilm e n t o f a k e y

g o al

S e lec tin g th e N e x t B a s e -m o v e N o w co n s id er th e q u e stio n o f w h ic h b a se -

m o v e to se a rch n ex t w h en a le a f n o d e h a s b e e n re a ch ed A n y o f s ix m e c h an is m s

m ay b e e n g a g e d F irst if th e le a f w a s e v a lu ate d w ith a h ig h risk o f er ro r th e s am e

se q u e n c e o f m o v e s is se a rc h ed a g ain in o rd e r to o b ta in a m o re re lia b le e stim a te

S e c o n d th e sa m e s eq u en c e o f m o v e s m a y b e se a rch e d a g a in to m a k e s u re th a t i t

h a s b e e n sto re d in L T M T h ird if a tem p la te h a s b e e n re co g n ise d a m e ta -se a rc h

(s ee la te r) is c arr ie d o u t F o u rth th e re is a b ia s to g iv e p re fe ren ce to n o rm a l b as e -

m o v e s ea rly in se a rch a n d to u n u su a l b a s e-m o v e s la ter (N ew ell amp S im o n 1 9 7 2

p 7 2 3) F ifth a m ov e re ac h e d at a n y le v e l o f d e p th in s ea rch in g a lin e m a y b e trie d

a s a ca n d id a te m o v e in th e n ex t lin e S ix th if th e e v alu a tio n o f an e p iso d e g iv e s a

fa v o u ra b le re su lt its an aly s is is c o n tin u e d if th e ev a lu a tio n is u n fa v o u rab le a

d iffe re n t b a se -m o v e is ta k e n u p (N e w e ll amp S im o n 1 9 7 2 )

M e ta -s e a rc h w ith T e m p la te s (A b stra c t P la n n in g ) S e arc h m ay b e c arrie d o u t

n o t o n ly a t th e m o v e le v e l b u t a lso a t th e te m p la te le v el P lay e rs s o m e tim es

d e v e lo p a tre e se a rc h b y g e n eratin g k ey p o sitio n s (te m p la tes ) in s tea d o f

d e v e lo p in g a tree se arch b y g e n e ra tin g m o v e s (e g D e G ro o t 1 9 7 8 p 1 5 3 ) P ath s

b e tw e en k e y p o sitio n s c o n s is t o f m a cro -o p e ra to r s o r in u n s p ec ifie d o p e ra to r s

w h ic h w ill b e fil le d in a t a la te r s ta g e o f se a rch if th e le a f p o sitio n s a re ju d g e d

fa v o u ra b le T h is ty p e o f se arch is c o n tin g en t to th e p res e n ce in p la y ers rsquo L T M o f

te m p la tes su ffic ie n tly c lo se to th e p o s itio n a t h a n d K o ed in g e r a n d A n d e rs o n

(1 9 9 0 ) h a v e p ro p o se d a s im ilar id e a w ith re sp e c t to g eo m e try T h is m e ta -se a rc h

m ec h a n ism is a ls o sim ilar to th e ldquoa p p e rc e p tio n rdquo m e c h a n ism su g g es ted b y

S a a rilu o m a (1 9 9 0 1 9 9 2 )

Theo re t ica l Im po rta n ce o f Tem p la te s

O b v io u s ly m an y o f th e p ro ce s se s ju st d es c rib ed c a n b e im p le m e n te d w ith in th e

e ar lie r C T w ith o u t h y p o th e sisin g th e p re se n c e o f te m p la tes T e m p la tes a re

h o w e v e r im p o rta n t fo r s o m e o f th e k ey c o g n itiv e p ro c es se s in c h e ss b e c au se

PATTERN -R ECOGN IT ION AND SEA RCH 297

(a ) s lo ts a llo w in fo rm a tio n ab o u t s tra te g ic o r tac tica l th e m e s a s w e ll a s a b o u t

e v a lu a tio n o f th e p o sitio n to b e en co d e d in L T M rap id ly (b ) lin k s b e tw e e n

te m p la tes a llo w fo r ldquo m e ta -se a rc h rdquo (c ) in fo rm a tio n s to re d b o th in th e c o re a n d in

th e slo ts o f th e te m p late c o m p en sa tes fo r d e c a y an d in te rfe re n c e in th e m in d rsquos

e y e as it m a y b e u se d to re in sta te fa d in g in fo rm a tio n T h is c o m p e n sa tio n

m ec h a n ism is p ar tic u la rly u se fu l w h e n p e rce p tu a l in fo rm a tio n fro m th e ex te rn a l

b o a rd is u n re liab le fo r ex a m p le b e ca u s e se v e ra l m o v e s h a v e b e en c arr ie d o u t in

th e m in d rsquos e y e

Em p ir ica l D a ta Sup po rtin g th e TT A ccoun t o f Sea rchand Pa tte rn R e cogn itio n

In th is se c tio n T T is q u alita tiv e ly ap p lie d to s o m e o f th e k ey d a ta f ro m e m p ir ic a l

stu d ie s o f ch e s s p ro b le m s o lv in g Q u a n tita tiv e a s se ss m e n t w ill b e th e to p ic o f

th e fo llo w in g se c tio n I h a v e sh o w n e lse w h e re (G o b e t 1 9 9 6 ) th at th e p re d ic tio n s

o f T T a re w e ll su p p o rted b y e m p ir ic a l d a ta fro m re se a rch o n m e m o ry a n d

p e rce p tio n

In c re a sin g th e n u m b e r o f c h u n k s a n d te m p la te s h a s tw o o p p o site ef fec ts w ith

re sp e c t to se a rch (G o b e t in p res s) O n th e o n e h a n d d e ep s e arc h is fac ilita te d as

c o m p are d w ith th e m o re co m p u ta tio n a lly e x p e n s iv e w e a k m e th o d s b e c au se

p a tte rn re c o g n itio n is a ra p id p ro c es s a n d b e ca u s e se q u e n c e s o f m o v es m a y b e

le arn e d an d su g g e ste d b y c h u n k s O n th e o th er h a n d th e n ee d fo r d e e p se a rc h

o fte n d isa p p e ar s b e ca u s e e v a lu atio n s su g g e ste d b y p a tte rn re c o g n itio n m a y b e

m o re re lia b le th a n e v a lu atio n s co m p u te d b y w e a k m eth o d s T h e s e tw o o p p o site

e ffe cts c a n e x p la in w h y th e sk ill d iffe re n c e s in a v e rag e d e p th o f se a rc h a re sm all

P a tte rn re co g n itio n a llo w s stro n g p la y e rs to b e h ig h ly s e le c tiv e in th e ir s ea rc h

T h is c a n b e s e en b o th in th e ra p id w a y M a s te rs ze ro in to th e k e y as p e cts o f a

p o s itio n (D e G ro o t 1 9 4 6 ) an d in th e w ay e y e m o v e m e n ts d iffe r a s a fu n c tio n o f

sk ill d u rin g th e firs t s ec o n d s o f th e p e rc ep tio n o f a p o sitio n (D e G ro o t amp G o b et

1 9 9 6 ) A d d itio n a l e v id e n ce is p ro v id e d b y S a a rilu o m a (1 9 9 0 ) w h o h a s sh o w n

th a t p la y e rs ch o o se ste re o ty p e d so lu tio n s in p ro b le m s w h e re fa ste r ( in th e

n u m b e r o f m o v es to r ea c h m a te) b u t u n c o m m o n so lu tio n s a re p re s en t T h e se d a ta

a d d s u p p o rt to T T b e c a u se p a ttern re co g n itio n lie s a t i ts c o re

F u r th er s tro n g e v id e n ce fo r th e ro le o f p atte rn re c o g n itio n is th a t M as te rs c a n

p la y s ev e ra l o p p o n en ts s im u lta n eo u sly a t a s tre n g th c lo se to th at in o n e -a g ain s t-

o n e p lay I t is in te re stin g th at in s im u lta n eo u s g a m e s th ey te n d to p la y ldquon o rm a lrdquo

m o v e s a n d re ly o n o p p o n e n ts rsquo e rro rs (G o b e t amp S im o n 1 9 9 6 c ) N o rm a l m o v es

m ay c o rre sp o n d to th e ty p e o f m o v e s su g g e ste d b y c h u n k s an d tem p la te s

A fea tu re o f c h es s ex p e rtise c a p tu re d u n iq u e ly b y T T is th e h ig h le v e ls a t

w h ic h ch e s s p lay e rs o rg a n is e th e ir k n o w le d g e D e G ro o t (1 9 4 6 ) p ro p o s e d th a t

p la y er s o rg an is e p o sitio n s a ro u n d la rg e ldquo c o m p le x e srdquo b ig g e r th a n th e c h u n k s th a t

w e re la te r p ro p o se d b y C h a se a n d S im o n (1 9 7 3 ) D e G ro o t a lso su g g es ted a s d id

C o o k e e t a l (1 9 9 3 ) th a t p la y e rs re p re s en t in fo rm a tio n a t a c o n c e p tu a l lev el In

p a rticu la r D e G ro o t (1 9 4 6 ) p ro p o se d th a t M a ste rsrsquo d e sc rip tio n s o f g am e s a re

298 GOBET

c en tred a ro u n d k ey p o sitio n s o f th e g a m e T T o ffe rs th eo retic al s tru c tu res

(te m p la te s) th a t co u ld a c c o u n t fo r p lay ers rsquo larg e c o m p le x es h ig h - le v e l re p re -

se n ta tio n s a n d k e y p o sitio n s T T a lso o ff ers m e ch a n ism s b as e d o n f req u en c y o f

o c c u rre n ce s e x p la in in g h o w th e s e h ig h - le v e l re p re se n ta tio n s a re d ev elo p e d a n d

m ec h a n ism s b a se d o n d isc rim in a tio n p ro c e sse s e x p la in in g h o w th ey c o u ld b e

a c ce ss e d ra p id ly

T T is a lso co m p a tib le w ith re su lts fro m e x p er im e n ts u s in g p o s itio n s fo r w h ic h

a cc e ss to k n o w le d g e is d iffic u lt In H o ld in g a n d R e y n o ld s rsquo (1 9 8 2 ) e x p e rim e n t

c h e ss s k ill d id n o t c o rr ela te w ith th e re c a ll o f s e m i-ra n d o m p o s itio n s sh o w n fo r a

fe w se co n d s b u t eff ec tiv en es s o f th e s ea rc h fo r th e b e st m o v e in th es e p o s itio n s

d id c o rr ela te w ith s k ill T T o f fer s a n ex p la n a tio n fo r th e fa c t th a t th e re w a s a

stro n g c o rre la tio n b e tw e en sk ill le v e l a n d q u a lity o f m o v e p ro p o se d P lay e rs

re c u rsiv e ly g e n e ra te a m o v e th ro u g h w ea k m e th o d s w h en n o c h u n k is

re c o g n ise d u n til o n e o f th e h a ltin g co n d itio n s (m en tio n e d e a rlier ) a p p lie s T h e n

g iv e n th eir la rg e r d ata b a se o f c h u n k s s tro n g p la y e rs a re m o re lik e ly th a n w e a k

p la y er s to f in d a u s efu l p a tte rn in p o sitio n s th a t h a v e b ee n n e w ly u p d ate d in th e

m in d rsquos e y e a n d th e re fo re a re m o re lik e ly to f in d g o o d m o v e s in th eir se a rch

I m en tio n e d e a rlier th at E ric ss o n a n d K in tsc h (1 9 9 5 ) p ro p o s ed m ec h a n ism s

(re trie v al s tru c tu re a n d ela b o ra tio n s o f L T M sc h e m a s ) th a t e n c o d e in fo rm a tio n

q u ic k ly a n d re lia b ly B y c o n tra st th e e n c o d in g c a p a c ity o f te m p la te s is r e la tiv ely

w e a k In p a rtic u la r T T p re d icts th at th e sa m e te m p la te m a y s o m e tim e s b e u se d to

e n c o d e s e v era l s im ilar p o sitio n s th u s in c re as in g th e ris k o f in terf ere n c e as se a rc h

p ro g re s se s A s a co n se q u e n ce a n d c o n trary to L T W M T rsquos p re d ic tio n s p lay e rs

sh o u ld o fte n re v isit p o sitio n s b y g e n era tin g m o v es in s tea d o f a cc e ss in g th e m

d ire ctly fro m m em o ry T h is is w h at p la y e rsmdash e v e n m a ste rs mdash d o (D e G ro o t

1 9 4 6 ) F in a lly T T m a y h a v e s o m e th in g to sa y a b o u t e rro rs in c h e ss K ro g iu s

(1 9 7 6 ) m e n tio n s th a t er ro rs o f te n o c c u r w h e n a m o v e h a s ca u s ed im p o rta n t

c h a n g es in th e p o s itio n T h is m a y b e d u e to p la y e rsrsquo in a b ility to re c o g n ise th a t a

p re v io u sly a d eq u ate te m p late h as b ec o m e in a d e q u a te

In s u m m a ry T T o ffe rs a g o o d q u alita tiv e a c co u n t o f s e v eral im p o rtan t c h e ss

p h e n o m en a I t is n o w tim e to tu rn to m o re o b je c tiv e q u an tita tiv e te sts o f th e

th eo ry

A COM PUTER M ODE L O F S EARCH IN CH ESS

In th e re m a in d e r o f th is p a p e r I p re s en t a c o m p u te r m o d e l c a lled S E A R C H

w h ic h im p le m e n ts T T in so m e d e ta il I f irs t d e s crib e th e im p le m en ta tio n o f

S E A R C H m a k in g cle a r w h a t a s p ec ts o f T T h a v e b e e n in c lu d ed a n d th en d isc u ss

its b e h a v io u r w ith r es p e ct to h u m a n d a ta

O ve rv iew o f M ode l

F u ll im p le m e n ta tio n o f T T a s a c h e ss-p la y in g c o m p u ter p ro g ram w o u ld b e a

m ajo r ta sk mdash th is d iffic u lty is d e m o n stra te d b y th e fa c t th a t n o c o m p le te co m p u te r

m o d e l o f ch e s s c o g n itio n in c lu d in g p e rc e p tio n m em o ry a n d p ro b le m so lv in g

PATTERN -R ECOGN IT ION AND SEA RCH 299

h a s e v e r b e e n d e v elo p e d I p u rs u e d a lim ited a im a co m p u te r m o d el th a t c o n tain s

so m e o f th e im p o rta n t p aram e te rs o f T T a n d th a t co m p u te s k e y b e h a v io u ra l

v a ria b le s T h is m o d el d o e s n o t c o n stitu te a co m p le te im p le m e n ta tio n o f th e

th e o ry (it d o e s n o t s ea rc h o r e v a lu a te c h e ss p o sitio n s) b u t is d e ta ile d en o u g h to

o ffe r a g o o d te st o f so m e a s p ec ts o f T T I t is s o b e rin g to n o tic e th a t e v e n th is

p a rtia l im p lem e n tatio n o f th e th e o ry is q u ite c o m p le x a n d re q u ire s m a n y

p a ra m e te rs T h is is th e p rice o f a v o id in g th e v ag u en e s s o f v e rb al th e o ris in g

The M a in P rob lem -so lv in g Loop

T h e m ain in te re st o f th e m o d el is in th e in te ra c tio n b etw ee n p atte rn re c o g n itio n

a n d s ea rc h T h e m o d e l g e n e ra tes in d e p en d en t ep is o d es fo llo w in g se v e ral ru les

fo r g e n eratin g m o v e s a n d ch o o sin g sto p co n d itio n s C o m p atib le w ith m o s t

h u m an p ro to co ls th e p ro g ra m c o n sid e rs o n ly o n e b ra n c h w ith in a n ep is o d e (th u s

th e re is n o b ra n c h in g p o in t w ith in a n e p iso d e) A s illu stra te d in F ig 1 th e m o d e l

is c lo se to th e d es crip tio n o f T T g iv en e a rlie r in th is p a p e r T h e v ario u s c o n d itio n s

a n d o p e ra tio n s in S E A R C H a re re p re se n te d as p ro b a b ilit ie s o r p ro b ab ility

d istr ib u tio n s an d n o t a s a ctu a l c h e ss m o v e s e v a lu atio n s o r s y m b o lic s tru c tu res

in S T M o r in th e m in d rsquos e y e

A tra c e o f S E A R C H is sh o w n in F ig 2 T h e an aly s is w ill c e n tre o n th e

fo llo w in g v a ria b les a s a fu n c tio n o f th e n u m b e r o f c h u n k s ra te o f g en e ra tin g a

m o v e le v el o f fu z zin e ss in th e m in d rsquos e y e w h en a n e p is o d e is e n d e d m e an d e p th

o f s ea rc h m eth o d s u se d fo r g en e ra tin g a m o v e a n d m eth o d s u se d fo r s to p p in g a n

e p iso d e

T h e c o n c ep t o f te m p la te is im p le m e n te d in tw o w a y s (a ) b y h ig h e r

p ro b a b ilitie s o f f in d in g (s eq u en c e s o f) m o v e s a n d ev a lu a tio n s th an w ith p la in

c h u n k s a n d (b ) b y a d e cre a se in th e le v e l o f fu zz in e ss m ad e p o s sib le b y th e L T M

re p re se n ta tio n o f th e c o re o f th e p o sitio n a n d o f s lo ts

T h e le v e l o f re lia b ility o f th e in fo rm a tio n in th e m in d rsquos ey e is c a p tu re d b y a

ldquo fu z zin e s srdquo p a ra m e te r e x p re ss ed in a rb itr ary u n its T h re e m a in c o g n itiv e

fe a tu res ar e c a p tu red b y th is p a ra m ete r w o rk in g m e m o ry c a p a c ity a b ility to

m ain ta in a v isu o -s p atia l im ag e a n d su b je ctiv e e s tim a te o f th e r isk o f m ak in g a n

e rro r T h e fu z z in es s p a ram e ter is th e n as su m e d to o rig in ate b o th fro m th e

h a rd w a re a n d th e so ftw a re o f th e sy s tem It m a y v a ry d u r in g th e life tim e o f a

p la y er b e c a u se o f b io lo g ic a l m a tu ra tio n o r a g e in g an d m a y b e a ffe c ted b y

e x p e rim e n ta l m a n ip u latio n s T h e re a re th ree re a so n s w h y S E A R C H en d s a

se a rc h th e lev el o f fu z z in e s s is to o h ig h a n e v a lu atio n is p ro p o se d o r n o m o v e is

p ro p o s e d T h e id e a o f ex p ec ta tio n le v e l is n o t e x p lic itly p re se n t in th e m o d el b u t

it is im p lic it in th e p ro b a b ility v alu e s o f f in d in g fe atu re s e n d in g th e s ea rc h o f a n

e p iso d e e ith er b y p a tte rn re c o g n itio n o r b y th e a p p lica tio n o f h e u ristic s

S e le ctio n o f th e n ex t b a se -m o v e (a k e y c o n c ern o f N ew e ll amp S im o n 1 9 6 5 a n d

W ag n e r amp S c u rra h 1 9 7 1 ) is n o t ad d res se d b y S E A R C H w h ic h in g e n e ra l lac k s

th e s em a n tic in fo rm a tio n n e c es sa ry fo r su c h a se le c tio n F in a lly m e ta -se a rc h

w ith te m p la te s is n o t d ire c tly im p le m e n te d in S E A R C H b u t it is im p lic itly

300 GOBET

300

FIG 1 F lo w c h a rt o f S E A R C H

PATTERN -R ECOGN IT ION AND SEA RCH 301

301

F IG 2 E x a m p le s o f e p is o d e s g e n e ra te d b y S E A R C H

302 GOBET

re p re se n te d b y th e re la tiv e ly h ig h p ro b ab ility o f f in d in g (s eq u e n c e s o f) m o v es

a n d e v a lu atio n s w ith tem p la tes as c o m p are d w ith ch u n k s

The M ode lrsquos P aram e te rs

S E A R C H h as m a n y p a ra m ete rs a n d it is o f c o u rs e n e c es sa ry to se t u p a f ew o f

th e m w ith in d e p e n d e n t d a ta in o rd er to re d u c e th e n u m b e r o f d e g re e s o f fre e d o m

in th e m o d e l W h e n p o ss ib le I h a v e u s e d sim u la tio n s w ith th e C H R E S T (D e

G ro o t amp G o b e t 1 9 9 6 G o b e t 1 9 9 3 ) an d C H U M P (G o b e t amp Ja n s en 1 9 9 4 )

p ro g ram s to se t p a ra m e te r v a lu es C H R E S T is a p ro g ra m im p le m e n tin g as p e cts

o f T T a n d s im u la tin g n u m e ro u s e x p er im e n ts o n p e rc ep tio n an d m e m o ry in ch e s s

a n d C H U M P is a p ro g ra m p la y in g (w e ak ) c h e ss b y p u re p a tte rn re co g n itio n

N u m b e r o f C h u n k s a n d T e m p la te s T ab le 1 sh o w s th e v a lu es th at w ill b e

u s ed w ith th e S E A R C H m o d e l fo r th e se p a ra m ete rs T o c h o o se th e v a lu e s re la te d

to th e n u m b e r o f ch u n k s a n d te m p la tes th e c u rre n t v e rsio n o f C H R E S T h a s b e e n

e m p lo y e d T h e p ro b a b ility o f f in d in g a tem p la te w a s e stim ate d b y ru n n in g

C H R E S T o n 5 0 p o s itio n s ran d o m ly tak e n fro m M as ters rsquo g am e s T h e firs t lin e (0

c h u n k ) w a s ad d e d to g e t p re d ic tio n s a t th e n o v ic e lev e l W ith n e ts o f 1 0 0 0 0 0

1 2 0 0 0 0 a n d 1 5 0 0 0 0 c h u n k s th e p ara m ete rs w ere e stim ate d w ith th e b e s t-fit t in g

fu n c tio n s av a ilab le ( th e ldquo n o v ice rdquo v alu e s w ere n o t u se d ) T h e n u m b er o f te m p la tes

is ro u g h ly a lin e ar fu n c tio n o f th e n u m b er o f c h u n k s (r 2 = 9 7 ) T h e p ro b a b ility

o f f in d in g a tem p la te is a p p ro x im a tely a lo g -fu n c tio n o f th e n u m b e r o f c h u n k s

(r 2 = 9 4 )

H e u r is tic s C h u n k s T e m p la tes a n d T h e ir R e la tio n to th e P ro b a b ility o f

F in d in g M o v e s a n d E v a lu a tio n s T ab le 2 g iv e s th e v a lu e s u s ed in th e

sim u la tio n s fo r th e p a ra m ete rs re la te d to h e u ristic s c h u n k s a n d te m p la te s

H e u ris tic s in c lu d e sim p le se a rc h te c h n iq u e s (e g ldquo ta k e a p ie c e b a c k rdquo o r ldquoc h e c k

th e K in g rdquo ) a s w ell a s m o re a b stra c t ru le s (e g ldquoo c c u p y th e c en tre rdquo ) T h eir m a in

c h a rac te ris tic in co m p a riso n w ith c h u n k s an d tem p la te s is th a t th ey are g e n e ra l

a n d re q u ire so m e co n sc io u s c o m p u tatio n in o rd e r to p ro d u ce a m o v e T h e

a ss u m p tio n u n d e rly in g T a b le 2 is th at th e p aram e ters re la ted to h e u ristic s s ta y

ro u g h ly c o n sta n t w h ile th e o th e r p aram e te rs v a ry as a lo g arith m ic fu n c tio n o f th e

n u m b e r o f c h u n k s in th e n e t (A lo g arith m ic fu n ctio n h a s b e e n c h o se n to in d ica te

th a t ch u n k s y ie ld a d im in ish in g re tu rn as th e ir n u m b e r in c re a se s) T h e

a ss u m p tio n th a t th e n u m b e r o f h e u ristic s is c o n sta n t ac ro s s s k ill le v e ls se e m s

re a so n a b le (p e rh a p s w ith th e e x ce p tio n o f th e n o v ic e le v e l) a s m o s t c h e ss

M a ste rs rsquo k n o w le d g e is v e ry sp ec ific to c erta in a sp e c ts o f th e g a m e (D e G ro o t

1 9 4 6 )

T h e fo llo w in g c o n s id era tio n s w e re m ad e in se ttin g th e v alu e s g iv e n in

T ab le 2 I t w a s d ee m e d p lau sib le th a t th e p ro b a b ility o f f in d in g so m e h e u ristic in

a p o s itio n b e h ig h ( 9 5 ) a s w e ll a s th e p ro b a b ility o f f in d in g s o m e c h u n k F in ally

PATTERN -R ECOGN IT ION AND SEA RCH 303

TA BLE 1

The V a lu es o f th e 14 N e ts U sed in th e S im u la tio ns

P ro b a b i li ty o f

re c o g n is in g a t le as t

P ro p o r t io n o f o n e te m p la te g iv e n a

N u m b e r o f c h u n k s N u m b e r o f te m p la te s te m p la te s p o s i t io n

0 0 0 0 0 0 0 0

1 0 0 2 0 0 0 0 0 0 0

2 6 8 0 5 0 0 2 1 8 0

5 0 0 3 3 6 0 0 7 1 4 0

1 0 0 1 1 1 0 0 0 1 0 2 4 0

2 0 0 0 3 2 6 5 0 1 3 3 0 0

3 0 0 0 1 4 9 3 0 1 6 3 6 0

4 0 0 0 5 7 7 4 0 1 9 4 6 0

5 0 0 0 6 1 1 4 2 0 2 3 4 0 0

7 2 0 4 4 2 1 3 6 0 3 0 4 8 0

8 0 0 1 0 2 2 8 5 0 2 9 5 4 0

1 0 0 0 0 0 2 7 6 5 0 2 8 5 1 0

1 2 0 0 0 0 3 3 5 7 0 2 8 5 4 0

1 5 0 0 0 0 4 2 4 5 0 2 8 5 6 0

T h e v a lu e s b e lo w 1 0 0 0 0 0 c h u n k s w e r e ta k e n f ro m s im u la t io n s w ith C H R E S T th e o the rs

e x t ra p o la te d S e e te x t f o r d e ta ils

TA BLE 2

H eur is t ic s C hun ks Tem pla tes and Their Re la tion to th e P ro bab ility of Fin d in g

M oves and Evalu ta tio ns

T y p e H e u r is tic s C h u n k s T e m p la te s

P ro b a b i li ty o f e v o k in g a n 9 5 g (n _ c h u n k s 9 5 )a se e T a b le 1

h e u ri s t ic a c h u n k o r a te m p la te

P ro b a b i li ty o f f in d in g a m o v e 5 0 g (n _ c h u n k s 5 0 ) g (n _ c h u n k s 9 0 )

g ive n th a t a n h e u r is tic a c h u n k

o r a te m p la te h a s b e e n e v o k e d

P ro b a b i li ty o f f in d in g a n e v a lu a tio n 1 5 g (n _ c h u n k s 0 5 ) g (n _ c h u n k s 5 0 )

g iv e n th a t a n h e u ri s t ic a c h u n k o r

a te m p la te h a s b e e n e v o k e d

aT h e fu n c tio n g i s d e f in e d a s

g (n _ c h un k s p ro b ) = p ro b 0 2 lo g1 0

(n _ c h un k s ) i f n _ c h u n k s gt 0

a n d

g (n _ c h u n k s p ro b ) = 0 i f n _ c h u n k s = 0

w h e re n _ c h u n k s i s th e n u m b e r o f c h u n k s in a g iv e n n e t a n d p ro b i s a c o n s ta n t

303

304 GOBET

th e p ro b a b ility o f re c o g n isin g a te m p la te in a p o sitio n is sm a lle r a n d is g iv e n in

T ab le 1

T h e p ro b a b ility o f f in d in g a m o v e g iv e n a h e u ristic is s e t to 5 0 in d ic atin g th a t

h e u ristic s m a y fa il to p ro d u ce a m o v e h a lf o f th e tim e T h is is b e c a u se so m e

h e u ristic s m ay n o t y ie ld a m o v e a n d b ec a u se so m e p ro p o se d m o v es m a y b e

ille g a l T h e p ro b a b ility o f f in d in g a m o v e g iv en a tem p la te is h ig h p a rtly

re fle ctin g th e ric h s em a n tic k n o w le d g e an d th e in te r-te m p la te lin k s a s su m e d to

c h a rac te rise te m p la te s F o r th e p ro b a b ility o f f in d in g a m o v e g iv e n th a t a ch u n k

h a s b e en re co g n ise d I u se d th e p ara m e te r p ro b in th e fu n ctio n g (s ee T a b le 2 ) so

th a t i t a p p ro x im a te s th e d ata p ro d u c ed b y th e C H U M P p ro g ram (G o b et amp Ja n se n

1 9 9 4 ) E v a lu a tio n s a re su p p o s ed to b e h a rd er to le arn a n d th e re fo re h a rd e r to u se

th a n m o v es H e n ce th e ir p ro b a b ilit ie s a re lo w e r th a n th e co r res p o n d in g p ro b -

a b ilit ie s w ith m o v es A g a in fo llo w in g d irec tly fro m th e th e o ry te m p la te s o ffe r

th e b e st so u rce o f ev alu a tio n s

W ith re sp e c t to th e n u m b e r o f se q u e n tia l m o v e s p ro p o s ed c o u n ted in p lie s

(i e m o v e s fo r W h ite o r B la ck ) i t is as su m e d th a t h e u ristic s g iv e a cc e ss to o n ly

o n e m o v e w h ile c h u n k s a n d te m p late s y ie ld se q u e n c es o f m o v e s w h o se n u m b e r

fo llo w s a g e o m e tric p ro b a b ility d is tr ib u tio n (th e c h o ice o f th is d is tr ib u tio n w as

in sp ire d b y sta tis tic s ta k e n fro m C H U M P ) T h e lo n g e s t s eq u e n c e ( ca ll i t k ) h as a

fre q u e n c y o f 1 th e s e co n d -lo n g e st a fre q u en cy o f 2 th e th ird -lo n g e st a fre q u e n c y

o f 4 a n d so o n u n til th e sh o rte st se q u e n c e w h o s e len g th is 1 m o v e an d w h o se

fre q u e n c y is 2 (k ndash 1 ) T h e m a x im u m se q u e n ce o f m o v es w a s se t to 1 8 F in a lly

S E A R C H atte m p ts to g e n e ra te a m o v e b y p a ttern re c o g n itio n ( ch u n k o r te m p la te )

fo u r tim e s b e fo re u sin g a n h e u ristic

T im e a n d F u zzin e ss P a ra m ete rs T h e tim e p a ram e ter s fo r th e re sp e c tiv e

o p e ra tio n s w e re s et u sin g p la u sib le v a lu e s (se e T a b le 3 ) M o v e g en era tio n b y

p a tte rn re c o g n itio n (c h u n k o r te m p late ) is as su m e d to b e v e ry sh o rt (a few

h u n d re d m illis e co n d s) n o tim e c o st is u se d in th e m o d e l T h e tim e fo r c o m p u tin g

a m o v e-g en e ra tin g h e u ristic w a s s et to th e ra th e r lo n g 2 0 s ec o n d s mdash g en era tin g a

m o v e w ith o u t u sin g p a tte rn r ec o g n itio n re q u ires p u ttin g to g eth e r v a rio u s ty p e s o f

in fo rm a tio n a n d a s k s fo r m a n y ch e c k in g p ro c ed u res T h e tim e fo r c a rry in g o u t

o n e m o v e (o n c e g e n erate d ) in th e m in d rsquos e y e w a s s et to tw o s ec o n d s T h is is

c o m p atib le w ith S a a rilu o m a rsquos (1 9 8 9 ) d ata w h ic h sh o w th a t a b lin d fo ld ed M a ste r

c an fo llo w a g a m e d icta ted a t tw o se c o n d s a m o v e F in ally th e tim e fo r ca rry in g

o u t a n ev a lu a tio n b y h eu ris tic is s e t to 1 0 s e co n d s T h is ra th e r s h o rt tim e m a y b e

ju stif ie d b y th e fa c t th a t p la y e rs ty p ic a lly co n s id e r o n ly o n e (s u b jec tiv e ) a sp e c t o f

th e p o sitio n (D e G ro o t 1 9 4 6 ) a n d th at m an y e v a lu atio n s c a n b e g ro u n d ed o n th e

b a sis o f c lea r m a teria l lo ss e s

T h e fu z zin e ss lev el o f th e s y ste m is e x p re ss ed in a rb itra ry u n its I t s ta rts w ith

th e v a lu e z e ro a n d it is in c re a se d w h e n a m o v e is c a rrie d o u t in th e m in d rsquos e y e

a n d w h e n tim e is s p e n t a p p ly in g a n h e u ris tic W h e n a te m p la te is fo u n d th e

PATTERN -R ECOGN IT ION AND SEA RCH 305

fu z z in es s lev el is d e cre a se d a s p a rt o f th e in fo rm atio n m ay b e sto re d in L T M

d ire c tly fre e in g c ap ac ity in w o rk in g m e m o ry a n d in th e m in d rsquos ey e

S im u la t io n s w ith th e ldquo C anon ica l M ode lrdquo

T h e sim u latio n s d e sc rib ed in th is s ec tio n a re s tra ig h tfo rw a rd U s in g th e

p a ra m e te r v alu e s d is cu sse d e a rlie r I le t th e p ro g ra m s ea rc h 1 0 0 0 ep iso d e s fo r

e ac h n e t s iz e S u m m a ry v alu e s fo r m e a n d ep th o f se a rc h t im e ra tio d e p th tim e

a n d fu z zin e s s a s w e ll a s fo r g e n e ra tio n an d s to p co n d itio n s w e re c o m p u ted fo r

e ac h n e t s iz e

M e a n D e p th o f S e a r ch R a te o f S e a rc h a n d F u z zin e ss A cc o rd in g to

S E A R C H m ea n d e p th o f s ea rc h fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f

c h u n k s (se e F ig 3 a) If w e as su m e a co n sta n t ra te o f le a rn in g n e w c h u n k s a s is

c o m m o n p ra ctic e in so m e c o g n itiv e a rch ite c tu res (c f N e w e ll 1 9 9 0 ) a n d if w e

a ss u m e th a t s k ille d p la y e rs h a v e sp e n t m o re p rac tice a n d stu d y tim e th a n

u n s k ille d p la y e rs th e n m e an d e p th fo llo w s a p o w e r fu n c tio n o f s k ill as w e ll T h is

p re d ic tio n w h ic h is a t v ar ia n c e w ith H o ld in g rsquos p re d ic tio n (1 9 8 5 p 1 8 2 ) o f a

lin ea r in c rea s e is p artly co n siste n t w ith C h a rn e ss rsquos (1 9 8 1 ) p ro p o s a l th a t d e p th o f

se a rc h is n o t l in e arly re la ted to s k ill b u t th at th e re is a ce ilin g a t h ig h s k ill le v e ls

T h e re su lt is a ls o c o m p atib le w ith th e w e a k lin e ar re la tio n fo u n d in e m p ir ic a l

stu d ie s (C h a rn e ss 1 9 8 1 G o b e t in p re ss ) b e tw e e n m e a n d e p th o f se a rch a n d sk ill

le v el b e c a u se re stric te d ra n g e s o f th e c u rv e c a n b e a p p ro x im a ted b y a lin e a r

fu n c tio n T h e a b so lu te v alu e s a re a lso q u ite r ea so n ab le th ey ris e f ro m lo w d ep th s

(le ss th a n 1 p ly ) w ith n o ch u n k s (co r res p o n d in g to th e n o v ic e le v el) to a ro u n d 2 5

p lies w ith a sm a ll n et (1 0 0 0 c h u n k s ) an d th e n to a ro u n d 4 p lie s w ith ex p ert le v e l

(a ro u n d 3 0 0 0 0 c h u n k s a s e s tim a te d b y s im u la tio n s o n th e re ca ll tas k ) T h e y th e n

slo w ly (s av e fo r a f ew ra n d o m v a ria tio n s ) in c re a se to m o re th an 5 p lie s w ith n e t

la rg er th an 1 0 0 0 0 0 c h u n k s w h ic h c o rre sp o n d s to G ran d m a ste r le v e l H o ld in g

(1 9 8 5 ) c o m p u te d m e a n d e p th o f se a rch fo r d e G ro o trsquos (1 9 4 6 ) d a ta a n d fo u n d th a t

TA BLE 3

T im e and ldquo Fuzz in ess rdquo Param e ters U sed in th e

S im ula t io n s

T im e fo r c a r ry in g o u t a m o v e 2 s

T im e fo r c o m p u t in g m o v e -g e n e r a tin g h e u r is tic 2 0 s

T im e fo r c o m p u t in g e v a lu a t io n 1 0 s

U p p e r l im it o f fu z z in e ss 5 0

In c r e a se o f fu z z in e s s p e r m o v e 1

In c re a se o f f u z z in e ss p e r s e c o n d 2

D e c re a s e in fu z z in e ss d u e to te m p la te 5

306 GOBET

E x p e rts a n d G ra n d m as ters h a d res p e ctiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 8 a n d

5 3 T h e reg res sio n e q u a tio n d e riv e d f ro m C h a rn e ss rsquos (1 9 8 1 ) d ata y ie ld a n

a v e rag e d e p th o f se a rc h o f a b o u t 2 3 p lies a t th e 1 3 0 0 E L O 1 le v e l o f 4 1 a t th e

E x p e rt le v e l (2 0 0 0 E L O ) a n d o f 5 7 a t th e G ra n d m a s te r le v el U n fo rtu n a tely n o

stu d y te ste d p la y e rs ra n g in g fro m n o v ic es to G ran d m a ste rs an d S E A R C H rsquos

p re d ic tio n o f a p o w e r la w o f p rac tic e c an n o t b e te ste d (y e t) I w ill re p o rt la te r

sim u la tio n s a d d re ssin g d a ta co lle c ted b y S a arilu o m a (1 9 9 0 ) w h e re In tern atio n a l

M a ste rs a n d G ra n d m a s te rs te n d e d to s e arc h le s s th a n M as te rs

T h e ra te o f s ea rc h a lso fo llo w s a p o w e r fu n ctio n o f th e n u m b e r o f c h u n k s (se e

F ig 3 b ) D e G ro o t (1 9 4 6 ) C h arn es s (1 9 8 1 ) a n d G o b e t ( in p res s) a ll f o u n d th a t

stro n g p la y er s te n d e d to s e arc h fa ste r F o r ex a m p le G o b e t ( in p re s s) fo u n d th a t

h is M a ste rs E x p e rts C la ss A a n d C la s s B p lay e rs re sp e c tiv ely se arch e d 4 8 4 1

3 2 an d 3 4 n o d e s p e r m in u te S E A R C H rsquos v a lu es a re h ig h e r b u t s til l p la u s ib le

F o r ex am p le W a g n e r a n d S c u rra h rsquos (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r

m in u te N o te a lso th a t a ll th e ex p erim e n ts m e n tio n e d e a rlier h a v e u se d v e rb a l

p ro to c o ls w h ic h m ay h av e s lo w e d d o w n th e ra te o f se a rc h (c f E ric ss o n amp

S im o n 1 9 8 0 ) F in a lly th e ra te o f se arch m a y h av e b e e n u n d e res tim a ted in th e

lite ra tu re b ec a u se th e r a te o f g e n e ratin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d

b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l t im e H o w e v e r to ta l t im e in c lu d es

tim e n o t sp e n t in s e arc h ( fo r e x a m p le w h a t D e G ro o t c a lls th e ldquo firs t p h a se rdquo)

T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a riab le th e le v e l o f fu zz in e ss a t

w h ic h a se a rc h is e n d e d is m o re d if fic u lt to ju d g e b ec a u se lit tle is k n o w n a b o u t

th e ro le o f fu z z in es s in c h es s th in k in g A g ain S E A R C H p ro p o se s th a t th is

v a riab le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s ee F ig 3 c ) W ith la rg e r

n e ts e p iso d es te n d to b e e n d e d w ith lo w er le v els o f fu z z in e s s T h is su g g es ts th at

in g e n e ra l s tro n g p la y ers s h o u ld b e m o re c o n fid e n t in th e ir c alc u la tio n s as th e y

a re n o t a t th e e d g e o f th eir p o s sib ilitie s N o te th a t th e ra te o f ch an g e is ra th e r h ig h

fo r th is p o w er law w h ic h s u g g e sts th at it sh o u ld b e p o ss ib le to d e te c t i t

e x p erim e n tally

G e n e ra tio n o f M o ve s H o w is m o v e g en e ra tio n af fec te d b y sk ill le v e l A s

sh o w n in F ig 4 a S E A R C H m a k es c le a r p re d ic tio n s W ith sm a ll n u m b e rs o f

c h u n k s th e tim e -c o n s u m in g p ro ce s s o f g en e ra tin g m o v es b y h e u ristic s is

e m p lo y e d T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y ch u n k s

w h ic h is in tu rn d o m in a te d b y te m p la te g e n eratio n

1 T h e E L O ra t in g i s a n in te r v a l sc a le th a t ra n k s c o m p e t it io n c h e ss p la y e rs I ts s ta n d a rd de v ia t io n

(2 0 0 p o in ts) is o f te n in te r p re te d a s a m e a su r e o f sk i ll c la s s in c h e ss G r a n d m a s te r s a re n o rm a lly ra te d

a b o v e 2 5 0 0 In te rn a t io n a l M a s te r s a b o v e 2 4 0 0 M a s te r s a b o v e 2 2 0 0 a n d E x p e rt s a b o v e 2 0 0 0

B e lo w c la sse s (A B e tc ) d iv id e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in ts

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

PATTERN -R ECOGN IT ION AND SEA RCH 293

sto re s p e rc ep tu a l s tru c tu res b o th fro m ex te rn a l in p u ts a n d fro m m e m o ry s to res )

P a tte rn -re c o g n itio n m e c h an is m s a p p ly re cu rs iv e ly in th e in tern al re p re se n ta tio n

o f p o s itio n s in th e m in d rsquos ey e T e rm in a tio n o f se a rch in a b ra n c h is o b ta in e d b y

e v a lu a tin g w h e th e r c erta in g o a ls a re a b o v e o r b e lo w a th res h o ld w h o s e v a lu e

m ay ch a n g e a s a fu n ctio n o f p lay e rs rsquo e x p e cta tio n lev el o f th e p o sitio n

V a rio u s c o m p u te r p ro g ra m s o f p ro b lem s o lv in g in c h e ss w e re d e v e lo p e d b y

S im o n a n d h is co lle a g u es b u t n o n e o f th em d ire ctly in co rp o ra te d th e

re c o g n itio n ndash as so c ia tio n m ec h a n ism o f th e c h u n k in g th eo ry T h e p ro g ra m s

w ritte n b y N ew ell S h a w a n d S im o n (1 9 6 3 ) an d B a y lo r a n d S im o n (1 9 6 6 )

im p le m e n te d th e id ea o f s e le c tiv e se a rc h m a d e p o ss ib le b y th e u se o f h e u ristic s

N e w e ll a n d S im o n rsquos m o d e l (1 9 6 5 se e a lso W a g n e r amp S c u rra h 1 9 7 1 ) fo rm u la te d

six p rin c ip les th a t d ic ta te th e g e n e ra tio n o f m o v es o r e p iso d es u s in g m a in ly th e

e v a lu a tio n o b ta in ed at th e e n d o f a b ra n c h

Ho ld ing rsquos S EEK Theo ry

H o ld in g (1 9 8 5 1 9 9 2 ) critic is e d C T an d p ro p o s ed in ste ad th e S E E K (S E a rc h

E v alu a tio n a n d K n o w led g e ) th e o ry a th eo ry th a t w a s h o w e v e r o n ly lo o se ly

fra m ed an d d id n o t re a ch th e th e o re tica l d e ta il o f C T T h e m a in th ru st o f S E E K

w a s to su g g es t th at m a ste ry in ch e s s d e p e n d s p rim a rily in th in k in g a h e a d an d n o t

in p a tte rn re c o g n itio n N o te th a t a ll th re e c o m p o n e n ts o f th e S E E K th e o ry a re

p re se n t in C T a n d th at i t is re ally th e w eig h t g iv en to e ac h o f th es e c o m p o n en ts

th a t d iff ere n tia te th e tw o th eo r ie s

S aa rilu om arsquos A ppe rcep tio n andR es tru c tu ra tio n Theo ry

R e ce n tly S a a rilu o m a (1 9 9 0 1 9 9 2 ) p ro p o se d th a t p la y e rs w h ile try in g to fin d a

m o v e in a p o sitio n a cc e ss g o a l p o s itio n s b y p a ttern re co g n itio n (S a ar ilu o m a u s es

th e o ld te rm ldquoa p p e rc e p tio n rdquo ) T h e y th e n try to c lo se th e p a th fro m th e p ro b le m

p o sitio n to th e g o al p o sitio n W h en it is n o t p o ss ib le to c lo se th e p a th th e p ro b le m

sp a c e is re stru c tu red T h u s p ro c e sse s le a d in g to a M as terrsquos c h o o sin g a m o v e m a y

b e d e sc rib e d a s a s eq u e n c e o f a p p e rc ep tio n ndash res tru ctu ratio n c y c les w h ic h m a k e it

p o s sib le to f in d so lu tio n s w ith o n ly a lim ite d s ea rc h in th e p ro b le m s p a ce

S a a rilu o m arsquos th e o ry a d m itte d ly s till a t i ts e arly s ta g e o f d ev e lo p m e n t is n o t

q u ite sa tisfa c to ry i t is u n c lea r w h a t d iffe ren tia te s it fro m N e w e ll a n d S im o n rsquos

(1 9 7 2 ) m e a n sndash e n d s a n a ly s is a n d it d o e s n o t m a k e p ro v is io n fo r w h at h ap p e n s

w h e n p la y e rs d o n o t h av e a g o a l p o sitio n in m in d

E ricsson and K in tsch rsquos Long -te rm W o rk ingM em o ry Theo ry

E rics so n a n d K in tsc h (1 9 9 5 ) p ro p o s e w ith in th e fr am e w o rk o f th e ir lo n g -term

w o rk in g m e m o ry th eo ry (L T W M T ) th a t sk ille d p lay e rs h av e c o n s tru cte d a n

h ie ra rch ic a l re tr ie v a l s tru c tu re n o t u n lik e th e stru c tu re c rea te d b y S F a n d D D

294 GOBET

tw o m n em o n is ts sp e c ia lise d in th e d ig it- sp a n ta s k (C h as e amp E ric s so n 1 9 8 2 )

T h is p o w e rfu l m e m o ry stru c tu re iso m o rp h ic to th e 6 4 s q u ares o f th e c h e ss b o a rd

a llo w s p la y e rs to u p d a te in fo rm a tio n ra p id ly d u rin g se a rc h T h e th eo ry a ls o

p ro p o s e s th a t c h e ss p lay e rs ca n c re ate n e w L T M as so c ia tio n s ra p id ly a lth o u g h

n o p ara m e te r is g iv e n to s p e cify th is s p ee d o f e n co d in g

I h av e sh o w n els ew h ere (G o b e t 1 9 9 6 ) th a t L T W M T in a d d itio n to b e in g

v a g u e a n d le a v in g m a n y d e ta ils u n s p e cifie d g e n e ra te s p re d ic tio n s th a t d o n o t

a g re e w ith th e e x p e rim en ta l d a ta o n c h es s p e rc ep tio n a n d m e m o ry In ad d itio n

th e m e m o ry m e ch a n ism s p ro p o s ed b y L T W M T (re tr ie v a l s tru c tu re a n d ra p id

e lab o ratio n o f L T M stru c tu re s) s ee m a t o d d s w ith th e fo llo w in g a sp e c t o f c h e ss

p la y er srsquo se arch b e h av io u r I t is co m m o n fo r c h e ss p la y er s to re v is it a n o d e d u rin g

th e ir a n aly s is o f th e p o sitio n H o w ev e r in ste a d o f ac c e ssin g th is n o d e d ire c tly as

su g g es ted b y L T W M T rsquos v e ry p o w erfu l m e ch a n is m s fo r s to rin g p o sitio n s ra p id ly

a n d a c c u rate ly p la y er s a c c es s th e targ e t p o sitio n b y g en era tin g a s e q u e n ce o f

in d iv id u a l m o v e s fro m th e g iv en p ro b le m p o s itio n (c f D e G ro o t 1 9 4 6 ) T h is

b e h a v io u r su g g e sts th a t p lay e rs m a y n o t s to re p o sitio n s a s q u ic k ly a s p ro p o s e d b y

L T W M T

TH E TEM P LA TE TH EO RY AN D ITS A PPL IC A T IO NTO PRO BLEM SO LV ING

In itia lly th e tem p la te th e o ry (T T ) w a s d e v elo p e d to re m o v e so m e w e a k n e ss es in

th e c h u n k in g th e o ry w ith r es p e ct to d ata fro m m e m o ry re se a rch (G o b e t amp S im o n

1 9 9 6 a ) C o n tra ry to C T rsquos p re d ic tio n s b a s ed o n a lim ited S T M ca p a c ity c h e ss

p la y er srsquo m e m o ry is res is ta n t to re tro a ctiv e in te rfe re n ce (C h arn es s 1 9 7 6 ) a n d

c h e ss p la y e rs c a n re c a ll s ev e ra l b rief ly p re s en te d p o sitio n s w ith re a so n a b le

a cc u ra c y (C o o k e A tla s L a n e amp B erg e r 1 9 9 3 G o b e t amp S im o n 1 9 9 6 a )

L ik e C T T T p ro p o s es th a t c h u n k s a re ac c e ss ed b y tra v e rsin g a d isc rim in a tio n

n e t C h u n k s a re lin k e d to o th e r in fo rm a tio n s to red in L T M s u ch a s m o v es p la n s

ta ctic al m o tiv es a n d s o o n In a d d itio n c h u n k s th a t o fte n o cc u r in a p lay e rrsquos

e x p er ie n c e c a n e v o lv e in to m o re c o m p le x d a ta s tru ctu re s ( te m p la tes ) w h ich h a v e

slo ts a llo w in g v a ria b les to b e e n c o d ed fo r e x a m p le to sp e c ify th e sq u a re

o c c u p ie d b y a p iec e A c c o rd in g to T T th is en c o d in g o cc u rs ra p id ly (a b o u t o n e

se c o n d p e r s lo t) In a d d itio n to s lo ts tem p la te s co n ta in a co r e w h ic h is m ad e u p

o f (v a ria b le -fre e ) c h u n k s A lto g e th er te m p late s a re as su m e d to s to re a t le as t

a b o u t 1 0 p iec e s F in ally te m p la te s m a y b e lin k e d to o th er te m p la tes T T als o

p ro p o s e s th a t in fo rm a tio n sto re d in th e m in d rsquos e y e a s tru ctu re s im ilar to th a t

p ro p o s e d b y C T d e ca y s ra p id ly a n d th at i t n e e d s to b e u p d a te d e ith e r b y in p u ts

fro m th e e x te rn a l w o rld o r b y in p u ts fro m m e m o ry s tru ctu re s

T T re m o v e s th e d iffic u lty o f C T w ith in te rfe ren c e p h e n o m en a f ir s t b e ca u s e it

h y p o th e sis es s o m e fa st L T M e n c o d in g (th ro u g h te m p late s lo ts) a n d se c o n d

b e c au s e te m p la te s co n ta in m o re in fo rm a tio n th a n th e ch u n k s p ro p o s ed b y C T

(C T a ssu m e d th a t c h u n k s co n ta in a t m o s t f iv e o r s ix p iec e s) F in a lly T T k ee p s

PATTERN -R ECOGN IT ION AND SEA RCH 295

th e p o w e r o f C T to e x p lain th e r ap id rec o g n itio n o f p o sitio n s sh o w n b y m a ste rs

a s th e s am e d isc rim in a tio n m e ch a n ism s are p res e n t (G o b e t 1 9 9 6 )

S ea rch M echan ism s

T T a n d C T p ro p o se th a t se a rc h is ca rrie d o u t in a fo rw ard fa sh io n b y re cu rsiv e

a p p lica tio n o f p a tte rn re co g n itio n p ro ce s se s in th e in te rn a l rep res e n ta tio n In th e

re m ain d e r o f th is se c tio n I w ill f le sh o u t th is m e c h an ism w ith ad d itio n a l sp e c ifi-

c atio n s I w ill a lso sh o w h o w c h u n k s an d te m p late s m a y b e u se d to te rm in a te

se a rc h a n d h o w te m p la te s m a y b e u se d to ca rry o u t s ea rc h a t a le v e l m o re

a b stra c t th a n th e m o v e le v e l

M o v e G e n e ra tio n A s m en tio n e d e arlie r p a ttern r ec o g n itio n is a p p lie d

re c u rsiv e ly in T T If a c h u n k mdash o r a te m p la te a s tem p la te s ar e a s p e cia l c as e o f

c h u n k smdash is rec o g n is ed i t m a y g iv e a c c es s to a m o v e (o r a se q u e n c e o f m o v e s ) o r

to a n h e u ris tic fo r se le ctin g th e n ex t m o v e E x a m p le s o f s u ch h e u ristic s a re

ldquo O c c u p y o p e n lin e s rdquo o r ldquo C o u n te r-a tta c k in th e ce n tre w h e n a ttac k e d o n th e

K in g rsquos s id e rdquo In th is ca s e th e m o v e(s ) is (a re ) c a rried o u t in th e m in d rsquos e y e If n o

m o v e re su lts fro m p a tte rn re co g n itio n o n e o f tw o o p era tio n s m a y b e ap p lie d

E ith e r th ere is a n e w atte m p t to g e n e rate a m o v e b y a cc e ss in g a d iffe re n t c h u n k

o r w ea k e r h e u ristic s a re a p p lie d

U p d a te o f In te rn a l R ep re se n ta tio n a n d S to r a g e o f In fo rm a tio n in to

T e m p la te W h en a m o v e o r a se q u e n c e o f m o v e s is c a rrie d o u t in th e m in d rsquos

e y e th e in te rn a l rep res e n ta tio n is u p d a te d a n d w h e n a te m p la te h as b e e n

a cc e ss e d s lo ts a re u p d ate d a s w e ll S lo ts m a y sto re in fo rm a tio n a b o u t th e

lo c atio n o f p ie ce s s tra teg ic in fo rm a tio n e v alu a tio n o f th e p o sitio n o r p a rt o f i t

a n d s o o n N o te th a t th is in fo rm a tio n fa c ilita te s s ea rc h b e c au se p o s sib le fo r -

g e ttin g th ro u g h d ec a y in th e m in d rsquos e y e m a y b e b ac k e d -u p b y in fo rm a tio n s to re d

in s lo ts

E va lu a tio n o f N o d e s E v a lu a tio n o f a p o sitio n is n o t c ar ried o u t af te r e ac h

m o v e b u t o n ly a t th e term in a l p o sitio n s E v a lu atio n is e ith e r r e trie v e d w h e n

p o s sib le fro m ch u n k s th a t h a v e b e en re c o g n ise d o r co m p u te d w h e n th e p la y e r

d e c id e s to te rm in a te s e arc h (s ee n e x t p a ra g ra p h ) D e G ro o trsquos (1 9 4 6 ) p ro to co ls

in d ic ate th a t p la y e rs e v a lu a te o n ly te rm in a l p o s itio n s a n d th a t th e ir e v a lu atio n s

a re ra th e r s im p le ta k in g in to a c co u n t a s in g le fe a tu re su c h as m o b ility o r c o n tro l

o f th e c e n tre a n d stro n g ly su g g e s t th a t e v a lu a tio n s are n o t co m p u te d b y

c o n jo in in g s e v eral fe atu re s

E n d in g S ea r c h o f a n E p iso d e A c ritic a l q u es tio n g iv e n a lim ite d

in fo rm a tio n -p ro c es sin g c a p a city is w h e n to s to p se a rc h in g a n e p iso d e (i e a

se q u e n c e o f m o v es g e n e ra ted fro m a b as e m o v e ) I p ro p o se th a t th e fo llo w in g

296 GOBET

c o n d itio n s ca n h alt th e se a rc h o f a n e p iso d e T o b e g in w ith th e p ro b a b ility o f

m ak in g a n e rro r is to o h ig h P s y ch o lo g ic a lly th is p ro b a b ility is a fu n ctio n o f th e

fo rg e ttin g a n d in ter fer en c e r a te s in th e m in d rsquo s ey e P h e n o m e n o lo g ic a lly p lay e rs

p ro b a b ly a s se ss th is p ro b a b ility b y ta k in g in to a c c o u n t th e d e p th o f se a rc h

re a ch e d a n d b y e s tim a tin g th e ir fa m ilia rity w ith th e p o s itio n

A n o th e r re a so n to h a lt s ea rc h o c cu r s w h e n th e le v e l o f e x p e c tatio n fo r th e

p o s itio n is m et o r w h e n a f ea tu re o f th e p o s itio n (e g sa fe ty o f th e K in g ) w as

e v a lu a te d to b e lo w e r th a n its a d m iss ib le v a lu e (N e w e ll amp S im o n 1 9 7 2 ) T h is

le v el o f e x p e c ta tio n is p ro v id e d b y a c h u n k en c o u n te re d d u rin g e arlie r s ea rc h o r

b y e x p lic it ev a lu a tio n o f th e p o s itio n a n d w a s s to re d e ith e r in S T M o r w h e n

a v a ila b le in a te m p late s lo t A fin a l h a ltin g c o n d itio n is th a t a d e c isiv e e v e n t

o c c u rre d s u ch a s m a te im p o rta n t m a teria l g a in o r lo ss o r fu lfilm e n t o f a k e y

g o al

S e lec tin g th e N e x t B a s e -m o v e N o w co n s id er th e q u e stio n o f w h ic h b a se -

m o v e to se a rch n ex t w h en a le a f n o d e h a s b e e n re a ch ed A n y o f s ix m e c h an is m s

m ay b e e n g a g e d F irst if th e le a f w a s e v a lu ate d w ith a h ig h risk o f er ro r th e s am e

se q u e n c e o f m o v e s is se a rc h ed a g ain in o rd e r to o b ta in a m o re re lia b le e stim a te

S e c o n d th e sa m e s eq u en c e o f m o v e s m a y b e se a rch e d a g a in to m a k e s u re th a t i t

h a s b e e n sto re d in L T M T h ird if a tem p la te h a s b e e n re co g n ise d a m e ta -se a rc h

(s ee la te r) is c arr ie d o u t F o u rth th e re is a b ia s to g iv e p re fe ren ce to n o rm a l b as e -

m o v e s ea rly in se a rch a n d to u n u su a l b a s e-m o v e s la ter (N ew ell amp S im o n 1 9 7 2

p 7 2 3) F ifth a m ov e re ac h e d at a n y le v e l o f d e p th in s ea rch in g a lin e m a y b e trie d

a s a ca n d id a te m o v e in th e n ex t lin e S ix th if th e e v alu a tio n o f an e p iso d e g iv e s a

fa v o u ra b le re su lt its an aly s is is c o n tin u e d if th e ev a lu a tio n is u n fa v o u rab le a

d iffe re n t b a se -m o v e is ta k e n u p (N e w e ll amp S im o n 1 9 7 2 )

M e ta -s e a rc h w ith T e m p la te s (A b stra c t P la n n in g ) S e arc h m ay b e c arrie d o u t

n o t o n ly a t th e m o v e le v e l b u t a lso a t th e te m p la te le v el P lay e rs s o m e tim es

d e v e lo p a tre e se a rc h b y g e n eratin g k ey p o sitio n s (te m p la tes ) in s tea d o f

d e v e lo p in g a tree se arch b y g e n e ra tin g m o v e s (e g D e G ro o t 1 9 7 8 p 1 5 3 ) P ath s

b e tw e en k e y p o sitio n s c o n s is t o f m a cro -o p e ra to r s o r in u n s p ec ifie d o p e ra to r s

w h ic h w ill b e fil le d in a t a la te r s ta g e o f se a rch if th e le a f p o sitio n s a re ju d g e d

fa v o u ra b le T h is ty p e o f se arch is c o n tin g en t to th e p res e n ce in p la y ers rsquo L T M o f

te m p la tes su ffic ie n tly c lo se to th e p o s itio n a t h a n d K o ed in g e r a n d A n d e rs o n

(1 9 9 0 ) h a v e p ro p o se d a s im ilar id e a w ith re sp e c t to g eo m e try T h is m e ta -se a rc h

m ec h a n ism is a ls o sim ilar to th e ldquoa p p e rc e p tio n rdquo m e c h a n ism su g g es ted b y

S a a rilu o m a (1 9 9 0 1 9 9 2 )

Theo re t ica l Im po rta n ce o f Tem p la te s

O b v io u s ly m an y o f th e p ro ce s se s ju st d es c rib ed c a n b e im p le m e n te d w ith in th e

e ar lie r C T w ith o u t h y p o th e sisin g th e p re se n c e o f te m p la tes T e m p la tes a re

h o w e v e r im p o rta n t fo r s o m e o f th e k ey c o g n itiv e p ro c es se s in c h e ss b e c au se

PATTERN -R ECOGN IT ION AND SEA RCH 297

(a ) s lo ts a llo w in fo rm a tio n ab o u t s tra te g ic o r tac tica l th e m e s a s w e ll a s a b o u t

e v a lu a tio n o f th e p o sitio n to b e en co d e d in L T M rap id ly (b ) lin k s b e tw e e n

te m p la tes a llo w fo r ldquo m e ta -se a rc h rdquo (c ) in fo rm a tio n s to re d b o th in th e c o re a n d in

th e slo ts o f th e te m p late c o m p en sa tes fo r d e c a y an d in te rfe re n c e in th e m in d rsquos

e y e as it m a y b e u se d to re in sta te fa d in g in fo rm a tio n T h is c o m p e n sa tio n

m ec h a n ism is p ar tic u la rly u se fu l w h e n p e rce p tu a l in fo rm a tio n fro m th e ex te rn a l

b o a rd is u n re liab le fo r ex a m p le b e ca u s e se v e ra l m o v e s h a v e b e en c arr ie d o u t in

th e m in d rsquos e y e

Em p ir ica l D a ta Sup po rtin g th e TT A ccoun t o f Sea rchand Pa tte rn R e cogn itio n

In th is se c tio n T T is q u alita tiv e ly ap p lie d to s o m e o f th e k ey d a ta f ro m e m p ir ic a l

stu d ie s o f ch e s s p ro b le m s o lv in g Q u a n tita tiv e a s se ss m e n t w ill b e th e to p ic o f

th e fo llo w in g se c tio n I h a v e sh o w n e lse w h e re (G o b e t 1 9 9 6 ) th at th e p re d ic tio n s

o f T T a re w e ll su p p o rted b y e m p ir ic a l d a ta fro m re se a rch o n m e m o ry a n d

p e rce p tio n

In c re a sin g th e n u m b e r o f c h u n k s a n d te m p la te s h a s tw o o p p o site ef fec ts w ith

re sp e c t to se a rch (G o b e t in p res s) O n th e o n e h a n d d e ep s e arc h is fac ilita te d as

c o m p are d w ith th e m o re co m p u ta tio n a lly e x p e n s iv e w e a k m e th o d s b e c au se

p a tte rn re c o g n itio n is a ra p id p ro c es s a n d b e ca u s e se q u e n c e s o f m o v es m a y b e

le arn e d an d su g g e ste d b y c h u n k s O n th e o th er h a n d th e n ee d fo r d e e p se a rc h

o fte n d isa p p e ar s b e ca u s e e v a lu atio n s su g g e ste d b y p a tte rn re c o g n itio n m a y b e

m o re re lia b le th a n e v a lu atio n s co m p u te d b y w e a k m eth o d s T h e s e tw o o p p o site

e ffe cts c a n e x p la in w h y th e sk ill d iffe re n c e s in a v e rag e d e p th o f se a rc h a re sm all

P a tte rn re co g n itio n a llo w s stro n g p la y e rs to b e h ig h ly s e le c tiv e in th e ir s ea rc h

T h is c a n b e s e en b o th in th e ra p id w a y M a s te rs ze ro in to th e k e y as p e cts o f a

p o s itio n (D e G ro o t 1 9 4 6 ) an d in th e w ay e y e m o v e m e n ts d iffe r a s a fu n c tio n o f

sk ill d u rin g th e firs t s ec o n d s o f th e p e rc ep tio n o f a p o sitio n (D e G ro o t amp G o b et

1 9 9 6 ) A d d itio n a l e v id e n ce is p ro v id e d b y S a a rilu o m a (1 9 9 0 ) w h o h a s sh o w n

th a t p la y e rs ch o o se ste re o ty p e d so lu tio n s in p ro b le m s w h e re fa ste r ( in th e

n u m b e r o f m o v es to r ea c h m a te) b u t u n c o m m o n so lu tio n s a re p re s en t T h e se d a ta

a d d s u p p o rt to T T b e c a u se p a ttern re co g n itio n lie s a t i ts c o re

F u r th er s tro n g e v id e n ce fo r th e ro le o f p atte rn re c o g n itio n is th a t M as te rs c a n

p la y s ev e ra l o p p o n en ts s im u lta n eo u sly a t a s tre n g th c lo se to th at in o n e -a g ain s t-

o n e p lay I t is in te re stin g th at in s im u lta n eo u s g a m e s th ey te n d to p la y ldquon o rm a lrdquo

m o v e s a n d re ly o n o p p o n e n ts rsquo e rro rs (G o b e t amp S im o n 1 9 9 6 c ) N o rm a l m o v es

m ay c o rre sp o n d to th e ty p e o f m o v e s su g g e ste d b y c h u n k s an d tem p la te s

A fea tu re o f c h es s ex p e rtise c a p tu re d u n iq u e ly b y T T is th e h ig h le v e ls a t

w h ic h ch e s s p lay e rs o rg a n is e th e ir k n o w le d g e D e G ro o t (1 9 4 6 ) p ro p o s e d th a t

p la y er s o rg an is e p o sitio n s a ro u n d la rg e ldquo c o m p le x e srdquo b ig g e r th a n th e c h u n k s th a t

w e re la te r p ro p o se d b y C h a se a n d S im o n (1 9 7 3 ) D e G ro o t a lso su g g es ted a s d id

C o o k e e t a l (1 9 9 3 ) th a t p la y e rs re p re s en t in fo rm a tio n a t a c o n c e p tu a l lev el In

p a rticu la r D e G ro o t (1 9 4 6 ) p ro p o se d th a t M a ste rsrsquo d e sc rip tio n s o f g am e s a re

298 GOBET

c en tred a ro u n d k ey p o sitio n s o f th e g a m e T T o ffe rs th eo retic al s tru c tu res

(te m p la te s) th a t co u ld a c c o u n t fo r p lay ers rsquo larg e c o m p le x es h ig h - le v e l re p re -

se n ta tio n s a n d k e y p o sitio n s T T a lso o ff ers m e ch a n ism s b as e d o n f req u en c y o f

o c c u rre n ce s e x p la in in g h o w th e s e h ig h - le v e l re p re se n ta tio n s a re d ev elo p e d a n d

m ec h a n ism s b a se d o n d isc rim in a tio n p ro c e sse s e x p la in in g h o w th ey c o u ld b e

a c ce ss e d ra p id ly

T T is a lso co m p a tib le w ith re su lts fro m e x p er im e n ts u s in g p o s itio n s fo r w h ic h

a cc e ss to k n o w le d g e is d iffic u lt In H o ld in g a n d R e y n o ld s rsquo (1 9 8 2 ) e x p e rim e n t

c h e ss s k ill d id n o t c o rr ela te w ith th e re c a ll o f s e m i-ra n d o m p o s itio n s sh o w n fo r a

fe w se co n d s b u t eff ec tiv en es s o f th e s ea rc h fo r th e b e st m o v e in th es e p o s itio n s

d id c o rr ela te w ith s k ill T T o f fer s a n ex p la n a tio n fo r th e fa c t th a t th e re w a s a

stro n g c o rre la tio n b e tw e en sk ill le v e l a n d q u a lity o f m o v e p ro p o se d P lay e rs

re c u rsiv e ly g e n e ra te a m o v e th ro u g h w ea k m e th o d s w h en n o c h u n k is

re c o g n ise d u n til o n e o f th e h a ltin g co n d itio n s (m en tio n e d e a rlier ) a p p lie s T h e n

g iv e n th eir la rg e r d ata b a se o f c h u n k s s tro n g p la y e rs a re m o re lik e ly th a n w e a k

p la y er s to f in d a u s efu l p a tte rn in p o sitio n s th a t h a v e b ee n n e w ly u p d ate d in th e

m in d rsquos e y e a n d th e re fo re a re m o re lik e ly to f in d g o o d m o v e s in th eir se a rch

I m en tio n e d e a rlier th at E ric ss o n a n d K in tsc h (1 9 9 5 ) p ro p o s ed m ec h a n ism s

(re trie v al s tru c tu re a n d ela b o ra tio n s o f L T M sc h e m a s ) th a t e n c o d e in fo rm a tio n

q u ic k ly a n d re lia b ly B y c o n tra st th e e n c o d in g c a p a c ity o f te m p la te s is r e la tiv ely

w e a k In p a rtic u la r T T p re d icts th at th e sa m e te m p la te m a y s o m e tim e s b e u se d to

e n c o d e s e v era l s im ilar p o sitio n s th u s in c re as in g th e ris k o f in terf ere n c e as se a rc h

p ro g re s se s A s a co n se q u e n ce a n d c o n trary to L T W M T rsquos p re d ic tio n s p lay e rs

sh o u ld o fte n re v isit p o sitio n s b y g e n era tin g m o v es in s tea d o f a cc e ss in g th e m

d ire ctly fro m m em o ry T h is is w h at p la y e rsmdash e v e n m a ste rs mdash d o (D e G ro o t

1 9 4 6 ) F in a lly T T m a y h a v e s o m e th in g to sa y a b o u t e rro rs in c h e ss K ro g iu s

(1 9 7 6 ) m e n tio n s th a t er ro rs o f te n o c c u r w h e n a m o v e h a s ca u s ed im p o rta n t

c h a n g es in th e p o s itio n T h is m a y b e d u e to p la y e rsrsquo in a b ility to re c o g n ise th a t a

p re v io u sly a d eq u ate te m p late h as b ec o m e in a d e q u a te

In s u m m a ry T T o ffe rs a g o o d q u alita tiv e a c co u n t o f s e v eral im p o rtan t c h e ss

p h e n o m en a I t is n o w tim e to tu rn to m o re o b je c tiv e q u an tita tiv e te sts o f th e

th eo ry

A COM PUTER M ODE L O F S EARCH IN CH ESS

In th e re m a in d e r o f th is p a p e r I p re s en t a c o m p u te r m o d e l c a lled S E A R C H

w h ic h im p le m e n ts T T in so m e d e ta il I f irs t d e s crib e th e im p le m en ta tio n o f

S E A R C H m a k in g cle a r w h a t a s p ec ts o f T T h a v e b e e n in c lu d ed a n d th en d isc u ss

its b e h a v io u r w ith r es p e ct to h u m a n d a ta

O ve rv iew o f M ode l

F u ll im p le m e n ta tio n o f T T a s a c h e ss-p la y in g c o m p u ter p ro g ram w o u ld b e a

m ajo r ta sk mdash th is d iffic u lty is d e m o n stra te d b y th e fa c t th a t n o c o m p le te co m p u te r

m o d e l o f ch e s s c o g n itio n in c lu d in g p e rc e p tio n m em o ry a n d p ro b le m so lv in g

PATTERN -R ECOGN IT ION AND SEA RCH 299

h a s e v e r b e e n d e v elo p e d I p u rs u e d a lim ited a im a co m p u te r m o d el th a t c o n tain s

so m e o f th e im p o rta n t p aram e te rs o f T T a n d th a t co m p u te s k e y b e h a v io u ra l

v a ria b le s T h is m o d el d o e s n o t c o n stitu te a co m p le te im p le m e n ta tio n o f th e

th e o ry (it d o e s n o t s ea rc h o r e v a lu a te c h e ss p o sitio n s) b u t is d e ta ile d en o u g h to

o ffe r a g o o d te st o f so m e a s p ec ts o f T T I t is s o b e rin g to n o tic e th a t e v e n th is

p a rtia l im p lem e n tatio n o f th e th e o ry is q u ite c o m p le x a n d re q u ire s m a n y

p a ra m e te rs T h is is th e p rice o f a v o id in g th e v ag u en e s s o f v e rb al th e o ris in g

The M a in P rob lem -so lv in g Loop

T h e m ain in te re st o f th e m o d el is in th e in te ra c tio n b etw ee n p atte rn re c o g n itio n

a n d s ea rc h T h e m o d e l g e n e ra tes in d e p en d en t ep is o d es fo llo w in g se v e ral ru les

fo r g e n eratin g m o v e s a n d ch o o sin g sto p co n d itio n s C o m p atib le w ith m o s t

h u m an p ro to co ls th e p ro g ra m c o n sid e rs o n ly o n e b ra n c h w ith in a n ep is o d e (th u s

th e re is n o b ra n c h in g p o in t w ith in a n e p iso d e) A s illu stra te d in F ig 1 th e m o d e l

is c lo se to th e d es crip tio n o f T T g iv en e a rlie r in th is p a p e r T h e v ario u s c o n d itio n s

a n d o p e ra tio n s in S E A R C H a re re p re se n te d as p ro b a b ilit ie s o r p ro b ab ility

d istr ib u tio n s an d n o t a s a ctu a l c h e ss m o v e s e v a lu atio n s o r s y m b o lic s tru c tu res

in S T M o r in th e m in d rsquos e y e

A tra c e o f S E A R C H is sh o w n in F ig 2 T h e an aly s is w ill c e n tre o n th e

fo llo w in g v a ria b les a s a fu n c tio n o f th e n u m b e r o f c h u n k s ra te o f g en e ra tin g a

m o v e le v el o f fu z zin e ss in th e m in d rsquos e y e w h en a n e p is o d e is e n d e d m e an d e p th

o f s ea rc h m eth o d s u se d fo r g en e ra tin g a m o v e a n d m eth o d s u se d fo r s to p p in g a n

e p iso d e

T h e c o n c ep t o f te m p la te is im p le m e n te d in tw o w a y s (a ) b y h ig h e r

p ro b a b ilitie s o f f in d in g (s eq u en c e s o f) m o v e s a n d ev a lu a tio n s th an w ith p la in

c h u n k s a n d (b ) b y a d e cre a se in th e le v e l o f fu zz in e ss m ad e p o s sib le b y th e L T M

re p re se n ta tio n o f th e c o re o f th e p o sitio n a n d o f s lo ts

T h e le v e l o f re lia b ility o f th e in fo rm a tio n in th e m in d rsquos ey e is c a p tu re d b y a

ldquo fu z zin e s srdquo p a ra m e te r e x p re ss ed in a rb itr ary u n its T h re e m a in c o g n itiv e

fe a tu res ar e c a p tu red b y th is p a ra m ete r w o rk in g m e m o ry c a p a c ity a b ility to

m ain ta in a v isu o -s p atia l im ag e a n d su b je ctiv e e s tim a te o f th e r isk o f m ak in g a n

e rro r T h e fu z z in es s p a ram e ter is th e n as su m e d to o rig in ate b o th fro m th e

h a rd w a re a n d th e so ftw a re o f th e sy s tem It m a y v a ry d u r in g th e life tim e o f a

p la y er b e c a u se o f b io lo g ic a l m a tu ra tio n o r a g e in g an d m a y b e a ffe c ted b y

e x p e rim e n ta l m a n ip u latio n s T h e re a re th ree re a so n s w h y S E A R C H en d s a

se a rc h th e lev el o f fu z z in e s s is to o h ig h a n e v a lu atio n is p ro p o se d o r n o m o v e is

p ro p o s e d T h e id e a o f ex p ec ta tio n le v e l is n o t e x p lic itly p re se n t in th e m o d el b u t

it is im p lic it in th e p ro b a b ility v alu e s o f f in d in g fe atu re s e n d in g th e s ea rc h o f a n

e p iso d e e ith er b y p a tte rn re c o g n itio n o r b y th e a p p lica tio n o f h e u ristic s

S e le ctio n o f th e n ex t b a se -m o v e (a k e y c o n c ern o f N ew e ll amp S im o n 1 9 6 5 a n d

W ag n e r amp S c u rra h 1 9 7 1 ) is n o t ad d res se d b y S E A R C H w h ic h in g e n e ra l lac k s

th e s em a n tic in fo rm a tio n n e c es sa ry fo r su c h a se le c tio n F in a lly m e ta -se a rc h

w ith te m p la te s is n o t d ire c tly im p le m e n te d in S E A R C H b u t it is im p lic itly

300 GOBET

300

FIG 1 F lo w c h a rt o f S E A R C H

PATTERN -R ECOGN IT ION AND SEA RCH 301

301

F IG 2 E x a m p le s o f e p is o d e s g e n e ra te d b y S E A R C H

302 GOBET

re p re se n te d b y th e re la tiv e ly h ig h p ro b ab ility o f f in d in g (s eq u e n c e s o f) m o v es

a n d e v a lu atio n s w ith tem p la tes as c o m p are d w ith ch u n k s

The M ode lrsquos P aram e te rs

S E A R C H h as m a n y p a ra m ete rs a n d it is o f c o u rs e n e c es sa ry to se t u p a f ew o f

th e m w ith in d e p e n d e n t d a ta in o rd er to re d u c e th e n u m b e r o f d e g re e s o f fre e d o m

in th e m o d e l W h e n p o ss ib le I h a v e u s e d sim u la tio n s w ith th e C H R E S T (D e

G ro o t amp G o b e t 1 9 9 6 G o b e t 1 9 9 3 ) an d C H U M P (G o b e t amp Ja n s en 1 9 9 4 )

p ro g ram s to se t p a ra m e te r v a lu es C H R E S T is a p ro g ra m im p le m e n tin g as p e cts

o f T T a n d s im u la tin g n u m e ro u s e x p er im e n ts o n p e rc ep tio n an d m e m o ry in ch e s s

a n d C H U M P is a p ro g ra m p la y in g (w e ak ) c h e ss b y p u re p a tte rn re co g n itio n

N u m b e r o f C h u n k s a n d T e m p la te s T ab le 1 sh o w s th e v a lu es th at w ill b e

u s ed w ith th e S E A R C H m o d e l fo r th e se p a ra m ete rs T o c h o o se th e v a lu e s re la te d

to th e n u m b e r o f ch u n k s a n d te m p la tes th e c u rre n t v e rsio n o f C H R E S T h a s b e e n

e m p lo y e d T h e p ro b a b ility o f f in d in g a tem p la te w a s e stim ate d b y ru n n in g

C H R E S T o n 5 0 p o s itio n s ran d o m ly tak e n fro m M as ters rsquo g am e s T h e firs t lin e (0

c h u n k ) w a s ad d e d to g e t p re d ic tio n s a t th e n o v ic e lev e l W ith n e ts o f 1 0 0 0 0 0

1 2 0 0 0 0 a n d 1 5 0 0 0 0 c h u n k s th e p ara m ete rs w ere e stim ate d w ith th e b e s t-fit t in g

fu n c tio n s av a ilab le ( th e ldquo n o v ice rdquo v alu e s w ere n o t u se d ) T h e n u m b er o f te m p la tes

is ro u g h ly a lin e ar fu n c tio n o f th e n u m b er o f c h u n k s (r 2 = 9 7 ) T h e p ro b a b ility

o f f in d in g a tem p la te is a p p ro x im a tely a lo g -fu n c tio n o f th e n u m b e r o f c h u n k s

(r 2 = 9 4 )

H e u r is tic s C h u n k s T e m p la tes a n d T h e ir R e la tio n to th e P ro b a b ility o f

F in d in g M o v e s a n d E v a lu a tio n s T ab le 2 g iv e s th e v a lu e s u s ed in th e

sim u la tio n s fo r th e p a ra m ete rs re la te d to h e u ristic s c h u n k s a n d te m p la te s

H e u ris tic s in c lu d e sim p le se a rc h te c h n iq u e s (e g ldquo ta k e a p ie c e b a c k rdquo o r ldquoc h e c k

th e K in g rdquo ) a s w ell a s m o re a b stra c t ru le s (e g ldquoo c c u p y th e c en tre rdquo ) T h eir m a in

c h a rac te ris tic in co m p a riso n w ith c h u n k s an d tem p la te s is th a t th ey are g e n e ra l

a n d re q u ire so m e co n sc io u s c o m p u tatio n in o rd e r to p ro d u ce a m o v e T h e

a ss u m p tio n u n d e rly in g T a b le 2 is th at th e p aram e ters re la ted to h e u ristic s s ta y

ro u g h ly c o n sta n t w h ile th e o th e r p aram e te rs v a ry as a lo g arith m ic fu n c tio n o f th e

n u m b e r o f c h u n k s in th e n e t (A lo g arith m ic fu n ctio n h a s b e e n c h o se n to in d ica te

th a t ch u n k s y ie ld a d im in ish in g re tu rn as th e ir n u m b e r in c re a se s) T h e

a ss u m p tio n th a t th e n u m b e r o f h e u ristic s is c o n sta n t ac ro s s s k ill le v e ls se e m s

re a so n a b le (p e rh a p s w ith th e e x ce p tio n o f th e n o v ic e le v e l) a s m o s t c h e ss

M a ste rs rsquo k n o w le d g e is v e ry sp ec ific to c erta in a sp e c ts o f th e g a m e (D e G ro o t

1 9 4 6 )

T h e fo llo w in g c o n s id era tio n s w e re m ad e in se ttin g th e v alu e s g iv e n in

T ab le 2 I t w a s d ee m e d p lau sib le th a t th e p ro b a b ility o f f in d in g so m e h e u ristic in

a p o s itio n b e h ig h ( 9 5 ) a s w e ll a s th e p ro b a b ility o f f in d in g s o m e c h u n k F in ally

PATTERN -R ECOGN IT ION AND SEA RCH 303

TA BLE 1

The V a lu es o f th e 14 N e ts U sed in th e S im u la tio ns

P ro b a b i li ty o f

re c o g n is in g a t le as t

P ro p o r t io n o f o n e te m p la te g iv e n a

N u m b e r o f c h u n k s N u m b e r o f te m p la te s te m p la te s p o s i t io n

0 0 0 0 0 0 0 0

1 0 0 2 0 0 0 0 0 0 0

2 6 8 0 5 0 0 2 1 8 0

5 0 0 3 3 6 0 0 7 1 4 0

1 0 0 1 1 1 0 0 0 1 0 2 4 0

2 0 0 0 3 2 6 5 0 1 3 3 0 0

3 0 0 0 1 4 9 3 0 1 6 3 6 0

4 0 0 0 5 7 7 4 0 1 9 4 6 0

5 0 0 0 6 1 1 4 2 0 2 3 4 0 0

7 2 0 4 4 2 1 3 6 0 3 0 4 8 0

8 0 0 1 0 2 2 8 5 0 2 9 5 4 0

1 0 0 0 0 0 2 7 6 5 0 2 8 5 1 0

1 2 0 0 0 0 3 3 5 7 0 2 8 5 4 0

1 5 0 0 0 0 4 2 4 5 0 2 8 5 6 0

T h e v a lu e s b e lo w 1 0 0 0 0 0 c h u n k s w e r e ta k e n f ro m s im u la t io n s w ith C H R E S T th e o the rs

e x t ra p o la te d S e e te x t f o r d e ta ils

TA BLE 2

H eur is t ic s C hun ks Tem pla tes and Their Re la tion to th e P ro bab ility of Fin d in g

M oves and Evalu ta tio ns

T y p e H e u r is tic s C h u n k s T e m p la te s

P ro b a b i li ty o f e v o k in g a n 9 5 g (n _ c h u n k s 9 5 )a se e T a b le 1

h e u ri s t ic a c h u n k o r a te m p la te

P ro b a b i li ty o f f in d in g a m o v e 5 0 g (n _ c h u n k s 5 0 ) g (n _ c h u n k s 9 0 )

g ive n th a t a n h e u r is tic a c h u n k

o r a te m p la te h a s b e e n e v o k e d

P ro b a b i li ty o f f in d in g a n e v a lu a tio n 1 5 g (n _ c h u n k s 0 5 ) g (n _ c h u n k s 5 0 )

g iv e n th a t a n h e u ri s t ic a c h u n k o r

a te m p la te h a s b e e n e v o k e d

aT h e fu n c tio n g i s d e f in e d a s

g (n _ c h un k s p ro b ) = p ro b 0 2 lo g1 0

(n _ c h un k s ) i f n _ c h u n k s gt 0

a n d

g (n _ c h u n k s p ro b ) = 0 i f n _ c h u n k s = 0

w h e re n _ c h u n k s i s th e n u m b e r o f c h u n k s in a g iv e n n e t a n d p ro b i s a c o n s ta n t

303

304 GOBET

th e p ro b a b ility o f re c o g n isin g a te m p la te in a p o sitio n is sm a lle r a n d is g iv e n in

T ab le 1

T h e p ro b a b ility o f f in d in g a m o v e g iv e n a h e u ristic is s e t to 5 0 in d ic atin g th a t

h e u ristic s m a y fa il to p ro d u ce a m o v e h a lf o f th e tim e T h is is b e c a u se so m e

h e u ristic s m ay n o t y ie ld a m o v e a n d b ec a u se so m e p ro p o se d m o v es m a y b e

ille g a l T h e p ro b a b ility o f f in d in g a m o v e g iv en a tem p la te is h ig h p a rtly

re fle ctin g th e ric h s em a n tic k n o w le d g e an d th e in te r-te m p la te lin k s a s su m e d to

c h a rac te rise te m p la te s F o r th e p ro b a b ility o f f in d in g a m o v e g iv e n th a t a ch u n k

h a s b e en re co g n ise d I u se d th e p ara m e te r p ro b in th e fu n ctio n g (s ee T a b le 2 ) so

th a t i t a p p ro x im a te s th e d ata p ro d u c ed b y th e C H U M P p ro g ram (G o b et amp Ja n se n

1 9 9 4 ) E v a lu a tio n s a re su p p o s ed to b e h a rd er to le arn a n d th e re fo re h a rd e r to u se

th a n m o v es H e n ce th e ir p ro b a b ilit ie s a re lo w e r th a n th e co r res p o n d in g p ro b -

a b ilit ie s w ith m o v es A g a in fo llo w in g d irec tly fro m th e th e o ry te m p la te s o ffe r

th e b e st so u rce o f ev alu a tio n s

W ith re sp e c t to th e n u m b e r o f se q u e n tia l m o v e s p ro p o s ed c o u n ted in p lie s

(i e m o v e s fo r W h ite o r B la ck ) i t is as su m e d th a t h e u ristic s g iv e a cc e ss to o n ly

o n e m o v e w h ile c h u n k s a n d te m p late s y ie ld se q u e n c es o f m o v e s w h o se n u m b e r

fo llo w s a g e o m e tric p ro b a b ility d is tr ib u tio n (th e c h o ice o f th is d is tr ib u tio n w as

in sp ire d b y sta tis tic s ta k e n fro m C H U M P ) T h e lo n g e s t s eq u e n c e ( ca ll i t k ) h as a

fre q u e n c y o f 1 th e s e co n d -lo n g e st a fre q u en cy o f 2 th e th ird -lo n g e st a fre q u e n c y

o f 4 a n d so o n u n til th e sh o rte st se q u e n c e w h o s e len g th is 1 m o v e an d w h o se

fre q u e n c y is 2 (k ndash 1 ) T h e m a x im u m se q u e n ce o f m o v es w a s se t to 1 8 F in a lly

S E A R C H atte m p ts to g e n e ra te a m o v e b y p a ttern re c o g n itio n ( ch u n k o r te m p la te )

fo u r tim e s b e fo re u sin g a n h e u ristic

T im e a n d F u zzin e ss P a ra m ete rs T h e tim e p a ram e ter s fo r th e re sp e c tiv e

o p e ra tio n s w e re s et u sin g p la u sib le v a lu e s (se e T a b le 3 ) M o v e g en era tio n b y

p a tte rn re c o g n itio n (c h u n k o r te m p late ) is as su m e d to b e v e ry sh o rt (a few

h u n d re d m illis e co n d s) n o tim e c o st is u se d in th e m o d e l T h e tim e fo r c o m p u tin g

a m o v e-g en e ra tin g h e u ristic w a s s et to th e ra th e r lo n g 2 0 s ec o n d s mdash g en era tin g a

m o v e w ith o u t u sin g p a tte rn r ec o g n itio n re q u ires p u ttin g to g eth e r v a rio u s ty p e s o f

in fo rm a tio n a n d a s k s fo r m a n y ch e c k in g p ro c ed u res T h e tim e fo r c a rry in g o u t

o n e m o v e (o n c e g e n erate d ) in th e m in d rsquos e y e w a s s et to tw o s ec o n d s T h is is

c o m p atib le w ith S a a rilu o m a rsquos (1 9 8 9 ) d ata w h ic h sh o w th a t a b lin d fo ld ed M a ste r

c an fo llo w a g a m e d icta ted a t tw o se c o n d s a m o v e F in ally th e tim e fo r ca rry in g

o u t a n ev a lu a tio n b y h eu ris tic is s e t to 1 0 s e co n d s T h is ra th e r s h o rt tim e m a y b e

ju stif ie d b y th e fa c t th a t p la y e rs ty p ic a lly co n s id e r o n ly o n e (s u b jec tiv e ) a sp e c t o f

th e p o sitio n (D e G ro o t 1 9 4 6 ) a n d th at m an y e v a lu atio n s c a n b e g ro u n d ed o n th e

b a sis o f c lea r m a teria l lo ss e s

T h e fu z zin e ss lev el o f th e s y ste m is e x p re ss ed in a rb itra ry u n its I t s ta rts w ith

th e v a lu e z e ro a n d it is in c re a se d w h e n a m o v e is c a rrie d o u t in th e m in d rsquos e y e

a n d w h e n tim e is s p e n t a p p ly in g a n h e u ris tic W h e n a te m p la te is fo u n d th e

PATTERN -R ECOGN IT ION AND SEA RCH 305

fu z z in es s lev el is d e cre a se d a s p a rt o f th e in fo rm atio n m ay b e sto re d in L T M

d ire c tly fre e in g c ap ac ity in w o rk in g m e m o ry a n d in th e m in d rsquos ey e

S im u la t io n s w ith th e ldquo C anon ica l M ode lrdquo

T h e sim u latio n s d e sc rib ed in th is s ec tio n a re s tra ig h tfo rw a rd U s in g th e

p a ra m e te r v alu e s d is cu sse d e a rlie r I le t th e p ro g ra m s ea rc h 1 0 0 0 ep iso d e s fo r

e ac h n e t s iz e S u m m a ry v alu e s fo r m e a n d ep th o f se a rc h t im e ra tio d e p th tim e

a n d fu z zin e s s a s w e ll a s fo r g e n e ra tio n an d s to p co n d itio n s w e re c o m p u ted fo r

e ac h n e t s iz e

M e a n D e p th o f S e a r ch R a te o f S e a rc h a n d F u z zin e ss A cc o rd in g to

S E A R C H m ea n d e p th o f s ea rc h fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f

c h u n k s (se e F ig 3 a) If w e as su m e a co n sta n t ra te o f le a rn in g n e w c h u n k s a s is

c o m m o n p ra ctic e in so m e c o g n itiv e a rch ite c tu res (c f N e w e ll 1 9 9 0 ) a n d if w e

a ss u m e th a t s k ille d p la y e rs h a v e sp e n t m o re p rac tice a n d stu d y tim e th a n

u n s k ille d p la y e rs th e n m e an d e p th fo llo w s a p o w e r fu n c tio n o f s k ill as w e ll T h is

p re d ic tio n w h ic h is a t v ar ia n c e w ith H o ld in g rsquos p re d ic tio n (1 9 8 5 p 1 8 2 ) o f a

lin ea r in c rea s e is p artly co n siste n t w ith C h a rn e ss rsquos (1 9 8 1 ) p ro p o s a l th a t d e p th o f

se a rc h is n o t l in e arly re la ted to s k ill b u t th at th e re is a ce ilin g a t h ig h s k ill le v e ls

T h e re su lt is a ls o c o m p atib le w ith th e w e a k lin e ar re la tio n fo u n d in e m p ir ic a l

stu d ie s (C h a rn e ss 1 9 8 1 G o b e t in p re ss ) b e tw e e n m e a n d e p th o f se a rch a n d sk ill

le v el b e c a u se re stric te d ra n g e s o f th e c u rv e c a n b e a p p ro x im a ted b y a lin e a r

fu n c tio n T h e a b so lu te v alu e s a re a lso q u ite r ea so n ab le th ey ris e f ro m lo w d ep th s

(le ss th a n 1 p ly ) w ith n o ch u n k s (co r res p o n d in g to th e n o v ic e le v el) to a ro u n d 2 5

p lies w ith a sm a ll n et (1 0 0 0 c h u n k s ) an d th e n to a ro u n d 4 p lie s w ith ex p ert le v e l

(a ro u n d 3 0 0 0 0 c h u n k s a s e s tim a te d b y s im u la tio n s o n th e re ca ll tas k ) T h e y th e n

slo w ly (s av e fo r a f ew ra n d o m v a ria tio n s ) in c re a se to m o re th an 5 p lie s w ith n e t

la rg er th an 1 0 0 0 0 0 c h u n k s w h ic h c o rre sp o n d s to G ran d m a ste r le v e l H o ld in g

(1 9 8 5 ) c o m p u te d m e a n d e p th o f se a rch fo r d e G ro o trsquos (1 9 4 6 ) d a ta a n d fo u n d th a t

TA BLE 3

T im e and ldquo Fuzz in ess rdquo Param e ters U sed in th e

S im ula t io n s

T im e fo r c a r ry in g o u t a m o v e 2 s

T im e fo r c o m p u t in g m o v e -g e n e r a tin g h e u r is tic 2 0 s

T im e fo r c o m p u t in g e v a lu a t io n 1 0 s

U p p e r l im it o f fu z z in e ss 5 0

In c r e a se o f fu z z in e s s p e r m o v e 1

In c re a se o f f u z z in e ss p e r s e c o n d 2

D e c re a s e in fu z z in e ss d u e to te m p la te 5

306 GOBET

E x p e rts a n d G ra n d m as ters h a d res p e ctiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 8 a n d

5 3 T h e reg res sio n e q u a tio n d e riv e d f ro m C h a rn e ss rsquos (1 9 8 1 ) d ata y ie ld a n

a v e rag e d e p th o f se a rc h o f a b o u t 2 3 p lies a t th e 1 3 0 0 E L O 1 le v e l o f 4 1 a t th e

E x p e rt le v e l (2 0 0 0 E L O ) a n d o f 5 7 a t th e G ra n d m a s te r le v el U n fo rtu n a tely n o

stu d y te ste d p la y e rs ra n g in g fro m n o v ic es to G ran d m a ste rs an d S E A R C H rsquos

p re d ic tio n o f a p o w e r la w o f p rac tic e c an n o t b e te ste d (y e t) I w ill re p o rt la te r

sim u la tio n s a d d re ssin g d a ta co lle c ted b y S a arilu o m a (1 9 9 0 ) w h e re In tern atio n a l

M a ste rs a n d G ra n d m a s te rs te n d e d to s e arc h le s s th a n M as te rs

T h e ra te o f s ea rc h a lso fo llo w s a p o w e r fu n ctio n o f th e n u m b e r o f c h u n k s (se e

F ig 3 b ) D e G ro o t (1 9 4 6 ) C h arn es s (1 9 8 1 ) a n d G o b e t ( in p res s) a ll f o u n d th a t

stro n g p la y er s te n d e d to s e arc h fa ste r F o r ex a m p le G o b e t ( in p re s s) fo u n d th a t

h is M a ste rs E x p e rts C la ss A a n d C la s s B p lay e rs re sp e c tiv ely se arch e d 4 8 4 1

3 2 an d 3 4 n o d e s p e r m in u te S E A R C H rsquos v a lu es a re h ig h e r b u t s til l p la u s ib le

F o r ex am p le W a g n e r a n d S c u rra h rsquos (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r

m in u te N o te a lso th a t a ll th e ex p erim e n ts m e n tio n e d e a rlier h a v e u se d v e rb a l

p ro to c o ls w h ic h m ay h av e s lo w e d d o w n th e ra te o f se a rc h (c f E ric ss o n amp

S im o n 1 9 8 0 ) F in a lly th e ra te o f se arch m a y h av e b e e n u n d e res tim a ted in th e

lite ra tu re b ec a u se th e r a te o f g e n e ratin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d

b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l t im e H o w e v e r to ta l t im e in c lu d es

tim e n o t sp e n t in s e arc h ( fo r e x a m p le w h a t D e G ro o t c a lls th e ldquo firs t p h a se rdquo)

T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a riab le th e le v e l o f fu zz in e ss a t

w h ic h a se a rc h is e n d e d is m o re d if fic u lt to ju d g e b ec a u se lit tle is k n o w n a b o u t

th e ro le o f fu z z in es s in c h es s th in k in g A g ain S E A R C H p ro p o se s th a t th is

v a riab le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s ee F ig 3 c ) W ith la rg e r

n e ts e p iso d es te n d to b e e n d e d w ith lo w er le v els o f fu z z in e s s T h is su g g es ts th at

in g e n e ra l s tro n g p la y ers s h o u ld b e m o re c o n fid e n t in th e ir c alc u la tio n s as th e y

a re n o t a t th e e d g e o f th eir p o s sib ilitie s N o te th a t th e ra te o f ch an g e is ra th e r h ig h

fo r th is p o w er law w h ic h s u g g e sts th at it sh o u ld b e p o ss ib le to d e te c t i t

e x p erim e n tally

G e n e ra tio n o f M o ve s H o w is m o v e g en e ra tio n af fec te d b y sk ill le v e l A s

sh o w n in F ig 4 a S E A R C H m a k es c le a r p re d ic tio n s W ith sm a ll n u m b e rs o f

c h u n k s th e tim e -c o n s u m in g p ro ce s s o f g en e ra tin g m o v es b y h e u ristic s is

e m p lo y e d T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y ch u n k s

w h ic h is in tu rn d o m in a te d b y te m p la te g e n eratio n

1 T h e E L O ra t in g i s a n in te r v a l sc a le th a t ra n k s c o m p e t it io n c h e ss p la y e rs I ts s ta n d a rd de v ia t io n

(2 0 0 p o in ts) is o f te n in te r p re te d a s a m e a su r e o f sk i ll c la s s in c h e ss G r a n d m a s te r s a re n o rm a lly ra te d

a b o v e 2 5 0 0 In te rn a t io n a l M a s te r s a b o v e 2 4 0 0 M a s te r s a b o v e 2 2 0 0 a n d E x p e rt s a b o v e 2 0 0 0

B e lo w c la sse s (A B e tc ) d iv id e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in ts

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

294 GOBET

tw o m n em o n is ts sp e c ia lise d in th e d ig it- sp a n ta s k (C h as e amp E ric s so n 1 9 8 2 )

T h is p o w e rfu l m e m o ry stru c tu re iso m o rp h ic to th e 6 4 s q u ares o f th e c h e ss b o a rd

a llo w s p la y e rs to u p d a te in fo rm a tio n ra p id ly d u rin g se a rc h T h e th eo ry a ls o

p ro p o s e s th a t c h e ss p lay e rs ca n c re ate n e w L T M as so c ia tio n s ra p id ly a lth o u g h

n o p ara m e te r is g iv e n to s p e cify th is s p ee d o f e n co d in g

I h av e sh o w n els ew h ere (G o b e t 1 9 9 6 ) th a t L T W M T in a d d itio n to b e in g

v a g u e a n d le a v in g m a n y d e ta ils u n s p e cifie d g e n e ra te s p re d ic tio n s th a t d o n o t

a g re e w ith th e e x p e rim en ta l d a ta o n c h es s p e rc ep tio n a n d m e m o ry In ad d itio n

th e m e m o ry m e ch a n ism s p ro p o s ed b y L T W M T (re tr ie v a l s tru c tu re a n d ra p id

e lab o ratio n o f L T M stru c tu re s) s ee m a t o d d s w ith th e fo llo w in g a sp e c t o f c h e ss

p la y er srsquo se arch b e h av io u r I t is co m m o n fo r c h e ss p la y er s to re v is it a n o d e d u rin g

th e ir a n aly s is o f th e p o sitio n H o w ev e r in ste a d o f ac c e ssin g th is n o d e d ire c tly as

su g g es ted b y L T W M T rsquos v e ry p o w erfu l m e ch a n is m s fo r s to rin g p o sitio n s ra p id ly

a n d a c c u rate ly p la y er s a c c es s th e targ e t p o sitio n b y g en era tin g a s e q u e n ce o f

in d iv id u a l m o v e s fro m th e g iv en p ro b le m p o s itio n (c f D e G ro o t 1 9 4 6 ) T h is

b e h a v io u r su g g e sts th a t p lay e rs m a y n o t s to re p o sitio n s a s q u ic k ly a s p ro p o s e d b y

L T W M T

TH E TEM P LA TE TH EO RY AN D ITS A PPL IC A T IO NTO PRO BLEM SO LV ING

In itia lly th e tem p la te th e o ry (T T ) w a s d e v elo p e d to re m o v e so m e w e a k n e ss es in

th e c h u n k in g th e o ry w ith r es p e ct to d ata fro m m e m o ry re se a rch (G o b e t amp S im o n

1 9 9 6 a ) C o n tra ry to C T rsquos p re d ic tio n s b a s ed o n a lim ited S T M ca p a c ity c h e ss

p la y er srsquo m e m o ry is res is ta n t to re tro a ctiv e in te rfe re n ce (C h arn es s 1 9 7 6 ) a n d

c h e ss p la y e rs c a n re c a ll s ev e ra l b rief ly p re s en te d p o sitio n s w ith re a so n a b le

a cc u ra c y (C o o k e A tla s L a n e amp B erg e r 1 9 9 3 G o b e t amp S im o n 1 9 9 6 a )

L ik e C T T T p ro p o s es th a t c h u n k s a re ac c e ss ed b y tra v e rsin g a d isc rim in a tio n

n e t C h u n k s a re lin k e d to o th e r in fo rm a tio n s to red in L T M s u ch a s m o v es p la n s

ta ctic al m o tiv es a n d s o o n In a d d itio n c h u n k s th a t o fte n o cc u r in a p lay e rrsquos

e x p er ie n c e c a n e v o lv e in to m o re c o m p le x d a ta s tru ctu re s ( te m p la tes ) w h ich h a v e

slo ts a llo w in g v a ria b les to b e e n c o d ed fo r e x a m p le to sp e c ify th e sq u a re

o c c u p ie d b y a p iec e A c c o rd in g to T T th is en c o d in g o cc u rs ra p id ly (a b o u t o n e

se c o n d p e r s lo t) In a d d itio n to s lo ts tem p la te s co n ta in a co r e w h ic h is m ad e u p

o f (v a ria b le -fre e ) c h u n k s A lto g e th er te m p late s a re as su m e d to s to re a t le as t

a b o u t 1 0 p iec e s F in ally te m p la te s m a y b e lin k e d to o th er te m p la tes T T als o

p ro p o s e s th a t in fo rm a tio n sto re d in th e m in d rsquos e y e a s tru ctu re s im ilar to th a t

p ro p o s e d b y C T d e ca y s ra p id ly a n d th at i t n e e d s to b e u p d a te d e ith e r b y in p u ts

fro m th e e x te rn a l w o rld o r b y in p u ts fro m m e m o ry s tru ctu re s

T T re m o v e s th e d iffic u lty o f C T w ith in te rfe ren c e p h e n o m en a f ir s t b e ca u s e it

h y p o th e sis es s o m e fa st L T M e n c o d in g (th ro u g h te m p late s lo ts) a n d se c o n d

b e c au s e te m p la te s co n ta in m o re in fo rm a tio n th a n th e ch u n k s p ro p o s ed b y C T

(C T a ssu m e d th a t c h u n k s co n ta in a t m o s t f iv e o r s ix p iec e s) F in a lly T T k ee p s

PATTERN -R ECOGN IT ION AND SEA RCH 295

th e p o w e r o f C T to e x p lain th e r ap id rec o g n itio n o f p o sitio n s sh o w n b y m a ste rs

a s th e s am e d isc rim in a tio n m e ch a n ism s are p res e n t (G o b e t 1 9 9 6 )

S ea rch M echan ism s

T T a n d C T p ro p o se th a t se a rc h is ca rrie d o u t in a fo rw ard fa sh io n b y re cu rsiv e

a p p lica tio n o f p a tte rn re co g n itio n p ro ce s se s in th e in te rn a l rep res e n ta tio n In th e

re m ain d e r o f th is se c tio n I w ill f le sh o u t th is m e c h an ism w ith ad d itio n a l sp e c ifi-

c atio n s I w ill a lso sh o w h o w c h u n k s an d te m p late s m a y b e u se d to te rm in a te

se a rc h a n d h o w te m p la te s m a y b e u se d to ca rry o u t s ea rc h a t a le v e l m o re

a b stra c t th a n th e m o v e le v e l

M o v e G e n e ra tio n A s m en tio n e d e arlie r p a ttern r ec o g n itio n is a p p lie d

re c u rsiv e ly in T T If a c h u n k mdash o r a te m p la te a s tem p la te s ar e a s p e cia l c as e o f

c h u n k smdash is rec o g n is ed i t m a y g iv e a c c es s to a m o v e (o r a se q u e n c e o f m o v e s ) o r

to a n h e u ris tic fo r se le ctin g th e n ex t m o v e E x a m p le s o f s u ch h e u ristic s a re

ldquo O c c u p y o p e n lin e s rdquo o r ldquo C o u n te r-a tta c k in th e ce n tre w h e n a ttac k e d o n th e

K in g rsquos s id e rdquo In th is ca s e th e m o v e(s ) is (a re ) c a rried o u t in th e m in d rsquos e y e If n o

m o v e re su lts fro m p a tte rn re co g n itio n o n e o f tw o o p era tio n s m a y b e ap p lie d

E ith e r th ere is a n e w atte m p t to g e n e rate a m o v e b y a cc e ss in g a d iffe re n t c h u n k

o r w ea k e r h e u ristic s a re a p p lie d

U p d a te o f In te rn a l R ep re se n ta tio n a n d S to r a g e o f In fo rm a tio n in to

T e m p la te W h en a m o v e o r a se q u e n c e o f m o v e s is c a rrie d o u t in th e m in d rsquos

e y e th e in te rn a l rep res e n ta tio n is u p d a te d a n d w h e n a te m p la te h as b e e n

a cc e ss e d s lo ts a re u p d ate d a s w e ll S lo ts m a y sto re in fo rm a tio n a b o u t th e

lo c atio n o f p ie ce s s tra teg ic in fo rm a tio n e v alu a tio n o f th e p o sitio n o r p a rt o f i t

a n d s o o n N o te th a t th is in fo rm a tio n fa c ilita te s s ea rc h b e c au se p o s sib le fo r -

g e ttin g th ro u g h d ec a y in th e m in d rsquos e y e m a y b e b ac k e d -u p b y in fo rm a tio n s to re d

in s lo ts

E va lu a tio n o f N o d e s E v a lu a tio n o f a p o sitio n is n o t c ar ried o u t af te r e ac h

m o v e b u t o n ly a t th e term in a l p o sitio n s E v a lu atio n is e ith e r r e trie v e d w h e n

p o s sib le fro m ch u n k s th a t h a v e b e en re c o g n ise d o r co m p u te d w h e n th e p la y e r

d e c id e s to te rm in a te s e arc h (s ee n e x t p a ra g ra p h ) D e G ro o trsquos (1 9 4 6 ) p ro to co ls

in d ic ate th a t p la y e rs e v a lu a te o n ly te rm in a l p o s itio n s a n d th a t th e ir e v a lu atio n s

a re ra th e r s im p le ta k in g in to a c co u n t a s in g le fe a tu re su c h as m o b ility o r c o n tro l

o f th e c e n tre a n d stro n g ly su g g e s t th a t e v a lu a tio n s are n o t co m p u te d b y

c o n jo in in g s e v eral fe atu re s

E n d in g S ea r c h o f a n E p iso d e A c ritic a l q u es tio n g iv e n a lim ite d

in fo rm a tio n -p ro c es sin g c a p a city is w h e n to s to p se a rc h in g a n e p iso d e (i e a

se q u e n c e o f m o v es g e n e ra ted fro m a b as e m o v e ) I p ro p o se th a t th e fo llo w in g

296 GOBET

c o n d itio n s ca n h alt th e se a rc h o f a n e p iso d e T o b e g in w ith th e p ro b a b ility o f

m ak in g a n e rro r is to o h ig h P s y ch o lo g ic a lly th is p ro b a b ility is a fu n ctio n o f th e

fo rg e ttin g a n d in ter fer en c e r a te s in th e m in d rsquo s ey e P h e n o m e n o lo g ic a lly p lay e rs

p ro b a b ly a s se ss th is p ro b a b ility b y ta k in g in to a c c o u n t th e d e p th o f se a rc h

re a ch e d a n d b y e s tim a tin g th e ir fa m ilia rity w ith th e p o s itio n

A n o th e r re a so n to h a lt s ea rc h o c cu r s w h e n th e le v e l o f e x p e c tatio n fo r th e

p o s itio n is m et o r w h e n a f ea tu re o f th e p o s itio n (e g sa fe ty o f th e K in g ) w as

e v a lu a te d to b e lo w e r th a n its a d m iss ib le v a lu e (N e w e ll amp S im o n 1 9 7 2 ) T h is

le v el o f e x p e c ta tio n is p ro v id e d b y a c h u n k en c o u n te re d d u rin g e arlie r s ea rc h o r

b y e x p lic it ev a lu a tio n o f th e p o s itio n a n d w a s s to re d e ith e r in S T M o r w h e n

a v a ila b le in a te m p late s lo t A fin a l h a ltin g c o n d itio n is th a t a d e c isiv e e v e n t

o c c u rre d s u ch a s m a te im p o rta n t m a teria l g a in o r lo ss o r fu lfilm e n t o f a k e y

g o al

S e lec tin g th e N e x t B a s e -m o v e N o w co n s id er th e q u e stio n o f w h ic h b a se -

m o v e to se a rch n ex t w h en a le a f n o d e h a s b e e n re a ch ed A n y o f s ix m e c h an is m s

m ay b e e n g a g e d F irst if th e le a f w a s e v a lu ate d w ith a h ig h risk o f er ro r th e s am e

se q u e n c e o f m o v e s is se a rc h ed a g ain in o rd e r to o b ta in a m o re re lia b le e stim a te

S e c o n d th e sa m e s eq u en c e o f m o v e s m a y b e se a rch e d a g a in to m a k e s u re th a t i t

h a s b e e n sto re d in L T M T h ird if a tem p la te h a s b e e n re co g n ise d a m e ta -se a rc h

(s ee la te r) is c arr ie d o u t F o u rth th e re is a b ia s to g iv e p re fe ren ce to n o rm a l b as e -

m o v e s ea rly in se a rch a n d to u n u su a l b a s e-m o v e s la ter (N ew ell amp S im o n 1 9 7 2

p 7 2 3) F ifth a m ov e re ac h e d at a n y le v e l o f d e p th in s ea rch in g a lin e m a y b e trie d

a s a ca n d id a te m o v e in th e n ex t lin e S ix th if th e e v alu a tio n o f an e p iso d e g iv e s a

fa v o u ra b le re su lt its an aly s is is c o n tin u e d if th e ev a lu a tio n is u n fa v o u rab le a

d iffe re n t b a se -m o v e is ta k e n u p (N e w e ll amp S im o n 1 9 7 2 )

M e ta -s e a rc h w ith T e m p la te s (A b stra c t P la n n in g ) S e arc h m ay b e c arrie d o u t

n o t o n ly a t th e m o v e le v e l b u t a lso a t th e te m p la te le v el P lay e rs s o m e tim es

d e v e lo p a tre e se a rc h b y g e n eratin g k ey p o sitio n s (te m p la tes ) in s tea d o f

d e v e lo p in g a tree se arch b y g e n e ra tin g m o v e s (e g D e G ro o t 1 9 7 8 p 1 5 3 ) P ath s

b e tw e en k e y p o sitio n s c o n s is t o f m a cro -o p e ra to r s o r in u n s p ec ifie d o p e ra to r s

w h ic h w ill b e fil le d in a t a la te r s ta g e o f se a rch if th e le a f p o sitio n s a re ju d g e d

fa v o u ra b le T h is ty p e o f se arch is c o n tin g en t to th e p res e n ce in p la y ers rsquo L T M o f

te m p la tes su ffic ie n tly c lo se to th e p o s itio n a t h a n d K o ed in g e r a n d A n d e rs o n

(1 9 9 0 ) h a v e p ro p o se d a s im ilar id e a w ith re sp e c t to g eo m e try T h is m e ta -se a rc h

m ec h a n ism is a ls o sim ilar to th e ldquoa p p e rc e p tio n rdquo m e c h a n ism su g g es ted b y

S a a rilu o m a (1 9 9 0 1 9 9 2 )

Theo re t ica l Im po rta n ce o f Tem p la te s

O b v io u s ly m an y o f th e p ro ce s se s ju st d es c rib ed c a n b e im p le m e n te d w ith in th e

e ar lie r C T w ith o u t h y p o th e sisin g th e p re se n c e o f te m p la tes T e m p la tes a re

h o w e v e r im p o rta n t fo r s o m e o f th e k ey c o g n itiv e p ro c es se s in c h e ss b e c au se

PATTERN -R ECOGN IT ION AND SEA RCH 297

(a ) s lo ts a llo w in fo rm a tio n ab o u t s tra te g ic o r tac tica l th e m e s a s w e ll a s a b o u t

e v a lu a tio n o f th e p o sitio n to b e en co d e d in L T M rap id ly (b ) lin k s b e tw e e n

te m p la tes a llo w fo r ldquo m e ta -se a rc h rdquo (c ) in fo rm a tio n s to re d b o th in th e c o re a n d in

th e slo ts o f th e te m p late c o m p en sa tes fo r d e c a y an d in te rfe re n c e in th e m in d rsquos

e y e as it m a y b e u se d to re in sta te fa d in g in fo rm a tio n T h is c o m p e n sa tio n

m ec h a n ism is p ar tic u la rly u se fu l w h e n p e rce p tu a l in fo rm a tio n fro m th e ex te rn a l

b o a rd is u n re liab le fo r ex a m p le b e ca u s e se v e ra l m o v e s h a v e b e en c arr ie d o u t in

th e m in d rsquos e y e

Em p ir ica l D a ta Sup po rtin g th e TT A ccoun t o f Sea rchand Pa tte rn R e cogn itio n

In th is se c tio n T T is q u alita tiv e ly ap p lie d to s o m e o f th e k ey d a ta f ro m e m p ir ic a l

stu d ie s o f ch e s s p ro b le m s o lv in g Q u a n tita tiv e a s se ss m e n t w ill b e th e to p ic o f

th e fo llo w in g se c tio n I h a v e sh o w n e lse w h e re (G o b e t 1 9 9 6 ) th at th e p re d ic tio n s

o f T T a re w e ll su p p o rted b y e m p ir ic a l d a ta fro m re se a rch o n m e m o ry a n d

p e rce p tio n

In c re a sin g th e n u m b e r o f c h u n k s a n d te m p la te s h a s tw o o p p o site ef fec ts w ith

re sp e c t to se a rch (G o b e t in p res s) O n th e o n e h a n d d e ep s e arc h is fac ilita te d as

c o m p are d w ith th e m o re co m p u ta tio n a lly e x p e n s iv e w e a k m e th o d s b e c au se

p a tte rn re c o g n itio n is a ra p id p ro c es s a n d b e ca u s e se q u e n c e s o f m o v es m a y b e

le arn e d an d su g g e ste d b y c h u n k s O n th e o th er h a n d th e n ee d fo r d e e p se a rc h

o fte n d isa p p e ar s b e ca u s e e v a lu atio n s su g g e ste d b y p a tte rn re c o g n itio n m a y b e

m o re re lia b le th a n e v a lu atio n s co m p u te d b y w e a k m eth o d s T h e s e tw o o p p o site

e ffe cts c a n e x p la in w h y th e sk ill d iffe re n c e s in a v e rag e d e p th o f se a rc h a re sm all

P a tte rn re co g n itio n a llo w s stro n g p la y e rs to b e h ig h ly s e le c tiv e in th e ir s ea rc h

T h is c a n b e s e en b o th in th e ra p id w a y M a s te rs ze ro in to th e k e y as p e cts o f a

p o s itio n (D e G ro o t 1 9 4 6 ) an d in th e w ay e y e m o v e m e n ts d iffe r a s a fu n c tio n o f

sk ill d u rin g th e firs t s ec o n d s o f th e p e rc ep tio n o f a p o sitio n (D e G ro o t amp G o b et

1 9 9 6 ) A d d itio n a l e v id e n ce is p ro v id e d b y S a a rilu o m a (1 9 9 0 ) w h o h a s sh o w n

th a t p la y e rs ch o o se ste re o ty p e d so lu tio n s in p ro b le m s w h e re fa ste r ( in th e

n u m b e r o f m o v es to r ea c h m a te) b u t u n c o m m o n so lu tio n s a re p re s en t T h e se d a ta

a d d s u p p o rt to T T b e c a u se p a ttern re co g n itio n lie s a t i ts c o re

F u r th er s tro n g e v id e n ce fo r th e ro le o f p atte rn re c o g n itio n is th a t M as te rs c a n

p la y s ev e ra l o p p o n en ts s im u lta n eo u sly a t a s tre n g th c lo se to th at in o n e -a g ain s t-

o n e p lay I t is in te re stin g th at in s im u lta n eo u s g a m e s th ey te n d to p la y ldquon o rm a lrdquo

m o v e s a n d re ly o n o p p o n e n ts rsquo e rro rs (G o b e t amp S im o n 1 9 9 6 c ) N o rm a l m o v es

m ay c o rre sp o n d to th e ty p e o f m o v e s su g g e ste d b y c h u n k s an d tem p la te s

A fea tu re o f c h es s ex p e rtise c a p tu re d u n iq u e ly b y T T is th e h ig h le v e ls a t

w h ic h ch e s s p lay e rs o rg a n is e th e ir k n o w le d g e D e G ro o t (1 9 4 6 ) p ro p o s e d th a t

p la y er s o rg an is e p o sitio n s a ro u n d la rg e ldquo c o m p le x e srdquo b ig g e r th a n th e c h u n k s th a t

w e re la te r p ro p o se d b y C h a se a n d S im o n (1 9 7 3 ) D e G ro o t a lso su g g es ted a s d id

C o o k e e t a l (1 9 9 3 ) th a t p la y e rs re p re s en t in fo rm a tio n a t a c o n c e p tu a l lev el In

p a rticu la r D e G ro o t (1 9 4 6 ) p ro p o se d th a t M a ste rsrsquo d e sc rip tio n s o f g am e s a re

298 GOBET

c en tred a ro u n d k ey p o sitio n s o f th e g a m e T T o ffe rs th eo retic al s tru c tu res

(te m p la te s) th a t co u ld a c c o u n t fo r p lay ers rsquo larg e c o m p le x es h ig h - le v e l re p re -

se n ta tio n s a n d k e y p o sitio n s T T a lso o ff ers m e ch a n ism s b as e d o n f req u en c y o f

o c c u rre n ce s e x p la in in g h o w th e s e h ig h - le v e l re p re se n ta tio n s a re d ev elo p e d a n d

m ec h a n ism s b a se d o n d isc rim in a tio n p ro c e sse s e x p la in in g h o w th ey c o u ld b e

a c ce ss e d ra p id ly

T T is a lso co m p a tib le w ith re su lts fro m e x p er im e n ts u s in g p o s itio n s fo r w h ic h

a cc e ss to k n o w le d g e is d iffic u lt In H o ld in g a n d R e y n o ld s rsquo (1 9 8 2 ) e x p e rim e n t

c h e ss s k ill d id n o t c o rr ela te w ith th e re c a ll o f s e m i-ra n d o m p o s itio n s sh o w n fo r a

fe w se co n d s b u t eff ec tiv en es s o f th e s ea rc h fo r th e b e st m o v e in th es e p o s itio n s

d id c o rr ela te w ith s k ill T T o f fer s a n ex p la n a tio n fo r th e fa c t th a t th e re w a s a

stro n g c o rre la tio n b e tw e en sk ill le v e l a n d q u a lity o f m o v e p ro p o se d P lay e rs

re c u rsiv e ly g e n e ra te a m o v e th ro u g h w ea k m e th o d s w h en n o c h u n k is

re c o g n ise d u n til o n e o f th e h a ltin g co n d itio n s (m en tio n e d e a rlier ) a p p lie s T h e n

g iv e n th eir la rg e r d ata b a se o f c h u n k s s tro n g p la y e rs a re m o re lik e ly th a n w e a k

p la y er s to f in d a u s efu l p a tte rn in p o sitio n s th a t h a v e b ee n n e w ly u p d ate d in th e

m in d rsquos e y e a n d th e re fo re a re m o re lik e ly to f in d g o o d m o v e s in th eir se a rch

I m en tio n e d e a rlier th at E ric ss o n a n d K in tsc h (1 9 9 5 ) p ro p o s ed m ec h a n ism s

(re trie v al s tru c tu re a n d ela b o ra tio n s o f L T M sc h e m a s ) th a t e n c o d e in fo rm a tio n

q u ic k ly a n d re lia b ly B y c o n tra st th e e n c o d in g c a p a c ity o f te m p la te s is r e la tiv ely

w e a k In p a rtic u la r T T p re d icts th at th e sa m e te m p la te m a y s o m e tim e s b e u se d to

e n c o d e s e v era l s im ilar p o sitio n s th u s in c re as in g th e ris k o f in terf ere n c e as se a rc h

p ro g re s se s A s a co n se q u e n ce a n d c o n trary to L T W M T rsquos p re d ic tio n s p lay e rs

sh o u ld o fte n re v isit p o sitio n s b y g e n era tin g m o v es in s tea d o f a cc e ss in g th e m

d ire ctly fro m m em o ry T h is is w h at p la y e rsmdash e v e n m a ste rs mdash d o (D e G ro o t

1 9 4 6 ) F in a lly T T m a y h a v e s o m e th in g to sa y a b o u t e rro rs in c h e ss K ro g iu s

(1 9 7 6 ) m e n tio n s th a t er ro rs o f te n o c c u r w h e n a m o v e h a s ca u s ed im p o rta n t

c h a n g es in th e p o s itio n T h is m a y b e d u e to p la y e rsrsquo in a b ility to re c o g n ise th a t a

p re v io u sly a d eq u ate te m p late h as b ec o m e in a d e q u a te

In s u m m a ry T T o ffe rs a g o o d q u alita tiv e a c co u n t o f s e v eral im p o rtan t c h e ss

p h e n o m en a I t is n o w tim e to tu rn to m o re o b je c tiv e q u an tita tiv e te sts o f th e

th eo ry

A COM PUTER M ODE L O F S EARCH IN CH ESS

In th e re m a in d e r o f th is p a p e r I p re s en t a c o m p u te r m o d e l c a lled S E A R C H

w h ic h im p le m e n ts T T in so m e d e ta il I f irs t d e s crib e th e im p le m en ta tio n o f

S E A R C H m a k in g cle a r w h a t a s p ec ts o f T T h a v e b e e n in c lu d ed a n d th en d isc u ss

its b e h a v io u r w ith r es p e ct to h u m a n d a ta

O ve rv iew o f M ode l

F u ll im p le m e n ta tio n o f T T a s a c h e ss-p la y in g c o m p u ter p ro g ram w o u ld b e a

m ajo r ta sk mdash th is d iffic u lty is d e m o n stra te d b y th e fa c t th a t n o c o m p le te co m p u te r

m o d e l o f ch e s s c o g n itio n in c lu d in g p e rc e p tio n m em o ry a n d p ro b le m so lv in g

PATTERN -R ECOGN IT ION AND SEA RCH 299

h a s e v e r b e e n d e v elo p e d I p u rs u e d a lim ited a im a co m p u te r m o d el th a t c o n tain s

so m e o f th e im p o rta n t p aram e te rs o f T T a n d th a t co m p u te s k e y b e h a v io u ra l

v a ria b le s T h is m o d el d o e s n o t c o n stitu te a co m p le te im p le m e n ta tio n o f th e

th e o ry (it d o e s n o t s ea rc h o r e v a lu a te c h e ss p o sitio n s) b u t is d e ta ile d en o u g h to

o ffe r a g o o d te st o f so m e a s p ec ts o f T T I t is s o b e rin g to n o tic e th a t e v e n th is

p a rtia l im p lem e n tatio n o f th e th e o ry is q u ite c o m p le x a n d re q u ire s m a n y

p a ra m e te rs T h is is th e p rice o f a v o id in g th e v ag u en e s s o f v e rb al th e o ris in g

The M a in P rob lem -so lv in g Loop

T h e m ain in te re st o f th e m o d el is in th e in te ra c tio n b etw ee n p atte rn re c o g n itio n

a n d s ea rc h T h e m o d e l g e n e ra tes in d e p en d en t ep is o d es fo llo w in g se v e ral ru les

fo r g e n eratin g m o v e s a n d ch o o sin g sto p co n d itio n s C o m p atib le w ith m o s t

h u m an p ro to co ls th e p ro g ra m c o n sid e rs o n ly o n e b ra n c h w ith in a n ep is o d e (th u s

th e re is n o b ra n c h in g p o in t w ith in a n e p iso d e) A s illu stra te d in F ig 1 th e m o d e l

is c lo se to th e d es crip tio n o f T T g iv en e a rlie r in th is p a p e r T h e v ario u s c o n d itio n s

a n d o p e ra tio n s in S E A R C H a re re p re se n te d as p ro b a b ilit ie s o r p ro b ab ility

d istr ib u tio n s an d n o t a s a ctu a l c h e ss m o v e s e v a lu atio n s o r s y m b o lic s tru c tu res

in S T M o r in th e m in d rsquos e y e

A tra c e o f S E A R C H is sh o w n in F ig 2 T h e an aly s is w ill c e n tre o n th e

fo llo w in g v a ria b les a s a fu n c tio n o f th e n u m b e r o f c h u n k s ra te o f g en e ra tin g a

m o v e le v el o f fu z zin e ss in th e m in d rsquos e y e w h en a n e p is o d e is e n d e d m e an d e p th

o f s ea rc h m eth o d s u se d fo r g en e ra tin g a m o v e a n d m eth o d s u se d fo r s to p p in g a n

e p iso d e

T h e c o n c ep t o f te m p la te is im p le m e n te d in tw o w a y s (a ) b y h ig h e r

p ro b a b ilitie s o f f in d in g (s eq u en c e s o f) m o v e s a n d ev a lu a tio n s th an w ith p la in

c h u n k s a n d (b ) b y a d e cre a se in th e le v e l o f fu zz in e ss m ad e p o s sib le b y th e L T M

re p re se n ta tio n o f th e c o re o f th e p o sitio n a n d o f s lo ts

T h e le v e l o f re lia b ility o f th e in fo rm a tio n in th e m in d rsquos ey e is c a p tu re d b y a

ldquo fu z zin e s srdquo p a ra m e te r e x p re ss ed in a rb itr ary u n its T h re e m a in c o g n itiv e

fe a tu res ar e c a p tu red b y th is p a ra m ete r w o rk in g m e m o ry c a p a c ity a b ility to

m ain ta in a v isu o -s p atia l im ag e a n d su b je ctiv e e s tim a te o f th e r isk o f m ak in g a n

e rro r T h e fu z z in es s p a ram e ter is th e n as su m e d to o rig in ate b o th fro m th e

h a rd w a re a n d th e so ftw a re o f th e sy s tem It m a y v a ry d u r in g th e life tim e o f a

p la y er b e c a u se o f b io lo g ic a l m a tu ra tio n o r a g e in g an d m a y b e a ffe c ted b y

e x p e rim e n ta l m a n ip u latio n s T h e re a re th ree re a so n s w h y S E A R C H en d s a

se a rc h th e lev el o f fu z z in e s s is to o h ig h a n e v a lu atio n is p ro p o se d o r n o m o v e is

p ro p o s e d T h e id e a o f ex p ec ta tio n le v e l is n o t e x p lic itly p re se n t in th e m o d el b u t

it is im p lic it in th e p ro b a b ility v alu e s o f f in d in g fe atu re s e n d in g th e s ea rc h o f a n

e p iso d e e ith er b y p a tte rn re c o g n itio n o r b y th e a p p lica tio n o f h e u ristic s

S e le ctio n o f th e n ex t b a se -m o v e (a k e y c o n c ern o f N ew e ll amp S im o n 1 9 6 5 a n d

W ag n e r amp S c u rra h 1 9 7 1 ) is n o t ad d res se d b y S E A R C H w h ic h in g e n e ra l lac k s

th e s em a n tic in fo rm a tio n n e c es sa ry fo r su c h a se le c tio n F in a lly m e ta -se a rc h

w ith te m p la te s is n o t d ire c tly im p le m e n te d in S E A R C H b u t it is im p lic itly

300 GOBET

300

FIG 1 F lo w c h a rt o f S E A R C H

PATTERN -R ECOGN IT ION AND SEA RCH 301

301

F IG 2 E x a m p le s o f e p is o d e s g e n e ra te d b y S E A R C H

302 GOBET

re p re se n te d b y th e re la tiv e ly h ig h p ro b ab ility o f f in d in g (s eq u e n c e s o f) m o v es

a n d e v a lu atio n s w ith tem p la tes as c o m p are d w ith ch u n k s

The M ode lrsquos P aram e te rs

S E A R C H h as m a n y p a ra m ete rs a n d it is o f c o u rs e n e c es sa ry to se t u p a f ew o f

th e m w ith in d e p e n d e n t d a ta in o rd er to re d u c e th e n u m b e r o f d e g re e s o f fre e d o m

in th e m o d e l W h e n p o ss ib le I h a v e u s e d sim u la tio n s w ith th e C H R E S T (D e

G ro o t amp G o b e t 1 9 9 6 G o b e t 1 9 9 3 ) an d C H U M P (G o b e t amp Ja n s en 1 9 9 4 )

p ro g ram s to se t p a ra m e te r v a lu es C H R E S T is a p ro g ra m im p le m e n tin g as p e cts

o f T T a n d s im u la tin g n u m e ro u s e x p er im e n ts o n p e rc ep tio n an d m e m o ry in ch e s s

a n d C H U M P is a p ro g ra m p la y in g (w e ak ) c h e ss b y p u re p a tte rn re co g n itio n

N u m b e r o f C h u n k s a n d T e m p la te s T ab le 1 sh o w s th e v a lu es th at w ill b e

u s ed w ith th e S E A R C H m o d e l fo r th e se p a ra m ete rs T o c h o o se th e v a lu e s re la te d

to th e n u m b e r o f ch u n k s a n d te m p la tes th e c u rre n t v e rsio n o f C H R E S T h a s b e e n

e m p lo y e d T h e p ro b a b ility o f f in d in g a tem p la te w a s e stim ate d b y ru n n in g

C H R E S T o n 5 0 p o s itio n s ran d o m ly tak e n fro m M as ters rsquo g am e s T h e firs t lin e (0

c h u n k ) w a s ad d e d to g e t p re d ic tio n s a t th e n o v ic e lev e l W ith n e ts o f 1 0 0 0 0 0

1 2 0 0 0 0 a n d 1 5 0 0 0 0 c h u n k s th e p ara m ete rs w ere e stim ate d w ith th e b e s t-fit t in g

fu n c tio n s av a ilab le ( th e ldquo n o v ice rdquo v alu e s w ere n o t u se d ) T h e n u m b er o f te m p la tes

is ro u g h ly a lin e ar fu n c tio n o f th e n u m b er o f c h u n k s (r 2 = 9 7 ) T h e p ro b a b ility

o f f in d in g a tem p la te is a p p ro x im a tely a lo g -fu n c tio n o f th e n u m b e r o f c h u n k s

(r 2 = 9 4 )

H e u r is tic s C h u n k s T e m p la tes a n d T h e ir R e la tio n to th e P ro b a b ility o f

F in d in g M o v e s a n d E v a lu a tio n s T ab le 2 g iv e s th e v a lu e s u s ed in th e

sim u la tio n s fo r th e p a ra m ete rs re la te d to h e u ristic s c h u n k s a n d te m p la te s

H e u ris tic s in c lu d e sim p le se a rc h te c h n iq u e s (e g ldquo ta k e a p ie c e b a c k rdquo o r ldquoc h e c k

th e K in g rdquo ) a s w ell a s m o re a b stra c t ru le s (e g ldquoo c c u p y th e c en tre rdquo ) T h eir m a in

c h a rac te ris tic in co m p a riso n w ith c h u n k s an d tem p la te s is th a t th ey are g e n e ra l

a n d re q u ire so m e co n sc io u s c o m p u tatio n in o rd e r to p ro d u ce a m o v e T h e

a ss u m p tio n u n d e rly in g T a b le 2 is th at th e p aram e ters re la ted to h e u ristic s s ta y

ro u g h ly c o n sta n t w h ile th e o th e r p aram e te rs v a ry as a lo g arith m ic fu n c tio n o f th e

n u m b e r o f c h u n k s in th e n e t (A lo g arith m ic fu n ctio n h a s b e e n c h o se n to in d ica te

th a t ch u n k s y ie ld a d im in ish in g re tu rn as th e ir n u m b e r in c re a se s) T h e

a ss u m p tio n th a t th e n u m b e r o f h e u ristic s is c o n sta n t ac ro s s s k ill le v e ls se e m s

re a so n a b le (p e rh a p s w ith th e e x ce p tio n o f th e n o v ic e le v e l) a s m o s t c h e ss

M a ste rs rsquo k n o w le d g e is v e ry sp ec ific to c erta in a sp e c ts o f th e g a m e (D e G ro o t

1 9 4 6 )

T h e fo llo w in g c o n s id era tio n s w e re m ad e in se ttin g th e v alu e s g iv e n in

T ab le 2 I t w a s d ee m e d p lau sib le th a t th e p ro b a b ility o f f in d in g so m e h e u ristic in

a p o s itio n b e h ig h ( 9 5 ) a s w e ll a s th e p ro b a b ility o f f in d in g s o m e c h u n k F in ally

PATTERN -R ECOGN IT ION AND SEA RCH 303

TA BLE 1

The V a lu es o f th e 14 N e ts U sed in th e S im u la tio ns

P ro b a b i li ty o f

re c o g n is in g a t le as t

P ro p o r t io n o f o n e te m p la te g iv e n a

N u m b e r o f c h u n k s N u m b e r o f te m p la te s te m p la te s p o s i t io n

0 0 0 0 0 0 0 0

1 0 0 2 0 0 0 0 0 0 0

2 6 8 0 5 0 0 2 1 8 0

5 0 0 3 3 6 0 0 7 1 4 0

1 0 0 1 1 1 0 0 0 1 0 2 4 0

2 0 0 0 3 2 6 5 0 1 3 3 0 0

3 0 0 0 1 4 9 3 0 1 6 3 6 0

4 0 0 0 5 7 7 4 0 1 9 4 6 0

5 0 0 0 6 1 1 4 2 0 2 3 4 0 0

7 2 0 4 4 2 1 3 6 0 3 0 4 8 0

8 0 0 1 0 2 2 8 5 0 2 9 5 4 0

1 0 0 0 0 0 2 7 6 5 0 2 8 5 1 0

1 2 0 0 0 0 3 3 5 7 0 2 8 5 4 0

1 5 0 0 0 0 4 2 4 5 0 2 8 5 6 0

T h e v a lu e s b e lo w 1 0 0 0 0 0 c h u n k s w e r e ta k e n f ro m s im u la t io n s w ith C H R E S T th e o the rs

e x t ra p o la te d S e e te x t f o r d e ta ils

TA BLE 2

H eur is t ic s C hun ks Tem pla tes and Their Re la tion to th e P ro bab ility of Fin d in g

M oves and Evalu ta tio ns

T y p e H e u r is tic s C h u n k s T e m p la te s

P ro b a b i li ty o f e v o k in g a n 9 5 g (n _ c h u n k s 9 5 )a se e T a b le 1

h e u ri s t ic a c h u n k o r a te m p la te

P ro b a b i li ty o f f in d in g a m o v e 5 0 g (n _ c h u n k s 5 0 ) g (n _ c h u n k s 9 0 )

g ive n th a t a n h e u r is tic a c h u n k

o r a te m p la te h a s b e e n e v o k e d

P ro b a b i li ty o f f in d in g a n e v a lu a tio n 1 5 g (n _ c h u n k s 0 5 ) g (n _ c h u n k s 5 0 )

g iv e n th a t a n h e u ri s t ic a c h u n k o r

a te m p la te h a s b e e n e v o k e d

aT h e fu n c tio n g i s d e f in e d a s

g (n _ c h un k s p ro b ) = p ro b 0 2 lo g1 0

(n _ c h un k s ) i f n _ c h u n k s gt 0

a n d

g (n _ c h u n k s p ro b ) = 0 i f n _ c h u n k s = 0

w h e re n _ c h u n k s i s th e n u m b e r o f c h u n k s in a g iv e n n e t a n d p ro b i s a c o n s ta n t

303

304 GOBET

th e p ro b a b ility o f re c o g n isin g a te m p la te in a p o sitio n is sm a lle r a n d is g iv e n in

T ab le 1

T h e p ro b a b ility o f f in d in g a m o v e g iv e n a h e u ristic is s e t to 5 0 in d ic atin g th a t

h e u ristic s m a y fa il to p ro d u ce a m o v e h a lf o f th e tim e T h is is b e c a u se so m e

h e u ristic s m ay n o t y ie ld a m o v e a n d b ec a u se so m e p ro p o se d m o v es m a y b e

ille g a l T h e p ro b a b ility o f f in d in g a m o v e g iv en a tem p la te is h ig h p a rtly

re fle ctin g th e ric h s em a n tic k n o w le d g e an d th e in te r-te m p la te lin k s a s su m e d to

c h a rac te rise te m p la te s F o r th e p ro b a b ility o f f in d in g a m o v e g iv e n th a t a ch u n k

h a s b e en re co g n ise d I u se d th e p ara m e te r p ro b in th e fu n ctio n g (s ee T a b le 2 ) so

th a t i t a p p ro x im a te s th e d ata p ro d u c ed b y th e C H U M P p ro g ram (G o b et amp Ja n se n

1 9 9 4 ) E v a lu a tio n s a re su p p o s ed to b e h a rd er to le arn a n d th e re fo re h a rd e r to u se

th a n m o v es H e n ce th e ir p ro b a b ilit ie s a re lo w e r th a n th e co r res p o n d in g p ro b -

a b ilit ie s w ith m o v es A g a in fo llo w in g d irec tly fro m th e th e o ry te m p la te s o ffe r

th e b e st so u rce o f ev alu a tio n s

W ith re sp e c t to th e n u m b e r o f se q u e n tia l m o v e s p ro p o s ed c o u n ted in p lie s

(i e m o v e s fo r W h ite o r B la ck ) i t is as su m e d th a t h e u ristic s g iv e a cc e ss to o n ly

o n e m o v e w h ile c h u n k s a n d te m p late s y ie ld se q u e n c es o f m o v e s w h o se n u m b e r

fo llo w s a g e o m e tric p ro b a b ility d is tr ib u tio n (th e c h o ice o f th is d is tr ib u tio n w as

in sp ire d b y sta tis tic s ta k e n fro m C H U M P ) T h e lo n g e s t s eq u e n c e ( ca ll i t k ) h as a

fre q u e n c y o f 1 th e s e co n d -lo n g e st a fre q u en cy o f 2 th e th ird -lo n g e st a fre q u e n c y

o f 4 a n d so o n u n til th e sh o rte st se q u e n c e w h o s e len g th is 1 m o v e an d w h o se

fre q u e n c y is 2 (k ndash 1 ) T h e m a x im u m se q u e n ce o f m o v es w a s se t to 1 8 F in a lly

S E A R C H atte m p ts to g e n e ra te a m o v e b y p a ttern re c o g n itio n ( ch u n k o r te m p la te )

fo u r tim e s b e fo re u sin g a n h e u ristic

T im e a n d F u zzin e ss P a ra m ete rs T h e tim e p a ram e ter s fo r th e re sp e c tiv e

o p e ra tio n s w e re s et u sin g p la u sib le v a lu e s (se e T a b le 3 ) M o v e g en era tio n b y

p a tte rn re c o g n itio n (c h u n k o r te m p late ) is as su m e d to b e v e ry sh o rt (a few

h u n d re d m illis e co n d s) n o tim e c o st is u se d in th e m o d e l T h e tim e fo r c o m p u tin g

a m o v e-g en e ra tin g h e u ristic w a s s et to th e ra th e r lo n g 2 0 s ec o n d s mdash g en era tin g a

m o v e w ith o u t u sin g p a tte rn r ec o g n itio n re q u ires p u ttin g to g eth e r v a rio u s ty p e s o f

in fo rm a tio n a n d a s k s fo r m a n y ch e c k in g p ro c ed u res T h e tim e fo r c a rry in g o u t

o n e m o v e (o n c e g e n erate d ) in th e m in d rsquos e y e w a s s et to tw o s ec o n d s T h is is

c o m p atib le w ith S a a rilu o m a rsquos (1 9 8 9 ) d ata w h ic h sh o w th a t a b lin d fo ld ed M a ste r

c an fo llo w a g a m e d icta ted a t tw o se c o n d s a m o v e F in ally th e tim e fo r ca rry in g

o u t a n ev a lu a tio n b y h eu ris tic is s e t to 1 0 s e co n d s T h is ra th e r s h o rt tim e m a y b e

ju stif ie d b y th e fa c t th a t p la y e rs ty p ic a lly co n s id e r o n ly o n e (s u b jec tiv e ) a sp e c t o f

th e p o sitio n (D e G ro o t 1 9 4 6 ) a n d th at m an y e v a lu atio n s c a n b e g ro u n d ed o n th e

b a sis o f c lea r m a teria l lo ss e s

T h e fu z zin e ss lev el o f th e s y ste m is e x p re ss ed in a rb itra ry u n its I t s ta rts w ith

th e v a lu e z e ro a n d it is in c re a se d w h e n a m o v e is c a rrie d o u t in th e m in d rsquos e y e

a n d w h e n tim e is s p e n t a p p ly in g a n h e u ris tic W h e n a te m p la te is fo u n d th e

PATTERN -R ECOGN IT ION AND SEA RCH 305

fu z z in es s lev el is d e cre a se d a s p a rt o f th e in fo rm atio n m ay b e sto re d in L T M

d ire c tly fre e in g c ap ac ity in w o rk in g m e m o ry a n d in th e m in d rsquos ey e

S im u la t io n s w ith th e ldquo C anon ica l M ode lrdquo

T h e sim u latio n s d e sc rib ed in th is s ec tio n a re s tra ig h tfo rw a rd U s in g th e

p a ra m e te r v alu e s d is cu sse d e a rlie r I le t th e p ro g ra m s ea rc h 1 0 0 0 ep iso d e s fo r

e ac h n e t s iz e S u m m a ry v alu e s fo r m e a n d ep th o f se a rc h t im e ra tio d e p th tim e

a n d fu z zin e s s a s w e ll a s fo r g e n e ra tio n an d s to p co n d itio n s w e re c o m p u ted fo r

e ac h n e t s iz e

M e a n D e p th o f S e a r ch R a te o f S e a rc h a n d F u z zin e ss A cc o rd in g to

S E A R C H m ea n d e p th o f s ea rc h fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f

c h u n k s (se e F ig 3 a) If w e as su m e a co n sta n t ra te o f le a rn in g n e w c h u n k s a s is

c o m m o n p ra ctic e in so m e c o g n itiv e a rch ite c tu res (c f N e w e ll 1 9 9 0 ) a n d if w e

a ss u m e th a t s k ille d p la y e rs h a v e sp e n t m o re p rac tice a n d stu d y tim e th a n

u n s k ille d p la y e rs th e n m e an d e p th fo llo w s a p o w e r fu n c tio n o f s k ill as w e ll T h is

p re d ic tio n w h ic h is a t v ar ia n c e w ith H o ld in g rsquos p re d ic tio n (1 9 8 5 p 1 8 2 ) o f a

lin ea r in c rea s e is p artly co n siste n t w ith C h a rn e ss rsquos (1 9 8 1 ) p ro p o s a l th a t d e p th o f

se a rc h is n o t l in e arly re la ted to s k ill b u t th at th e re is a ce ilin g a t h ig h s k ill le v e ls

T h e re su lt is a ls o c o m p atib le w ith th e w e a k lin e ar re la tio n fo u n d in e m p ir ic a l

stu d ie s (C h a rn e ss 1 9 8 1 G o b e t in p re ss ) b e tw e e n m e a n d e p th o f se a rch a n d sk ill

le v el b e c a u se re stric te d ra n g e s o f th e c u rv e c a n b e a p p ro x im a ted b y a lin e a r

fu n c tio n T h e a b so lu te v alu e s a re a lso q u ite r ea so n ab le th ey ris e f ro m lo w d ep th s

(le ss th a n 1 p ly ) w ith n o ch u n k s (co r res p o n d in g to th e n o v ic e le v el) to a ro u n d 2 5

p lies w ith a sm a ll n et (1 0 0 0 c h u n k s ) an d th e n to a ro u n d 4 p lie s w ith ex p ert le v e l

(a ro u n d 3 0 0 0 0 c h u n k s a s e s tim a te d b y s im u la tio n s o n th e re ca ll tas k ) T h e y th e n

slo w ly (s av e fo r a f ew ra n d o m v a ria tio n s ) in c re a se to m o re th an 5 p lie s w ith n e t

la rg er th an 1 0 0 0 0 0 c h u n k s w h ic h c o rre sp o n d s to G ran d m a ste r le v e l H o ld in g

(1 9 8 5 ) c o m p u te d m e a n d e p th o f se a rch fo r d e G ro o trsquos (1 9 4 6 ) d a ta a n d fo u n d th a t

TA BLE 3

T im e and ldquo Fuzz in ess rdquo Param e ters U sed in th e

S im ula t io n s

T im e fo r c a r ry in g o u t a m o v e 2 s

T im e fo r c o m p u t in g m o v e -g e n e r a tin g h e u r is tic 2 0 s

T im e fo r c o m p u t in g e v a lu a t io n 1 0 s

U p p e r l im it o f fu z z in e ss 5 0

In c r e a se o f fu z z in e s s p e r m o v e 1

In c re a se o f f u z z in e ss p e r s e c o n d 2

D e c re a s e in fu z z in e ss d u e to te m p la te 5

306 GOBET

E x p e rts a n d G ra n d m as ters h a d res p e ctiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 8 a n d

5 3 T h e reg res sio n e q u a tio n d e riv e d f ro m C h a rn e ss rsquos (1 9 8 1 ) d ata y ie ld a n

a v e rag e d e p th o f se a rc h o f a b o u t 2 3 p lies a t th e 1 3 0 0 E L O 1 le v e l o f 4 1 a t th e

E x p e rt le v e l (2 0 0 0 E L O ) a n d o f 5 7 a t th e G ra n d m a s te r le v el U n fo rtu n a tely n o

stu d y te ste d p la y e rs ra n g in g fro m n o v ic es to G ran d m a ste rs an d S E A R C H rsquos

p re d ic tio n o f a p o w e r la w o f p rac tic e c an n o t b e te ste d (y e t) I w ill re p o rt la te r

sim u la tio n s a d d re ssin g d a ta co lle c ted b y S a arilu o m a (1 9 9 0 ) w h e re In tern atio n a l

M a ste rs a n d G ra n d m a s te rs te n d e d to s e arc h le s s th a n M as te rs

T h e ra te o f s ea rc h a lso fo llo w s a p o w e r fu n ctio n o f th e n u m b e r o f c h u n k s (se e

F ig 3 b ) D e G ro o t (1 9 4 6 ) C h arn es s (1 9 8 1 ) a n d G o b e t ( in p res s) a ll f o u n d th a t

stro n g p la y er s te n d e d to s e arc h fa ste r F o r ex a m p le G o b e t ( in p re s s) fo u n d th a t

h is M a ste rs E x p e rts C la ss A a n d C la s s B p lay e rs re sp e c tiv ely se arch e d 4 8 4 1

3 2 an d 3 4 n o d e s p e r m in u te S E A R C H rsquos v a lu es a re h ig h e r b u t s til l p la u s ib le

F o r ex am p le W a g n e r a n d S c u rra h rsquos (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r

m in u te N o te a lso th a t a ll th e ex p erim e n ts m e n tio n e d e a rlier h a v e u se d v e rb a l

p ro to c o ls w h ic h m ay h av e s lo w e d d o w n th e ra te o f se a rc h (c f E ric ss o n amp

S im o n 1 9 8 0 ) F in a lly th e ra te o f se arch m a y h av e b e e n u n d e res tim a ted in th e

lite ra tu re b ec a u se th e r a te o f g e n e ratin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d

b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l t im e H o w e v e r to ta l t im e in c lu d es

tim e n o t sp e n t in s e arc h ( fo r e x a m p le w h a t D e G ro o t c a lls th e ldquo firs t p h a se rdquo)

T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a riab le th e le v e l o f fu zz in e ss a t

w h ic h a se a rc h is e n d e d is m o re d if fic u lt to ju d g e b ec a u se lit tle is k n o w n a b o u t

th e ro le o f fu z z in es s in c h es s th in k in g A g ain S E A R C H p ro p o se s th a t th is

v a riab le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s ee F ig 3 c ) W ith la rg e r

n e ts e p iso d es te n d to b e e n d e d w ith lo w er le v els o f fu z z in e s s T h is su g g es ts th at

in g e n e ra l s tro n g p la y ers s h o u ld b e m o re c o n fid e n t in th e ir c alc u la tio n s as th e y

a re n o t a t th e e d g e o f th eir p o s sib ilitie s N o te th a t th e ra te o f ch an g e is ra th e r h ig h

fo r th is p o w er law w h ic h s u g g e sts th at it sh o u ld b e p o ss ib le to d e te c t i t

e x p erim e n tally

G e n e ra tio n o f M o ve s H o w is m o v e g en e ra tio n af fec te d b y sk ill le v e l A s

sh o w n in F ig 4 a S E A R C H m a k es c le a r p re d ic tio n s W ith sm a ll n u m b e rs o f

c h u n k s th e tim e -c o n s u m in g p ro ce s s o f g en e ra tin g m o v es b y h e u ristic s is

e m p lo y e d T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y ch u n k s

w h ic h is in tu rn d o m in a te d b y te m p la te g e n eratio n

1 T h e E L O ra t in g i s a n in te r v a l sc a le th a t ra n k s c o m p e t it io n c h e ss p la y e rs I ts s ta n d a rd de v ia t io n

(2 0 0 p o in ts) is o f te n in te r p re te d a s a m e a su r e o f sk i ll c la s s in c h e ss G r a n d m a s te r s a re n o rm a lly ra te d

a b o v e 2 5 0 0 In te rn a t io n a l M a s te r s a b o v e 2 4 0 0 M a s te r s a b o v e 2 2 0 0 a n d E x p e rt s a b o v e 2 0 0 0

B e lo w c la sse s (A B e tc ) d iv id e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in ts

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

PATTERN -R ECOGN IT ION AND SEA RCH 295

th e p o w e r o f C T to e x p lain th e r ap id rec o g n itio n o f p o sitio n s sh o w n b y m a ste rs

a s th e s am e d isc rim in a tio n m e ch a n ism s are p res e n t (G o b e t 1 9 9 6 )

S ea rch M echan ism s

T T a n d C T p ro p o se th a t se a rc h is ca rrie d o u t in a fo rw ard fa sh io n b y re cu rsiv e

a p p lica tio n o f p a tte rn re co g n itio n p ro ce s se s in th e in te rn a l rep res e n ta tio n In th e

re m ain d e r o f th is se c tio n I w ill f le sh o u t th is m e c h an ism w ith ad d itio n a l sp e c ifi-

c atio n s I w ill a lso sh o w h o w c h u n k s an d te m p late s m a y b e u se d to te rm in a te

se a rc h a n d h o w te m p la te s m a y b e u se d to ca rry o u t s ea rc h a t a le v e l m o re

a b stra c t th a n th e m o v e le v e l

M o v e G e n e ra tio n A s m en tio n e d e arlie r p a ttern r ec o g n itio n is a p p lie d

re c u rsiv e ly in T T If a c h u n k mdash o r a te m p la te a s tem p la te s ar e a s p e cia l c as e o f

c h u n k smdash is rec o g n is ed i t m a y g iv e a c c es s to a m o v e (o r a se q u e n c e o f m o v e s ) o r

to a n h e u ris tic fo r se le ctin g th e n ex t m o v e E x a m p le s o f s u ch h e u ristic s a re

ldquo O c c u p y o p e n lin e s rdquo o r ldquo C o u n te r-a tta c k in th e ce n tre w h e n a ttac k e d o n th e

K in g rsquos s id e rdquo In th is ca s e th e m o v e(s ) is (a re ) c a rried o u t in th e m in d rsquos e y e If n o

m o v e re su lts fro m p a tte rn re co g n itio n o n e o f tw o o p era tio n s m a y b e ap p lie d

E ith e r th ere is a n e w atte m p t to g e n e rate a m o v e b y a cc e ss in g a d iffe re n t c h u n k

o r w ea k e r h e u ristic s a re a p p lie d

U p d a te o f In te rn a l R ep re se n ta tio n a n d S to r a g e o f In fo rm a tio n in to

T e m p la te W h en a m o v e o r a se q u e n c e o f m o v e s is c a rrie d o u t in th e m in d rsquos

e y e th e in te rn a l rep res e n ta tio n is u p d a te d a n d w h e n a te m p la te h as b e e n

a cc e ss e d s lo ts a re u p d ate d a s w e ll S lo ts m a y sto re in fo rm a tio n a b o u t th e

lo c atio n o f p ie ce s s tra teg ic in fo rm a tio n e v alu a tio n o f th e p o sitio n o r p a rt o f i t

a n d s o o n N o te th a t th is in fo rm a tio n fa c ilita te s s ea rc h b e c au se p o s sib le fo r -

g e ttin g th ro u g h d ec a y in th e m in d rsquos e y e m a y b e b ac k e d -u p b y in fo rm a tio n s to re d

in s lo ts

E va lu a tio n o f N o d e s E v a lu a tio n o f a p o sitio n is n o t c ar ried o u t af te r e ac h

m o v e b u t o n ly a t th e term in a l p o sitio n s E v a lu atio n is e ith e r r e trie v e d w h e n

p o s sib le fro m ch u n k s th a t h a v e b e en re c o g n ise d o r co m p u te d w h e n th e p la y e r

d e c id e s to te rm in a te s e arc h (s ee n e x t p a ra g ra p h ) D e G ro o trsquos (1 9 4 6 ) p ro to co ls

in d ic ate th a t p la y e rs e v a lu a te o n ly te rm in a l p o s itio n s a n d th a t th e ir e v a lu atio n s

a re ra th e r s im p le ta k in g in to a c co u n t a s in g le fe a tu re su c h as m o b ility o r c o n tro l

o f th e c e n tre a n d stro n g ly su g g e s t th a t e v a lu a tio n s are n o t co m p u te d b y

c o n jo in in g s e v eral fe atu re s

E n d in g S ea r c h o f a n E p iso d e A c ritic a l q u es tio n g iv e n a lim ite d

in fo rm a tio n -p ro c es sin g c a p a city is w h e n to s to p se a rc h in g a n e p iso d e (i e a

se q u e n c e o f m o v es g e n e ra ted fro m a b as e m o v e ) I p ro p o se th a t th e fo llo w in g

296 GOBET

c o n d itio n s ca n h alt th e se a rc h o f a n e p iso d e T o b e g in w ith th e p ro b a b ility o f

m ak in g a n e rro r is to o h ig h P s y ch o lo g ic a lly th is p ro b a b ility is a fu n ctio n o f th e

fo rg e ttin g a n d in ter fer en c e r a te s in th e m in d rsquo s ey e P h e n o m e n o lo g ic a lly p lay e rs

p ro b a b ly a s se ss th is p ro b a b ility b y ta k in g in to a c c o u n t th e d e p th o f se a rc h

re a ch e d a n d b y e s tim a tin g th e ir fa m ilia rity w ith th e p o s itio n

A n o th e r re a so n to h a lt s ea rc h o c cu r s w h e n th e le v e l o f e x p e c tatio n fo r th e

p o s itio n is m et o r w h e n a f ea tu re o f th e p o s itio n (e g sa fe ty o f th e K in g ) w as

e v a lu a te d to b e lo w e r th a n its a d m iss ib le v a lu e (N e w e ll amp S im o n 1 9 7 2 ) T h is

le v el o f e x p e c ta tio n is p ro v id e d b y a c h u n k en c o u n te re d d u rin g e arlie r s ea rc h o r

b y e x p lic it ev a lu a tio n o f th e p o s itio n a n d w a s s to re d e ith e r in S T M o r w h e n

a v a ila b le in a te m p late s lo t A fin a l h a ltin g c o n d itio n is th a t a d e c isiv e e v e n t

o c c u rre d s u ch a s m a te im p o rta n t m a teria l g a in o r lo ss o r fu lfilm e n t o f a k e y

g o al

S e lec tin g th e N e x t B a s e -m o v e N o w co n s id er th e q u e stio n o f w h ic h b a se -

m o v e to se a rch n ex t w h en a le a f n o d e h a s b e e n re a ch ed A n y o f s ix m e c h an is m s

m ay b e e n g a g e d F irst if th e le a f w a s e v a lu ate d w ith a h ig h risk o f er ro r th e s am e

se q u e n c e o f m o v e s is se a rc h ed a g ain in o rd e r to o b ta in a m o re re lia b le e stim a te

S e c o n d th e sa m e s eq u en c e o f m o v e s m a y b e se a rch e d a g a in to m a k e s u re th a t i t

h a s b e e n sto re d in L T M T h ird if a tem p la te h a s b e e n re co g n ise d a m e ta -se a rc h

(s ee la te r) is c arr ie d o u t F o u rth th e re is a b ia s to g iv e p re fe ren ce to n o rm a l b as e -

m o v e s ea rly in se a rch a n d to u n u su a l b a s e-m o v e s la ter (N ew ell amp S im o n 1 9 7 2

p 7 2 3) F ifth a m ov e re ac h e d at a n y le v e l o f d e p th in s ea rch in g a lin e m a y b e trie d

a s a ca n d id a te m o v e in th e n ex t lin e S ix th if th e e v alu a tio n o f an e p iso d e g iv e s a

fa v o u ra b le re su lt its an aly s is is c o n tin u e d if th e ev a lu a tio n is u n fa v o u rab le a

d iffe re n t b a se -m o v e is ta k e n u p (N e w e ll amp S im o n 1 9 7 2 )

M e ta -s e a rc h w ith T e m p la te s (A b stra c t P la n n in g ) S e arc h m ay b e c arrie d o u t

n o t o n ly a t th e m o v e le v e l b u t a lso a t th e te m p la te le v el P lay e rs s o m e tim es

d e v e lo p a tre e se a rc h b y g e n eratin g k ey p o sitio n s (te m p la tes ) in s tea d o f

d e v e lo p in g a tree se arch b y g e n e ra tin g m o v e s (e g D e G ro o t 1 9 7 8 p 1 5 3 ) P ath s

b e tw e en k e y p o sitio n s c o n s is t o f m a cro -o p e ra to r s o r in u n s p ec ifie d o p e ra to r s

w h ic h w ill b e fil le d in a t a la te r s ta g e o f se a rch if th e le a f p o sitio n s a re ju d g e d

fa v o u ra b le T h is ty p e o f se arch is c o n tin g en t to th e p res e n ce in p la y ers rsquo L T M o f

te m p la tes su ffic ie n tly c lo se to th e p o s itio n a t h a n d K o ed in g e r a n d A n d e rs o n

(1 9 9 0 ) h a v e p ro p o se d a s im ilar id e a w ith re sp e c t to g eo m e try T h is m e ta -se a rc h

m ec h a n ism is a ls o sim ilar to th e ldquoa p p e rc e p tio n rdquo m e c h a n ism su g g es ted b y

S a a rilu o m a (1 9 9 0 1 9 9 2 )

Theo re t ica l Im po rta n ce o f Tem p la te s

O b v io u s ly m an y o f th e p ro ce s se s ju st d es c rib ed c a n b e im p le m e n te d w ith in th e

e ar lie r C T w ith o u t h y p o th e sisin g th e p re se n c e o f te m p la tes T e m p la tes a re

h o w e v e r im p o rta n t fo r s o m e o f th e k ey c o g n itiv e p ro c es se s in c h e ss b e c au se

PATTERN -R ECOGN IT ION AND SEA RCH 297

(a ) s lo ts a llo w in fo rm a tio n ab o u t s tra te g ic o r tac tica l th e m e s a s w e ll a s a b o u t

e v a lu a tio n o f th e p o sitio n to b e en co d e d in L T M rap id ly (b ) lin k s b e tw e e n

te m p la tes a llo w fo r ldquo m e ta -se a rc h rdquo (c ) in fo rm a tio n s to re d b o th in th e c o re a n d in

th e slo ts o f th e te m p late c o m p en sa tes fo r d e c a y an d in te rfe re n c e in th e m in d rsquos

e y e as it m a y b e u se d to re in sta te fa d in g in fo rm a tio n T h is c o m p e n sa tio n

m ec h a n ism is p ar tic u la rly u se fu l w h e n p e rce p tu a l in fo rm a tio n fro m th e ex te rn a l

b o a rd is u n re liab le fo r ex a m p le b e ca u s e se v e ra l m o v e s h a v e b e en c arr ie d o u t in

th e m in d rsquos e y e

Em p ir ica l D a ta Sup po rtin g th e TT A ccoun t o f Sea rchand Pa tte rn R e cogn itio n

In th is se c tio n T T is q u alita tiv e ly ap p lie d to s o m e o f th e k ey d a ta f ro m e m p ir ic a l

stu d ie s o f ch e s s p ro b le m s o lv in g Q u a n tita tiv e a s se ss m e n t w ill b e th e to p ic o f

th e fo llo w in g se c tio n I h a v e sh o w n e lse w h e re (G o b e t 1 9 9 6 ) th at th e p re d ic tio n s

o f T T a re w e ll su p p o rted b y e m p ir ic a l d a ta fro m re se a rch o n m e m o ry a n d

p e rce p tio n

In c re a sin g th e n u m b e r o f c h u n k s a n d te m p la te s h a s tw o o p p o site ef fec ts w ith

re sp e c t to se a rch (G o b e t in p res s) O n th e o n e h a n d d e ep s e arc h is fac ilita te d as

c o m p are d w ith th e m o re co m p u ta tio n a lly e x p e n s iv e w e a k m e th o d s b e c au se

p a tte rn re c o g n itio n is a ra p id p ro c es s a n d b e ca u s e se q u e n c e s o f m o v es m a y b e

le arn e d an d su g g e ste d b y c h u n k s O n th e o th er h a n d th e n ee d fo r d e e p se a rc h

o fte n d isa p p e ar s b e ca u s e e v a lu atio n s su g g e ste d b y p a tte rn re c o g n itio n m a y b e

m o re re lia b le th a n e v a lu atio n s co m p u te d b y w e a k m eth o d s T h e s e tw o o p p o site

e ffe cts c a n e x p la in w h y th e sk ill d iffe re n c e s in a v e rag e d e p th o f se a rc h a re sm all

P a tte rn re co g n itio n a llo w s stro n g p la y e rs to b e h ig h ly s e le c tiv e in th e ir s ea rc h

T h is c a n b e s e en b o th in th e ra p id w a y M a s te rs ze ro in to th e k e y as p e cts o f a

p o s itio n (D e G ro o t 1 9 4 6 ) an d in th e w ay e y e m o v e m e n ts d iffe r a s a fu n c tio n o f

sk ill d u rin g th e firs t s ec o n d s o f th e p e rc ep tio n o f a p o sitio n (D e G ro o t amp G o b et

1 9 9 6 ) A d d itio n a l e v id e n ce is p ro v id e d b y S a a rilu o m a (1 9 9 0 ) w h o h a s sh o w n

th a t p la y e rs ch o o se ste re o ty p e d so lu tio n s in p ro b le m s w h e re fa ste r ( in th e

n u m b e r o f m o v es to r ea c h m a te) b u t u n c o m m o n so lu tio n s a re p re s en t T h e se d a ta

a d d s u p p o rt to T T b e c a u se p a ttern re co g n itio n lie s a t i ts c o re

F u r th er s tro n g e v id e n ce fo r th e ro le o f p atte rn re c o g n itio n is th a t M as te rs c a n

p la y s ev e ra l o p p o n en ts s im u lta n eo u sly a t a s tre n g th c lo se to th at in o n e -a g ain s t-

o n e p lay I t is in te re stin g th at in s im u lta n eo u s g a m e s th ey te n d to p la y ldquon o rm a lrdquo

m o v e s a n d re ly o n o p p o n e n ts rsquo e rro rs (G o b e t amp S im o n 1 9 9 6 c ) N o rm a l m o v es

m ay c o rre sp o n d to th e ty p e o f m o v e s su g g e ste d b y c h u n k s an d tem p la te s

A fea tu re o f c h es s ex p e rtise c a p tu re d u n iq u e ly b y T T is th e h ig h le v e ls a t

w h ic h ch e s s p lay e rs o rg a n is e th e ir k n o w le d g e D e G ro o t (1 9 4 6 ) p ro p o s e d th a t

p la y er s o rg an is e p o sitio n s a ro u n d la rg e ldquo c o m p le x e srdquo b ig g e r th a n th e c h u n k s th a t

w e re la te r p ro p o se d b y C h a se a n d S im o n (1 9 7 3 ) D e G ro o t a lso su g g es ted a s d id

C o o k e e t a l (1 9 9 3 ) th a t p la y e rs re p re s en t in fo rm a tio n a t a c o n c e p tu a l lev el In

p a rticu la r D e G ro o t (1 9 4 6 ) p ro p o se d th a t M a ste rsrsquo d e sc rip tio n s o f g am e s a re

298 GOBET

c en tred a ro u n d k ey p o sitio n s o f th e g a m e T T o ffe rs th eo retic al s tru c tu res

(te m p la te s) th a t co u ld a c c o u n t fo r p lay ers rsquo larg e c o m p le x es h ig h - le v e l re p re -

se n ta tio n s a n d k e y p o sitio n s T T a lso o ff ers m e ch a n ism s b as e d o n f req u en c y o f

o c c u rre n ce s e x p la in in g h o w th e s e h ig h - le v e l re p re se n ta tio n s a re d ev elo p e d a n d

m ec h a n ism s b a se d o n d isc rim in a tio n p ro c e sse s e x p la in in g h o w th ey c o u ld b e

a c ce ss e d ra p id ly

T T is a lso co m p a tib le w ith re su lts fro m e x p er im e n ts u s in g p o s itio n s fo r w h ic h

a cc e ss to k n o w le d g e is d iffic u lt In H o ld in g a n d R e y n o ld s rsquo (1 9 8 2 ) e x p e rim e n t

c h e ss s k ill d id n o t c o rr ela te w ith th e re c a ll o f s e m i-ra n d o m p o s itio n s sh o w n fo r a

fe w se co n d s b u t eff ec tiv en es s o f th e s ea rc h fo r th e b e st m o v e in th es e p o s itio n s

d id c o rr ela te w ith s k ill T T o f fer s a n ex p la n a tio n fo r th e fa c t th a t th e re w a s a

stro n g c o rre la tio n b e tw e en sk ill le v e l a n d q u a lity o f m o v e p ro p o se d P lay e rs

re c u rsiv e ly g e n e ra te a m o v e th ro u g h w ea k m e th o d s w h en n o c h u n k is

re c o g n ise d u n til o n e o f th e h a ltin g co n d itio n s (m en tio n e d e a rlier ) a p p lie s T h e n

g iv e n th eir la rg e r d ata b a se o f c h u n k s s tro n g p la y e rs a re m o re lik e ly th a n w e a k

p la y er s to f in d a u s efu l p a tte rn in p o sitio n s th a t h a v e b ee n n e w ly u p d ate d in th e

m in d rsquos e y e a n d th e re fo re a re m o re lik e ly to f in d g o o d m o v e s in th eir se a rch

I m en tio n e d e a rlier th at E ric ss o n a n d K in tsc h (1 9 9 5 ) p ro p o s ed m ec h a n ism s

(re trie v al s tru c tu re a n d ela b o ra tio n s o f L T M sc h e m a s ) th a t e n c o d e in fo rm a tio n

q u ic k ly a n d re lia b ly B y c o n tra st th e e n c o d in g c a p a c ity o f te m p la te s is r e la tiv ely

w e a k In p a rtic u la r T T p re d icts th at th e sa m e te m p la te m a y s o m e tim e s b e u se d to

e n c o d e s e v era l s im ilar p o sitio n s th u s in c re as in g th e ris k o f in terf ere n c e as se a rc h

p ro g re s se s A s a co n se q u e n ce a n d c o n trary to L T W M T rsquos p re d ic tio n s p lay e rs

sh o u ld o fte n re v isit p o sitio n s b y g e n era tin g m o v es in s tea d o f a cc e ss in g th e m

d ire ctly fro m m em o ry T h is is w h at p la y e rsmdash e v e n m a ste rs mdash d o (D e G ro o t

1 9 4 6 ) F in a lly T T m a y h a v e s o m e th in g to sa y a b o u t e rro rs in c h e ss K ro g iu s

(1 9 7 6 ) m e n tio n s th a t er ro rs o f te n o c c u r w h e n a m o v e h a s ca u s ed im p o rta n t

c h a n g es in th e p o s itio n T h is m a y b e d u e to p la y e rsrsquo in a b ility to re c o g n ise th a t a

p re v io u sly a d eq u ate te m p late h as b ec o m e in a d e q u a te

In s u m m a ry T T o ffe rs a g o o d q u alita tiv e a c co u n t o f s e v eral im p o rtan t c h e ss

p h e n o m en a I t is n o w tim e to tu rn to m o re o b je c tiv e q u an tita tiv e te sts o f th e

th eo ry

A COM PUTER M ODE L O F S EARCH IN CH ESS

In th e re m a in d e r o f th is p a p e r I p re s en t a c o m p u te r m o d e l c a lled S E A R C H

w h ic h im p le m e n ts T T in so m e d e ta il I f irs t d e s crib e th e im p le m en ta tio n o f

S E A R C H m a k in g cle a r w h a t a s p ec ts o f T T h a v e b e e n in c lu d ed a n d th en d isc u ss

its b e h a v io u r w ith r es p e ct to h u m a n d a ta

O ve rv iew o f M ode l

F u ll im p le m e n ta tio n o f T T a s a c h e ss-p la y in g c o m p u ter p ro g ram w o u ld b e a

m ajo r ta sk mdash th is d iffic u lty is d e m o n stra te d b y th e fa c t th a t n o c o m p le te co m p u te r

m o d e l o f ch e s s c o g n itio n in c lu d in g p e rc e p tio n m em o ry a n d p ro b le m so lv in g

PATTERN -R ECOGN IT ION AND SEA RCH 299

h a s e v e r b e e n d e v elo p e d I p u rs u e d a lim ited a im a co m p u te r m o d el th a t c o n tain s

so m e o f th e im p o rta n t p aram e te rs o f T T a n d th a t co m p u te s k e y b e h a v io u ra l

v a ria b le s T h is m o d el d o e s n o t c o n stitu te a co m p le te im p le m e n ta tio n o f th e

th e o ry (it d o e s n o t s ea rc h o r e v a lu a te c h e ss p o sitio n s) b u t is d e ta ile d en o u g h to

o ffe r a g o o d te st o f so m e a s p ec ts o f T T I t is s o b e rin g to n o tic e th a t e v e n th is

p a rtia l im p lem e n tatio n o f th e th e o ry is q u ite c o m p le x a n d re q u ire s m a n y

p a ra m e te rs T h is is th e p rice o f a v o id in g th e v ag u en e s s o f v e rb al th e o ris in g

The M a in P rob lem -so lv in g Loop

T h e m ain in te re st o f th e m o d el is in th e in te ra c tio n b etw ee n p atte rn re c o g n itio n

a n d s ea rc h T h e m o d e l g e n e ra tes in d e p en d en t ep is o d es fo llo w in g se v e ral ru les

fo r g e n eratin g m o v e s a n d ch o o sin g sto p co n d itio n s C o m p atib le w ith m o s t

h u m an p ro to co ls th e p ro g ra m c o n sid e rs o n ly o n e b ra n c h w ith in a n ep is o d e (th u s

th e re is n o b ra n c h in g p o in t w ith in a n e p iso d e) A s illu stra te d in F ig 1 th e m o d e l

is c lo se to th e d es crip tio n o f T T g iv en e a rlie r in th is p a p e r T h e v ario u s c o n d itio n s

a n d o p e ra tio n s in S E A R C H a re re p re se n te d as p ro b a b ilit ie s o r p ro b ab ility

d istr ib u tio n s an d n o t a s a ctu a l c h e ss m o v e s e v a lu atio n s o r s y m b o lic s tru c tu res

in S T M o r in th e m in d rsquos e y e

A tra c e o f S E A R C H is sh o w n in F ig 2 T h e an aly s is w ill c e n tre o n th e

fo llo w in g v a ria b les a s a fu n c tio n o f th e n u m b e r o f c h u n k s ra te o f g en e ra tin g a

m o v e le v el o f fu z zin e ss in th e m in d rsquos e y e w h en a n e p is o d e is e n d e d m e an d e p th

o f s ea rc h m eth o d s u se d fo r g en e ra tin g a m o v e a n d m eth o d s u se d fo r s to p p in g a n

e p iso d e

T h e c o n c ep t o f te m p la te is im p le m e n te d in tw o w a y s (a ) b y h ig h e r

p ro b a b ilitie s o f f in d in g (s eq u en c e s o f) m o v e s a n d ev a lu a tio n s th an w ith p la in

c h u n k s a n d (b ) b y a d e cre a se in th e le v e l o f fu zz in e ss m ad e p o s sib le b y th e L T M

re p re se n ta tio n o f th e c o re o f th e p o sitio n a n d o f s lo ts

T h e le v e l o f re lia b ility o f th e in fo rm a tio n in th e m in d rsquos ey e is c a p tu re d b y a

ldquo fu z zin e s srdquo p a ra m e te r e x p re ss ed in a rb itr ary u n its T h re e m a in c o g n itiv e

fe a tu res ar e c a p tu red b y th is p a ra m ete r w o rk in g m e m o ry c a p a c ity a b ility to

m ain ta in a v isu o -s p atia l im ag e a n d su b je ctiv e e s tim a te o f th e r isk o f m ak in g a n

e rro r T h e fu z z in es s p a ram e ter is th e n as su m e d to o rig in ate b o th fro m th e

h a rd w a re a n d th e so ftw a re o f th e sy s tem It m a y v a ry d u r in g th e life tim e o f a

p la y er b e c a u se o f b io lo g ic a l m a tu ra tio n o r a g e in g an d m a y b e a ffe c ted b y

e x p e rim e n ta l m a n ip u latio n s T h e re a re th ree re a so n s w h y S E A R C H en d s a

se a rc h th e lev el o f fu z z in e s s is to o h ig h a n e v a lu atio n is p ro p o se d o r n o m o v e is

p ro p o s e d T h e id e a o f ex p ec ta tio n le v e l is n o t e x p lic itly p re se n t in th e m o d el b u t

it is im p lic it in th e p ro b a b ility v alu e s o f f in d in g fe atu re s e n d in g th e s ea rc h o f a n

e p iso d e e ith er b y p a tte rn re c o g n itio n o r b y th e a p p lica tio n o f h e u ristic s

S e le ctio n o f th e n ex t b a se -m o v e (a k e y c o n c ern o f N ew e ll amp S im o n 1 9 6 5 a n d

W ag n e r amp S c u rra h 1 9 7 1 ) is n o t ad d res se d b y S E A R C H w h ic h in g e n e ra l lac k s

th e s em a n tic in fo rm a tio n n e c es sa ry fo r su c h a se le c tio n F in a lly m e ta -se a rc h

w ith te m p la te s is n o t d ire c tly im p le m e n te d in S E A R C H b u t it is im p lic itly

300 GOBET

300

FIG 1 F lo w c h a rt o f S E A R C H

PATTERN -R ECOGN IT ION AND SEA RCH 301

301

F IG 2 E x a m p le s o f e p is o d e s g e n e ra te d b y S E A R C H

302 GOBET

re p re se n te d b y th e re la tiv e ly h ig h p ro b ab ility o f f in d in g (s eq u e n c e s o f) m o v es

a n d e v a lu atio n s w ith tem p la tes as c o m p are d w ith ch u n k s

The M ode lrsquos P aram e te rs

S E A R C H h as m a n y p a ra m ete rs a n d it is o f c o u rs e n e c es sa ry to se t u p a f ew o f

th e m w ith in d e p e n d e n t d a ta in o rd er to re d u c e th e n u m b e r o f d e g re e s o f fre e d o m

in th e m o d e l W h e n p o ss ib le I h a v e u s e d sim u la tio n s w ith th e C H R E S T (D e

G ro o t amp G o b e t 1 9 9 6 G o b e t 1 9 9 3 ) an d C H U M P (G o b e t amp Ja n s en 1 9 9 4 )

p ro g ram s to se t p a ra m e te r v a lu es C H R E S T is a p ro g ra m im p le m e n tin g as p e cts

o f T T a n d s im u la tin g n u m e ro u s e x p er im e n ts o n p e rc ep tio n an d m e m o ry in ch e s s

a n d C H U M P is a p ro g ra m p la y in g (w e ak ) c h e ss b y p u re p a tte rn re co g n itio n

N u m b e r o f C h u n k s a n d T e m p la te s T ab le 1 sh o w s th e v a lu es th at w ill b e

u s ed w ith th e S E A R C H m o d e l fo r th e se p a ra m ete rs T o c h o o se th e v a lu e s re la te d

to th e n u m b e r o f ch u n k s a n d te m p la tes th e c u rre n t v e rsio n o f C H R E S T h a s b e e n

e m p lo y e d T h e p ro b a b ility o f f in d in g a tem p la te w a s e stim ate d b y ru n n in g

C H R E S T o n 5 0 p o s itio n s ran d o m ly tak e n fro m M as ters rsquo g am e s T h e firs t lin e (0

c h u n k ) w a s ad d e d to g e t p re d ic tio n s a t th e n o v ic e lev e l W ith n e ts o f 1 0 0 0 0 0

1 2 0 0 0 0 a n d 1 5 0 0 0 0 c h u n k s th e p ara m ete rs w ere e stim ate d w ith th e b e s t-fit t in g

fu n c tio n s av a ilab le ( th e ldquo n o v ice rdquo v alu e s w ere n o t u se d ) T h e n u m b er o f te m p la tes

is ro u g h ly a lin e ar fu n c tio n o f th e n u m b er o f c h u n k s (r 2 = 9 7 ) T h e p ro b a b ility

o f f in d in g a tem p la te is a p p ro x im a tely a lo g -fu n c tio n o f th e n u m b e r o f c h u n k s

(r 2 = 9 4 )

H e u r is tic s C h u n k s T e m p la tes a n d T h e ir R e la tio n to th e P ro b a b ility o f

F in d in g M o v e s a n d E v a lu a tio n s T ab le 2 g iv e s th e v a lu e s u s ed in th e

sim u la tio n s fo r th e p a ra m ete rs re la te d to h e u ristic s c h u n k s a n d te m p la te s

H e u ris tic s in c lu d e sim p le se a rc h te c h n iq u e s (e g ldquo ta k e a p ie c e b a c k rdquo o r ldquoc h e c k

th e K in g rdquo ) a s w ell a s m o re a b stra c t ru le s (e g ldquoo c c u p y th e c en tre rdquo ) T h eir m a in

c h a rac te ris tic in co m p a riso n w ith c h u n k s an d tem p la te s is th a t th ey are g e n e ra l

a n d re q u ire so m e co n sc io u s c o m p u tatio n in o rd e r to p ro d u ce a m o v e T h e

a ss u m p tio n u n d e rly in g T a b le 2 is th at th e p aram e ters re la ted to h e u ristic s s ta y

ro u g h ly c o n sta n t w h ile th e o th e r p aram e te rs v a ry as a lo g arith m ic fu n c tio n o f th e

n u m b e r o f c h u n k s in th e n e t (A lo g arith m ic fu n ctio n h a s b e e n c h o se n to in d ica te

th a t ch u n k s y ie ld a d im in ish in g re tu rn as th e ir n u m b e r in c re a se s) T h e

a ss u m p tio n th a t th e n u m b e r o f h e u ristic s is c o n sta n t ac ro s s s k ill le v e ls se e m s

re a so n a b le (p e rh a p s w ith th e e x ce p tio n o f th e n o v ic e le v e l) a s m o s t c h e ss

M a ste rs rsquo k n o w le d g e is v e ry sp ec ific to c erta in a sp e c ts o f th e g a m e (D e G ro o t

1 9 4 6 )

T h e fo llo w in g c o n s id era tio n s w e re m ad e in se ttin g th e v alu e s g iv e n in

T ab le 2 I t w a s d ee m e d p lau sib le th a t th e p ro b a b ility o f f in d in g so m e h e u ristic in

a p o s itio n b e h ig h ( 9 5 ) a s w e ll a s th e p ro b a b ility o f f in d in g s o m e c h u n k F in ally

PATTERN -R ECOGN IT ION AND SEA RCH 303

TA BLE 1

The V a lu es o f th e 14 N e ts U sed in th e S im u la tio ns

P ro b a b i li ty o f

re c o g n is in g a t le as t

P ro p o r t io n o f o n e te m p la te g iv e n a

N u m b e r o f c h u n k s N u m b e r o f te m p la te s te m p la te s p o s i t io n

0 0 0 0 0 0 0 0

1 0 0 2 0 0 0 0 0 0 0

2 6 8 0 5 0 0 2 1 8 0

5 0 0 3 3 6 0 0 7 1 4 0

1 0 0 1 1 1 0 0 0 1 0 2 4 0

2 0 0 0 3 2 6 5 0 1 3 3 0 0

3 0 0 0 1 4 9 3 0 1 6 3 6 0

4 0 0 0 5 7 7 4 0 1 9 4 6 0

5 0 0 0 6 1 1 4 2 0 2 3 4 0 0

7 2 0 4 4 2 1 3 6 0 3 0 4 8 0

8 0 0 1 0 2 2 8 5 0 2 9 5 4 0

1 0 0 0 0 0 2 7 6 5 0 2 8 5 1 0

1 2 0 0 0 0 3 3 5 7 0 2 8 5 4 0

1 5 0 0 0 0 4 2 4 5 0 2 8 5 6 0

T h e v a lu e s b e lo w 1 0 0 0 0 0 c h u n k s w e r e ta k e n f ro m s im u la t io n s w ith C H R E S T th e o the rs

e x t ra p o la te d S e e te x t f o r d e ta ils

TA BLE 2

H eur is t ic s C hun ks Tem pla tes and Their Re la tion to th e P ro bab ility of Fin d in g

M oves and Evalu ta tio ns

T y p e H e u r is tic s C h u n k s T e m p la te s

P ro b a b i li ty o f e v o k in g a n 9 5 g (n _ c h u n k s 9 5 )a se e T a b le 1

h e u ri s t ic a c h u n k o r a te m p la te

P ro b a b i li ty o f f in d in g a m o v e 5 0 g (n _ c h u n k s 5 0 ) g (n _ c h u n k s 9 0 )

g ive n th a t a n h e u r is tic a c h u n k

o r a te m p la te h a s b e e n e v o k e d

P ro b a b i li ty o f f in d in g a n e v a lu a tio n 1 5 g (n _ c h u n k s 0 5 ) g (n _ c h u n k s 5 0 )

g iv e n th a t a n h e u ri s t ic a c h u n k o r

a te m p la te h a s b e e n e v o k e d

aT h e fu n c tio n g i s d e f in e d a s

g (n _ c h un k s p ro b ) = p ro b 0 2 lo g1 0

(n _ c h un k s ) i f n _ c h u n k s gt 0

a n d

g (n _ c h u n k s p ro b ) = 0 i f n _ c h u n k s = 0

w h e re n _ c h u n k s i s th e n u m b e r o f c h u n k s in a g iv e n n e t a n d p ro b i s a c o n s ta n t

303

304 GOBET

th e p ro b a b ility o f re c o g n isin g a te m p la te in a p o sitio n is sm a lle r a n d is g iv e n in

T ab le 1

T h e p ro b a b ility o f f in d in g a m o v e g iv e n a h e u ristic is s e t to 5 0 in d ic atin g th a t

h e u ristic s m a y fa il to p ro d u ce a m o v e h a lf o f th e tim e T h is is b e c a u se so m e

h e u ristic s m ay n o t y ie ld a m o v e a n d b ec a u se so m e p ro p o se d m o v es m a y b e

ille g a l T h e p ro b a b ility o f f in d in g a m o v e g iv en a tem p la te is h ig h p a rtly

re fle ctin g th e ric h s em a n tic k n o w le d g e an d th e in te r-te m p la te lin k s a s su m e d to

c h a rac te rise te m p la te s F o r th e p ro b a b ility o f f in d in g a m o v e g iv e n th a t a ch u n k

h a s b e en re co g n ise d I u se d th e p ara m e te r p ro b in th e fu n ctio n g (s ee T a b le 2 ) so

th a t i t a p p ro x im a te s th e d ata p ro d u c ed b y th e C H U M P p ro g ram (G o b et amp Ja n se n

1 9 9 4 ) E v a lu a tio n s a re su p p o s ed to b e h a rd er to le arn a n d th e re fo re h a rd e r to u se

th a n m o v es H e n ce th e ir p ro b a b ilit ie s a re lo w e r th a n th e co r res p o n d in g p ro b -

a b ilit ie s w ith m o v es A g a in fo llo w in g d irec tly fro m th e th e o ry te m p la te s o ffe r

th e b e st so u rce o f ev alu a tio n s

W ith re sp e c t to th e n u m b e r o f se q u e n tia l m o v e s p ro p o s ed c o u n ted in p lie s

(i e m o v e s fo r W h ite o r B la ck ) i t is as su m e d th a t h e u ristic s g iv e a cc e ss to o n ly

o n e m o v e w h ile c h u n k s a n d te m p late s y ie ld se q u e n c es o f m o v e s w h o se n u m b e r

fo llo w s a g e o m e tric p ro b a b ility d is tr ib u tio n (th e c h o ice o f th is d is tr ib u tio n w as

in sp ire d b y sta tis tic s ta k e n fro m C H U M P ) T h e lo n g e s t s eq u e n c e ( ca ll i t k ) h as a

fre q u e n c y o f 1 th e s e co n d -lo n g e st a fre q u en cy o f 2 th e th ird -lo n g e st a fre q u e n c y

o f 4 a n d so o n u n til th e sh o rte st se q u e n c e w h o s e len g th is 1 m o v e an d w h o se

fre q u e n c y is 2 (k ndash 1 ) T h e m a x im u m se q u e n ce o f m o v es w a s se t to 1 8 F in a lly

S E A R C H atte m p ts to g e n e ra te a m o v e b y p a ttern re c o g n itio n ( ch u n k o r te m p la te )

fo u r tim e s b e fo re u sin g a n h e u ristic

T im e a n d F u zzin e ss P a ra m ete rs T h e tim e p a ram e ter s fo r th e re sp e c tiv e

o p e ra tio n s w e re s et u sin g p la u sib le v a lu e s (se e T a b le 3 ) M o v e g en era tio n b y

p a tte rn re c o g n itio n (c h u n k o r te m p late ) is as su m e d to b e v e ry sh o rt (a few

h u n d re d m illis e co n d s) n o tim e c o st is u se d in th e m o d e l T h e tim e fo r c o m p u tin g

a m o v e-g en e ra tin g h e u ristic w a s s et to th e ra th e r lo n g 2 0 s ec o n d s mdash g en era tin g a

m o v e w ith o u t u sin g p a tte rn r ec o g n itio n re q u ires p u ttin g to g eth e r v a rio u s ty p e s o f

in fo rm a tio n a n d a s k s fo r m a n y ch e c k in g p ro c ed u res T h e tim e fo r c a rry in g o u t

o n e m o v e (o n c e g e n erate d ) in th e m in d rsquos e y e w a s s et to tw o s ec o n d s T h is is

c o m p atib le w ith S a a rilu o m a rsquos (1 9 8 9 ) d ata w h ic h sh o w th a t a b lin d fo ld ed M a ste r

c an fo llo w a g a m e d icta ted a t tw o se c o n d s a m o v e F in ally th e tim e fo r ca rry in g

o u t a n ev a lu a tio n b y h eu ris tic is s e t to 1 0 s e co n d s T h is ra th e r s h o rt tim e m a y b e

ju stif ie d b y th e fa c t th a t p la y e rs ty p ic a lly co n s id e r o n ly o n e (s u b jec tiv e ) a sp e c t o f

th e p o sitio n (D e G ro o t 1 9 4 6 ) a n d th at m an y e v a lu atio n s c a n b e g ro u n d ed o n th e

b a sis o f c lea r m a teria l lo ss e s

T h e fu z zin e ss lev el o f th e s y ste m is e x p re ss ed in a rb itra ry u n its I t s ta rts w ith

th e v a lu e z e ro a n d it is in c re a se d w h e n a m o v e is c a rrie d o u t in th e m in d rsquos e y e

a n d w h e n tim e is s p e n t a p p ly in g a n h e u ris tic W h e n a te m p la te is fo u n d th e

PATTERN -R ECOGN IT ION AND SEA RCH 305

fu z z in es s lev el is d e cre a se d a s p a rt o f th e in fo rm atio n m ay b e sto re d in L T M

d ire c tly fre e in g c ap ac ity in w o rk in g m e m o ry a n d in th e m in d rsquos ey e

S im u la t io n s w ith th e ldquo C anon ica l M ode lrdquo

T h e sim u latio n s d e sc rib ed in th is s ec tio n a re s tra ig h tfo rw a rd U s in g th e

p a ra m e te r v alu e s d is cu sse d e a rlie r I le t th e p ro g ra m s ea rc h 1 0 0 0 ep iso d e s fo r

e ac h n e t s iz e S u m m a ry v alu e s fo r m e a n d ep th o f se a rc h t im e ra tio d e p th tim e

a n d fu z zin e s s a s w e ll a s fo r g e n e ra tio n an d s to p co n d itio n s w e re c o m p u ted fo r

e ac h n e t s iz e

M e a n D e p th o f S e a r ch R a te o f S e a rc h a n d F u z zin e ss A cc o rd in g to

S E A R C H m ea n d e p th o f s ea rc h fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f

c h u n k s (se e F ig 3 a) If w e as su m e a co n sta n t ra te o f le a rn in g n e w c h u n k s a s is

c o m m o n p ra ctic e in so m e c o g n itiv e a rch ite c tu res (c f N e w e ll 1 9 9 0 ) a n d if w e

a ss u m e th a t s k ille d p la y e rs h a v e sp e n t m o re p rac tice a n d stu d y tim e th a n

u n s k ille d p la y e rs th e n m e an d e p th fo llo w s a p o w e r fu n c tio n o f s k ill as w e ll T h is

p re d ic tio n w h ic h is a t v ar ia n c e w ith H o ld in g rsquos p re d ic tio n (1 9 8 5 p 1 8 2 ) o f a

lin ea r in c rea s e is p artly co n siste n t w ith C h a rn e ss rsquos (1 9 8 1 ) p ro p o s a l th a t d e p th o f

se a rc h is n o t l in e arly re la ted to s k ill b u t th at th e re is a ce ilin g a t h ig h s k ill le v e ls

T h e re su lt is a ls o c o m p atib le w ith th e w e a k lin e ar re la tio n fo u n d in e m p ir ic a l

stu d ie s (C h a rn e ss 1 9 8 1 G o b e t in p re ss ) b e tw e e n m e a n d e p th o f se a rch a n d sk ill

le v el b e c a u se re stric te d ra n g e s o f th e c u rv e c a n b e a p p ro x im a ted b y a lin e a r

fu n c tio n T h e a b so lu te v alu e s a re a lso q u ite r ea so n ab le th ey ris e f ro m lo w d ep th s

(le ss th a n 1 p ly ) w ith n o ch u n k s (co r res p o n d in g to th e n o v ic e le v el) to a ro u n d 2 5

p lies w ith a sm a ll n et (1 0 0 0 c h u n k s ) an d th e n to a ro u n d 4 p lie s w ith ex p ert le v e l

(a ro u n d 3 0 0 0 0 c h u n k s a s e s tim a te d b y s im u la tio n s o n th e re ca ll tas k ) T h e y th e n

slo w ly (s av e fo r a f ew ra n d o m v a ria tio n s ) in c re a se to m o re th an 5 p lie s w ith n e t

la rg er th an 1 0 0 0 0 0 c h u n k s w h ic h c o rre sp o n d s to G ran d m a ste r le v e l H o ld in g

(1 9 8 5 ) c o m p u te d m e a n d e p th o f se a rch fo r d e G ro o trsquos (1 9 4 6 ) d a ta a n d fo u n d th a t

TA BLE 3

T im e and ldquo Fuzz in ess rdquo Param e ters U sed in th e

S im ula t io n s

T im e fo r c a r ry in g o u t a m o v e 2 s

T im e fo r c o m p u t in g m o v e -g e n e r a tin g h e u r is tic 2 0 s

T im e fo r c o m p u t in g e v a lu a t io n 1 0 s

U p p e r l im it o f fu z z in e ss 5 0

In c r e a se o f fu z z in e s s p e r m o v e 1

In c re a se o f f u z z in e ss p e r s e c o n d 2

D e c re a s e in fu z z in e ss d u e to te m p la te 5

306 GOBET

E x p e rts a n d G ra n d m as ters h a d res p e ctiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 8 a n d

5 3 T h e reg res sio n e q u a tio n d e riv e d f ro m C h a rn e ss rsquos (1 9 8 1 ) d ata y ie ld a n

a v e rag e d e p th o f se a rc h o f a b o u t 2 3 p lies a t th e 1 3 0 0 E L O 1 le v e l o f 4 1 a t th e

E x p e rt le v e l (2 0 0 0 E L O ) a n d o f 5 7 a t th e G ra n d m a s te r le v el U n fo rtu n a tely n o

stu d y te ste d p la y e rs ra n g in g fro m n o v ic es to G ran d m a ste rs an d S E A R C H rsquos

p re d ic tio n o f a p o w e r la w o f p rac tic e c an n o t b e te ste d (y e t) I w ill re p o rt la te r

sim u la tio n s a d d re ssin g d a ta co lle c ted b y S a arilu o m a (1 9 9 0 ) w h e re In tern atio n a l

M a ste rs a n d G ra n d m a s te rs te n d e d to s e arc h le s s th a n M as te rs

T h e ra te o f s ea rc h a lso fo llo w s a p o w e r fu n ctio n o f th e n u m b e r o f c h u n k s (se e

F ig 3 b ) D e G ro o t (1 9 4 6 ) C h arn es s (1 9 8 1 ) a n d G o b e t ( in p res s) a ll f o u n d th a t

stro n g p la y er s te n d e d to s e arc h fa ste r F o r ex a m p le G o b e t ( in p re s s) fo u n d th a t

h is M a ste rs E x p e rts C la ss A a n d C la s s B p lay e rs re sp e c tiv ely se arch e d 4 8 4 1

3 2 an d 3 4 n o d e s p e r m in u te S E A R C H rsquos v a lu es a re h ig h e r b u t s til l p la u s ib le

F o r ex am p le W a g n e r a n d S c u rra h rsquos (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r

m in u te N o te a lso th a t a ll th e ex p erim e n ts m e n tio n e d e a rlier h a v e u se d v e rb a l

p ro to c o ls w h ic h m ay h av e s lo w e d d o w n th e ra te o f se a rc h (c f E ric ss o n amp

S im o n 1 9 8 0 ) F in a lly th e ra te o f se arch m a y h av e b e e n u n d e res tim a ted in th e

lite ra tu re b ec a u se th e r a te o f g e n e ratin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d

b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l t im e H o w e v e r to ta l t im e in c lu d es

tim e n o t sp e n t in s e arc h ( fo r e x a m p le w h a t D e G ro o t c a lls th e ldquo firs t p h a se rdquo)

T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a riab le th e le v e l o f fu zz in e ss a t

w h ic h a se a rc h is e n d e d is m o re d if fic u lt to ju d g e b ec a u se lit tle is k n o w n a b o u t

th e ro le o f fu z z in es s in c h es s th in k in g A g ain S E A R C H p ro p o se s th a t th is

v a riab le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s ee F ig 3 c ) W ith la rg e r

n e ts e p iso d es te n d to b e e n d e d w ith lo w er le v els o f fu z z in e s s T h is su g g es ts th at

in g e n e ra l s tro n g p la y ers s h o u ld b e m o re c o n fid e n t in th e ir c alc u la tio n s as th e y

a re n o t a t th e e d g e o f th eir p o s sib ilitie s N o te th a t th e ra te o f ch an g e is ra th e r h ig h

fo r th is p o w er law w h ic h s u g g e sts th at it sh o u ld b e p o ss ib le to d e te c t i t

e x p erim e n tally

G e n e ra tio n o f M o ve s H o w is m o v e g en e ra tio n af fec te d b y sk ill le v e l A s

sh o w n in F ig 4 a S E A R C H m a k es c le a r p re d ic tio n s W ith sm a ll n u m b e rs o f

c h u n k s th e tim e -c o n s u m in g p ro ce s s o f g en e ra tin g m o v es b y h e u ristic s is

e m p lo y e d T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y ch u n k s

w h ic h is in tu rn d o m in a te d b y te m p la te g e n eratio n

1 T h e E L O ra t in g i s a n in te r v a l sc a le th a t ra n k s c o m p e t it io n c h e ss p la y e rs I ts s ta n d a rd de v ia t io n

(2 0 0 p o in ts) is o f te n in te r p re te d a s a m e a su r e o f sk i ll c la s s in c h e ss G r a n d m a s te r s a re n o rm a lly ra te d

a b o v e 2 5 0 0 In te rn a t io n a l M a s te r s a b o v e 2 4 0 0 M a s te r s a b o v e 2 2 0 0 a n d E x p e rt s a b o v e 2 0 0 0

B e lo w c la sse s (A B e tc ) d iv id e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in ts

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

296 GOBET

c o n d itio n s ca n h alt th e se a rc h o f a n e p iso d e T o b e g in w ith th e p ro b a b ility o f

m ak in g a n e rro r is to o h ig h P s y ch o lo g ic a lly th is p ro b a b ility is a fu n ctio n o f th e

fo rg e ttin g a n d in ter fer en c e r a te s in th e m in d rsquo s ey e P h e n o m e n o lo g ic a lly p lay e rs

p ro b a b ly a s se ss th is p ro b a b ility b y ta k in g in to a c c o u n t th e d e p th o f se a rc h

re a ch e d a n d b y e s tim a tin g th e ir fa m ilia rity w ith th e p o s itio n

A n o th e r re a so n to h a lt s ea rc h o c cu r s w h e n th e le v e l o f e x p e c tatio n fo r th e

p o s itio n is m et o r w h e n a f ea tu re o f th e p o s itio n (e g sa fe ty o f th e K in g ) w as

e v a lu a te d to b e lo w e r th a n its a d m iss ib le v a lu e (N e w e ll amp S im o n 1 9 7 2 ) T h is

le v el o f e x p e c ta tio n is p ro v id e d b y a c h u n k en c o u n te re d d u rin g e arlie r s ea rc h o r

b y e x p lic it ev a lu a tio n o f th e p o s itio n a n d w a s s to re d e ith e r in S T M o r w h e n

a v a ila b le in a te m p late s lo t A fin a l h a ltin g c o n d itio n is th a t a d e c isiv e e v e n t

o c c u rre d s u ch a s m a te im p o rta n t m a teria l g a in o r lo ss o r fu lfilm e n t o f a k e y

g o al

S e lec tin g th e N e x t B a s e -m o v e N o w co n s id er th e q u e stio n o f w h ic h b a se -

m o v e to se a rch n ex t w h en a le a f n o d e h a s b e e n re a ch ed A n y o f s ix m e c h an is m s

m ay b e e n g a g e d F irst if th e le a f w a s e v a lu ate d w ith a h ig h risk o f er ro r th e s am e

se q u e n c e o f m o v e s is se a rc h ed a g ain in o rd e r to o b ta in a m o re re lia b le e stim a te

S e c o n d th e sa m e s eq u en c e o f m o v e s m a y b e se a rch e d a g a in to m a k e s u re th a t i t

h a s b e e n sto re d in L T M T h ird if a tem p la te h a s b e e n re co g n ise d a m e ta -se a rc h

(s ee la te r) is c arr ie d o u t F o u rth th e re is a b ia s to g iv e p re fe ren ce to n o rm a l b as e -

m o v e s ea rly in se a rch a n d to u n u su a l b a s e-m o v e s la ter (N ew ell amp S im o n 1 9 7 2

p 7 2 3) F ifth a m ov e re ac h e d at a n y le v e l o f d e p th in s ea rch in g a lin e m a y b e trie d

a s a ca n d id a te m o v e in th e n ex t lin e S ix th if th e e v alu a tio n o f an e p iso d e g iv e s a

fa v o u ra b le re su lt its an aly s is is c o n tin u e d if th e ev a lu a tio n is u n fa v o u rab le a

d iffe re n t b a se -m o v e is ta k e n u p (N e w e ll amp S im o n 1 9 7 2 )

M e ta -s e a rc h w ith T e m p la te s (A b stra c t P la n n in g ) S e arc h m ay b e c arrie d o u t

n o t o n ly a t th e m o v e le v e l b u t a lso a t th e te m p la te le v el P lay e rs s o m e tim es

d e v e lo p a tre e se a rc h b y g e n eratin g k ey p o sitio n s (te m p la tes ) in s tea d o f

d e v e lo p in g a tree se arch b y g e n e ra tin g m o v e s (e g D e G ro o t 1 9 7 8 p 1 5 3 ) P ath s

b e tw e en k e y p o sitio n s c o n s is t o f m a cro -o p e ra to r s o r in u n s p ec ifie d o p e ra to r s

w h ic h w ill b e fil le d in a t a la te r s ta g e o f se a rch if th e le a f p o sitio n s a re ju d g e d

fa v o u ra b le T h is ty p e o f se arch is c o n tin g en t to th e p res e n ce in p la y ers rsquo L T M o f

te m p la tes su ffic ie n tly c lo se to th e p o s itio n a t h a n d K o ed in g e r a n d A n d e rs o n

(1 9 9 0 ) h a v e p ro p o se d a s im ilar id e a w ith re sp e c t to g eo m e try T h is m e ta -se a rc h

m ec h a n ism is a ls o sim ilar to th e ldquoa p p e rc e p tio n rdquo m e c h a n ism su g g es ted b y

S a a rilu o m a (1 9 9 0 1 9 9 2 )

Theo re t ica l Im po rta n ce o f Tem p la te s

O b v io u s ly m an y o f th e p ro ce s se s ju st d es c rib ed c a n b e im p le m e n te d w ith in th e

e ar lie r C T w ith o u t h y p o th e sisin g th e p re se n c e o f te m p la tes T e m p la tes a re

h o w e v e r im p o rta n t fo r s o m e o f th e k ey c o g n itiv e p ro c es se s in c h e ss b e c au se

PATTERN -R ECOGN IT ION AND SEA RCH 297

(a ) s lo ts a llo w in fo rm a tio n ab o u t s tra te g ic o r tac tica l th e m e s a s w e ll a s a b o u t

e v a lu a tio n o f th e p o sitio n to b e en co d e d in L T M rap id ly (b ) lin k s b e tw e e n

te m p la tes a llo w fo r ldquo m e ta -se a rc h rdquo (c ) in fo rm a tio n s to re d b o th in th e c o re a n d in

th e slo ts o f th e te m p late c o m p en sa tes fo r d e c a y an d in te rfe re n c e in th e m in d rsquos

e y e as it m a y b e u se d to re in sta te fa d in g in fo rm a tio n T h is c o m p e n sa tio n

m ec h a n ism is p ar tic u la rly u se fu l w h e n p e rce p tu a l in fo rm a tio n fro m th e ex te rn a l

b o a rd is u n re liab le fo r ex a m p le b e ca u s e se v e ra l m o v e s h a v e b e en c arr ie d o u t in

th e m in d rsquos e y e

Em p ir ica l D a ta Sup po rtin g th e TT A ccoun t o f Sea rchand Pa tte rn R e cogn itio n

In th is se c tio n T T is q u alita tiv e ly ap p lie d to s o m e o f th e k ey d a ta f ro m e m p ir ic a l

stu d ie s o f ch e s s p ro b le m s o lv in g Q u a n tita tiv e a s se ss m e n t w ill b e th e to p ic o f

th e fo llo w in g se c tio n I h a v e sh o w n e lse w h e re (G o b e t 1 9 9 6 ) th at th e p re d ic tio n s

o f T T a re w e ll su p p o rted b y e m p ir ic a l d a ta fro m re se a rch o n m e m o ry a n d

p e rce p tio n

In c re a sin g th e n u m b e r o f c h u n k s a n d te m p la te s h a s tw o o p p o site ef fec ts w ith

re sp e c t to se a rch (G o b e t in p res s) O n th e o n e h a n d d e ep s e arc h is fac ilita te d as

c o m p are d w ith th e m o re co m p u ta tio n a lly e x p e n s iv e w e a k m e th o d s b e c au se

p a tte rn re c o g n itio n is a ra p id p ro c es s a n d b e ca u s e se q u e n c e s o f m o v es m a y b e

le arn e d an d su g g e ste d b y c h u n k s O n th e o th er h a n d th e n ee d fo r d e e p se a rc h

o fte n d isa p p e ar s b e ca u s e e v a lu atio n s su g g e ste d b y p a tte rn re c o g n itio n m a y b e

m o re re lia b le th a n e v a lu atio n s co m p u te d b y w e a k m eth o d s T h e s e tw o o p p o site

e ffe cts c a n e x p la in w h y th e sk ill d iffe re n c e s in a v e rag e d e p th o f se a rc h a re sm all

P a tte rn re co g n itio n a llo w s stro n g p la y e rs to b e h ig h ly s e le c tiv e in th e ir s ea rc h

T h is c a n b e s e en b o th in th e ra p id w a y M a s te rs ze ro in to th e k e y as p e cts o f a

p o s itio n (D e G ro o t 1 9 4 6 ) an d in th e w ay e y e m o v e m e n ts d iffe r a s a fu n c tio n o f

sk ill d u rin g th e firs t s ec o n d s o f th e p e rc ep tio n o f a p o sitio n (D e G ro o t amp G o b et

1 9 9 6 ) A d d itio n a l e v id e n ce is p ro v id e d b y S a a rilu o m a (1 9 9 0 ) w h o h a s sh o w n

th a t p la y e rs ch o o se ste re o ty p e d so lu tio n s in p ro b le m s w h e re fa ste r ( in th e

n u m b e r o f m o v es to r ea c h m a te) b u t u n c o m m o n so lu tio n s a re p re s en t T h e se d a ta

a d d s u p p o rt to T T b e c a u se p a ttern re co g n itio n lie s a t i ts c o re

F u r th er s tro n g e v id e n ce fo r th e ro le o f p atte rn re c o g n itio n is th a t M as te rs c a n

p la y s ev e ra l o p p o n en ts s im u lta n eo u sly a t a s tre n g th c lo se to th at in o n e -a g ain s t-

o n e p lay I t is in te re stin g th at in s im u lta n eo u s g a m e s th ey te n d to p la y ldquon o rm a lrdquo

m o v e s a n d re ly o n o p p o n e n ts rsquo e rro rs (G o b e t amp S im o n 1 9 9 6 c ) N o rm a l m o v es

m ay c o rre sp o n d to th e ty p e o f m o v e s su g g e ste d b y c h u n k s an d tem p la te s

A fea tu re o f c h es s ex p e rtise c a p tu re d u n iq u e ly b y T T is th e h ig h le v e ls a t

w h ic h ch e s s p lay e rs o rg a n is e th e ir k n o w le d g e D e G ro o t (1 9 4 6 ) p ro p o s e d th a t

p la y er s o rg an is e p o sitio n s a ro u n d la rg e ldquo c o m p le x e srdquo b ig g e r th a n th e c h u n k s th a t

w e re la te r p ro p o se d b y C h a se a n d S im o n (1 9 7 3 ) D e G ro o t a lso su g g es ted a s d id

C o o k e e t a l (1 9 9 3 ) th a t p la y e rs re p re s en t in fo rm a tio n a t a c o n c e p tu a l lev el In

p a rticu la r D e G ro o t (1 9 4 6 ) p ro p o se d th a t M a ste rsrsquo d e sc rip tio n s o f g am e s a re

298 GOBET

c en tred a ro u n d k ey p o sitio n s o f th e g a m e T T o ffe rs th eo retic al s tru c tu res

(te m p la te s) th a t co u ld a c c o u n t fo r p lay ers rsquo larg e c o m p le x es h ig h - le v e l re p re -

se n ta tio n s a n d k e y p o sitio n s T T a lso o ff ers m e ch a n ism s b as e d o n f req u en c y o f

o c c u rre n ce s e x p la in in g h o w th e s e h ig h - le v e l re p re se n ta tio n s a re d ev elo p e d a n d

m ec h a n ism s b a se d o n d isc rim in a tio n p ro c e sse s e x p la in in g h o w th ey c o u ld b e

a c ce ss e d ra p id ly

T T is a lso co m p a tib le w ith re su lts fro m e x p er im e n ts u s in g p o s itio n s fo r w h ic h

a cc e ss to k n o w le d g e is d iffic u lt In H o ld in g a n d R e y n o ld s rsquo (1 9 8 2 ) e x p e rim e n t

c h e ss s k ill d id n o t c o rr ela te w ith th e re c a ll o f s e m i-ra n d o m p o s itio n s sh o w n fo r a

fe w se co n d s b u t eff ec tiv en es s o f th e s ea rc h fo r th e b e st m o v e in th es e p o s itio n s

d id c o rr ela te w ith s k ill T T o f fer s a n ex p la n a tio n fo r th e fa c t th a t th e re w a s a

stro n g c o rre la tio n b e tw e en sk ill le v e l a n d q u a lity o f m o v e p ro p o se d P lay e rs

re c u rsiv e ly g e n e ra te a m o v e th ro u g h w ea k m e th o d s w h en n o c h u n k is

re c o g n ise d u n til o n e o f th e h a ltin g co n d itio n s (m en tio n e d e a rlier ) a p p lie s T h e n

g iv e n th eir la rg e r d ata b a se o f c h u n k s s tro n g p la y e rs a re m o re lik e ly th a n w e a k

p la y er s to f in d a u s efu l p a tte rn in p o sitio n s th a t h a v e b ee n n e w ly u p d ate d in th e

m in d rsquos e y e a n d th e re fo re a re m o re lik e ly to f in d g o o d m o v e s in th eir se a rch

I m en tio n e d e a rlier th at E ric ss o n a n d K in tsc h (1 9 9 5 ) p ro p o s ed m ec h a n ism s

(re trie v al s tru c tu re a n d ela b o ra tio n s o f L T M sc h e m a s ) th a t e n c o d e in fo rm a tio n

q u ic k ly a n d re lia b ly B y c o n tra st th e e n c o d in g c a p a c ity o f te m p la te s is r e la tiv ely

w e a k In p a rtic u la r T T p re d icts th at th e sa m e te m p la te m a y s o m e tim e s b e u se d to

e n c o d e s e v era l s im ilar p o sitio n s th u s in c re as in g th e ris k o f in terf ere n c e as se a rc h

p ro g re s se s A s a co n se q u e n ce a n d c o n trary to L T W M T rsquos p re d ic tio n s p lay e rs

sh o u ld o fte n re v isit p o sitio n s b y g e n era tin g m o v es in s tea d o f a cc e ss in g th e m

d ire ctly fro m m em o ry T h is is w h at p la y e rsmdash e v e n m a ste rs mdash d o (D e G ro o t

1 9 4 6 ) F in a lly T T m a y h a v e s o m e th in g to sa y a b o u t e rro rs in c h e ss K ro g iu s

(1 9 7 6 ) m e n tio n s th a t er ro rs o f te n o c c u r w h e n a m o v e h a s ca u s ed im p o rta n t

c h a n g es in th e p o s itio n T h is m a y b e d u e to p la y e rsrsquo in a b ility to re c o g n ise th a t a

p re v io u sly a d eq u ate te m p late h as b ec o m e in a d e q u a te

In s u m m a ry T T o ffe rs a g o o d q u alita tiv e a c co u n t o f s e v eral im p o rtan t c h e ss

p h e n o m en a I t is n o w tim e to tu rn to m o re o b je c tiv e q u an tita tiv e te sts o f th e

th eo ry

A COM PUTER M ODE L O F S EARCH IN CH ESS

In th e re m a in d e r o f th is p a p e r I p re s en t a c o m p u te r m o d e l c a lled S E A R C H

w h ic h im p le m e n ts T T in so m e d e ta il I f irs t d e s crib e th e im p le m en ta tio n o f

S E A R C H m a k in g cle a r w h a t a s p ec ts o f T T h a v e b e e n in c lu d ed a n d th en d isc u ss

its b e h a v io u r w ith r es p e ct to h u m a n d a ta

O ve rv iew o f M ode l

F u ll im p le m e n ta tio n o f T T a s a c h e ss-p la y in g c o m p u ter p ro g ram w o u ld b e a

m ajo r ta sk mdash th is d iffic u lty is d e m o n stra te d b y th e fa c t th a t n o c o m p le te co m p u te r

m o d e l o f ch e s s c o g n itio n in c lu d in g p e rc e p tio n m em o ry a n d p ro b le m so lv in g

PATTERN -R ECOGN IT ION AND SEA RCH 299

h a s e v e r b e e n d e v elo p e d I p u rs u e d a lim ited a im a co m p u te r m o d el th a t c o n tain s

so m e o f th e im p o rta n t p aram e te rs o f T T a n d th a t co m p u te s k e y b e h a v io u ra l

v a ria b le s T h is m o d el d o e s n o t c o n stitu te a co m p le te im p le m e n ta tio n o f th e

th e o ry (it d o e s n o t s ea rc h o r e v a lu a te c h e ss p o sitio n s) b u t is d e ta ile d en o u g h to

o ffe r a g o o d te st o f so m e a s p ec ts o f T T I t is s o b e rin g to n o tic e th a t e v e n th is

p a rtia l im p lem e n tatio n o f th e th e o ry is q u ite c o m p le x a n d re q u ire s m a n y

p a ra m e te rs T h is is th e p rice o f a v o id in g th e v ag u en e s s o f v e rb al th e o ris in g

The M a in P rob lem -so lv in g Loop

T h e m ain in te re st o f th e m o d el is in th e in te ra c tio n b etw ee n p atte rn re c o g n itio n

a n d s ea rc h T h e m o d e l g e n e ra tes in d e p en d en t ep is o d es fo llo w in g se v e ral ru les

fo r g e n eratin g m o v e s a n d ch o o sin g sto p co n d itio n s C o m p atib le w ith m o s t

h u m an p ro to co ls th e p ro g ra m c o n sid e rs o n ly o n e b ra n c h w ith in a n ep is o d e (th u s

th e re is n o b ra n c h in g p o in t w ith in a n e p iso d e) A s illu stra te d in F ig 1 th e m o d e l

is c lo se to th e d es crip tio n o f T T g iv en e a rlie r in th is p a p e r T h e v ario u s c o n d itio n s

a n d o p e ra tio n s in S E A R C H a re re p re se n te d as p ro b a b ilit ie s o r p ro b ab ility

d istr ib u tio n s an d n o t a s a ctu a l c h e ss m o v e s e v a lu atio n s o r s y m b o lic s tru c tu res

in S T M o r in th e m in d rsquos e y e

A tra c e o f S E A R C H is sh o w n in F ig 2 T h e an aly s is w ill c e n tre o n th e

fo llo w in g v a ria b les a s a fu n c tio n o f th e n u m b e r o f c h u n k s ra te o f g en e ra tin g a

m o v e le v el o f fu z zin e ss in th e m in d rsquos e y e w h en a n e p is o d e is e n d e d m e an d e p th

o f s ea rc h m eth o d s u se d fo r g en e ra tin g a m o v e a n d m eth o d s u se d fo r s to p p in g a n

e p iso d e

T h e c o n c ep t o f te m p la te is im p le m e n te d in tw o w a y s (a ) b y h ig h e r

p ro b a b ilitie s o f f in d in g (s eq u en c e s o f) m o v e s a n d ev a lu a tio n s th an w ith p la in

c h u n k s a n d (b ) b y a d e cre a se in th e le v e l o f fu zz in e ss m ad e p o s sib le b y th e L T M

re p re se n ta tio n o f th e c o re o f th e p o sitio n a n d o f s lo ts

T h e le v e l o f re lia b ility o f th e in fo rm a tio n in th e m in d rsquos ey e is c a p tu re d b y a

ldquo fu z zin e s srdquo p a ra m e te r e x p re ss ed in a rb itr ary u n its T h re e m a in c o g n itiv e

fe a tu res ar e c a p tu red b y th is p a ra m ete r w o rk in g m e m o ry c a p a c ity a b ility to

m ain ta in a v isu o -s p atia l im ag e a n d su b je ctiv e e s tim a te o f th e r isk o f m ak in g a n

e rro r T h e fu z z in es s p a ram e ter is th e n as su m e d to o rig in ate b o th fro m th e

h a rd w a re a n d th e so ftw a re o f th e sy s tem It m a y v a ry d u r in g th e life tim e o f a

p la y er b e c a u se o f b io lo g ic a l m a tu ra tio n o r a g e in g an d m a y b e a ffe c ted b y

e x p e rim e n ta l m a n ip u latio n s T h e re a re th ree re a so n s w h y S E A R C H en d s a

se a rc h th e lev el o f fu z z in e s s is to o h ig h a n e v a lu atio n is p ro p o se d o r n o m o v e is

p ro p o s e d T h e id e a o f ex p ec ta tio n le v e l is n o t e x p lic itly p re se n t in th e m o d el b u t

it is im p lic it in th e p ro b a b ility v alu e s o f f in d in g fe atu re s e n d in g th e s ea rc h o f a n

e p iso d e e ith er b y p a tte rn re c o g n itio n o r b y th e a p p lica tio n o f h e u ristic s

S e le ctio n o f th e n ex t b a se -m o v e (a k e y c o n c ern o f N ew e ll amp S im o n 1 9 6 5 a n d

W ag n e r amp S c u rra h 1 9 7 1 ) is n o t ad d res se d b y S E A R C H w h ic h in g e n e ra l lac k s

th e s em a n tic in fo rm a tio n n e c es sa ry fo r su c h a se le c tio n F in a lly m e ta -se a rc h

w ith te m p la te s is n o t d ire c tly im p le m e n te d in S E A R C H b u t it is im p lic itly

300 GOBET

300

FIG 1 F lo w c h a rt o f S E A R C H

PATTERN -R ECOGN IT ION AND SEA RCH 301

301

F IG 2 E x a m p le s o f e p is o d e s g e n e ra te d b y S E A R C H

302 GOBET

re p re se n te d b y th e re la tiv e ly h ig h p ro b ab ility o f f in d in g (s eq u e n c e s o f) m o v es

a n d e v a lu atio n s w ith tem p la tes as c o m p are d w ith ch u n k s

The M ode lrsquos P aram e te rs

S E A R C H h as m a n y p a ra m ete rs a n d it is o f c o u rs e n e c es sa ry to se t u p a f ew o f

th e m w ith in d e p e n d e n t d a ta in o rd er to re d u c e th e n u m b e r o f d e g re e s o f fre e d o m

in th e m o d e l W h e n p o ss ib le I h a v e u s e d sim u la tio n s w ith th e C H R E S T (D e

G ro o t amp G o b e t 1 9 9 6 G o b e t 1 9 9 3 ) an d C H U M P (G o b e t amp Ja n s en 1 9 9 4 )

p ro g ram s to se t p a ra m e te r v a lu es C H R E S T is a p ro g ra m im p le m e n tin g as p e cts

o f T T a n d s im u la tin g n u m e ro u s e x p er im e n ts o n p e rc ep tio n an d m e m o ry in ch e s s

a n d C H U M P is a p ro g ra m p la y in g (w e ak ) c h e ss b y p u re p a tte rn re co g n itio n

N u m b e r o f C h u n k s a n d T e m p la te s T ab le 1 sh o w s th e v a lu es th at w ill b e

u s ed w ith th e S E A R C H m o d e l fo r th e se p a ra m ete rs T o c h o o se th e v a lu e s re la te d

to th e n u m b e r o f ch u n k s a n d te m p la tes th e c u rre n t v e rsio n o f C H R E S T h a s b e e n

e m p lo y e d T h e p ro b a b ility o f f in d in g a tem p la te w a s e stim ate d b y ru n n in g

C H R E S T o n 5 0 p o s itio n s ran d o m ly tak e n fro m M as ters rsquo g am e s T h e firs t lin e (0

c h u n k ) w a s ad d e d to g e t p re d ic tio n s a t th e n o v ic e lev e l W ith n e ts o f 1 0 0 0 0 0

1 2 0 0 0 0 a n d 1 5 0 0 0 0 c h u n k s th e p ara m ete rs w ere e stim ate d w ith th e b e s t-fit t in g

fu n c tio n s av a ilab le ( th e ldquo n o v ice rdquo v alu e s w ere n o t u se d ) T h e n u m b er o f te m p la tes

is ro u g h ly a lin e ar fu n c tio n o f th e n u m b er o f c h u n k s (r 2 = 9 7 ) T h e p ro b a b ility

o f f in d in g a tem p la te is a p p ro x im a tely a lo g -fu n c tio n o f th e n u m b e r o f c h u n k s

(r 2 = 9 4 )

H e u r is tic s C h u n k s T e m p la tes a n d T h e ir R e la tio n to th e P ro b a b ility o f

F in d in g M o v e s a n d E v a lu a tio n s T ab le 2 g iv e s th e v a lu e s u s ed in th e

sim u la tio n s fo r th e p a ra m ete rs re la te d to h e u ristic s c h u n k s a n d te m p la te s

H e u ris tic s in c lu d e sim p le se a rc h te c h n iq u e s (e g ldquo ta k e a p ie c e b a c k rdquo o r ldquoc h e c k

th e K in g rdquo ) a s w ell a s m o re a b stra c t ru le s (e g ldquoo c c u p y th e c en tre rdquo ) T h eir m a in

c h a rac te ris tic in co m p a riso n w ith c h u n k s an d tem p la te s is th a t th ey are g e n e ra l

a n d re q u ire so m e co n sc io u s c o m p u tatio n in o rd e r to p ro d u ce a m o v e T h e

a ss u m p tio n u n d e rly in g T a b le 2 is th at th e p aram e ters re la ted to h e u ristic s s ta y

ro u g h ly c o n sta n t w h ile th e o th e r p aram e te rs v a ry as a lo g arith m ic fu n c tio n o f th e

n u m b e r o f c h u n k s in th e n e t (A lo g arith m ic fu n ctio n h a s b e e n c h o se n to in d ica te

th a t ch u n k s y ie ld a d im in ish in g re tu rn as th e ir n u m b e r in c re a se s) T h e

a ss u m p tio n th a t th e n u m b e r o f h e u ristic s is c o n sta n t ac ro s s s k ill le v e ls se e m s

re a so n a b le (p e rh a p s w ith th e e x ce p tio n o f th e n o v ic e le v e l) a s m o s t c h e ss

M a ste rs rsquo k n o w le d g e is v e ry sp ec ific to c erta in a sp e c ts o f th e g a m e (D e G ro o t

1 9 4 6 )

T h e fo llo w in g c o n s id era tio n s w e re m ad e in se ttin g th e v alu e s g iv e n in

T ab le 2 I t w a s d ee m e d p lau sib le th a t th e p ro b a b ility o f f in d in g so m e h e u ristic in

a p o s itio n b e h ig h ( 9 5 ) a s w e ll a s th e p ro b a b ility o f f in d in g s o m e c h u n k F in ally

PATTERN -R ECOGN IT ION AND SEA RCH 303

TA BLE 1

The V a lu es o f th e 14 N e ts U sed in th e S im u la tio ns

P ro b a b i li ty o f

re c o g n is in g a t le as t

P ro p o r t io n o f o n e te m p la te g iv e n a

N u m b e r o f c h u n k s N u m b e r o f te m p la te s te m p la te s p o s i t io n

0 0 0 0 0 0 0 0

1 0 0 2 0 0 0 0 0 0 0

2 6 8 0 5 0 0 2 1 8 0

5 0 0 3 3 6 0 0 7 1 4 0

1 0 0 1 1 1 0 0 0 1 0 2 4 0

2 0 0 0 3 2 6 5 0 1 3 3 0 0

3 0 0 0 1 4 9 3 0 1 6 3 6 0

4 0 0 0 5 7 7 4 0 1 9 4 6 0

5 0 0 0 6 1 1 4 2 0 2 3 4 0 0

7 2 0 4 4 2 1 3 6 0 3 0 4 8 0

8 0 0 1 0 2 2 8 5 0 2 9 5 4 0

1 0 0 0 0 0 2 7 6 5 0 2 8 5 1 0

1 2 0 0 0 0 3 3 5 7 0 2 8 5 4 0

1 5 0 0 0 0 4 2 4 5 0 2 8 5 6 0

T h e v a lu e s b e lo w 1 0 0 0 0 0 c h u n k s w e r e ta k e n f ro m s im u la t io n s w ith C H R E S T th e o the rs

e x t ra p o la te d S e e te x t f o r d e ta ils

TA BLE 2

H eur is t ic s C hun ks Tem pla tes and Their Re la tion to th e P ro bab ility of Fin d in g

M oves and Evalu ta tio ns

T y p e H e u r is tic s C h u n k s T e m p la te s

P ro b a b i li ty o f e v o k in g a n 9 5 g (n _ c h u n k s 9 5 )a se e T a b le 1

h e u ri s t ic a c h u n k o r a te m p la te

P ro b a b i li ty o f f in d in g a m o v e 5 0 g (n _ c h u n k s 5 0 ) g (n _ c h u n k s 9 0 )

g ive n th a t a n h e u r is tic a c h u n k

o r a te m p la te h a s b e e n e v o k e d

P ro b a b i li ty o f f in d in g a n e v a lu a tio n 1 5 g (n _ c h u n k s 0 5 ) g (n _ c h u n k s 5 0 )

g iv e n th a t a n h e u ri s t ic a c h u n k o r

a te m p la te h a s b e e n e v o k e d

aT h e fu n c tio n g i s d e f in e d a s

g (n _ c h un k s p ro b ) = p ro b 0 2 lo g1 0

(n _ c h un k s ) i f n _ c h u n k s gt 0

a n d

g (n _ c h u n k s p ro b ) = 0 i f n _ c h u n k s = 0

w h e re n _ c h u n k s i s th e n u m b e r o f c h u n k s in a g iv e n n e t a n d p ro b i s a c o n s ta n t

303

304 GOBET

th e p ro b a b ility o f re c o g n isin g a te m p la te in a p o sitio n is sm a lle r a n d is g iv e n in

T ab le 1

T h e p ro b a b ility o f f in d in g a m o v e g iv e n a h e u ristic is s e t to 5 0 in d ic atin g th a t

h e u ristic s m a y fa il to p ro d u ce a m o v e h a lf o f th e tim e T h is is b e c a u se so m e

h e u ristic s m ay n o t y ie ld a m o v e a n d b ec a u se so m e p ro p o se d m o v es m a y b e

ille g a l T h e p ro b a b ility o f f in d in g a m o v e g iv en a tem p la te is h ig h p a rtly

re fle ctin g th e ric h s em a n tic k n o w le d g e an d th e in te r-te m p la te lin k s a s su m e d to

c h a rac te rise te m p la te s F o r th e p ro b a b ility o f f in d in g a m o v e g iv e n th a t a ch u n k

h a s b e en re co g n ise d I u se d th e p ara m e te r p ro b in th e fu n ctio n g (s ee T a b le 2 ) so

th a t i t a p p ro x im a te s th e d ata p ro d u c ed b y th e C H U M P p ro g ram (G o b et amp Ja n se n

1 9 9 4 ) E v a lu a tio n s a re su p p o s ed to b e h a rd er to le arn a n d th e re fo re h a rd e r to u se

th a n m o v es H e n ce th e ir p ro b a b ilit ie s a re lo w e r th a n th e co r res p o n d in g p ro b -

a b ilit ie s w ith m o v es A g a in fo llo w in g d irec tly fro m th e th e o ry te m p la te s o ffe r

th e b e st so u rce o f ev alu a tio n s

W ith re sp e c t to th e n u m b e r o f se q u e n tia l m o v e s p ro p o s ed c o u n ted in p lie s

(i e m o v e s fo r W h ite o r B la ck ) i t is as su m e d th a t h e u ristic s g iv e a cc e ss to o n ly

o n e m o v e w h ile c h u n k s a n d te m p late s y ie ld se q u e n c es o f m o v e s w h o se n u m b e r

fo llo w s a g e o m e tric p ro b a b ility d is tr ib u tio n (th e c h o ice o f th is d is tr ib u tio n w as

in sp ire d b y sta tis tic s ta k e n fro m C H U M P ) T h e lo n g e s t s eq u e n c e ( ca ll i t k ) h as a

fre q u e n c y o f 1 th e s e co n d -lo n g e st a fre q u en cy o f 2 th e th ird -lo n g e st a fre q u e n c y

o f 4 a n d so o n u n til th e sh o rte st se q u e n c e w h o s e len g th is 1 m o v e an d w h o se

fre q u e n c y is 2 (k ndash 1 ) T h e m a x im u m se q u e n ce o f m o v es w a s se t to 1 8 F in a lly

S E A R C H atte m p ts to g e n e ra te a m o v e b y p a ttern re c o g n itio n ( ch u n k o r te m p la te )

fo u r tim e s b e fo re u sin g a n h e u ristic

T im e a n d F u zzin e ss P a ra m ete rs T h e tim e p a ram e ter s fo r th e re sp e c tiv e

o p e ra tio n s w e re s et u sin g p la u sib le v a lu e s (se e T a b le 3 ) M o v e g en era tio n b y

p a tte rn re c o g n itio n (c h u n k o r te m p late ) is as su m e d to b e v e ry sh o rt (a few

h u n d re d m illis e co n d s) n o tim e c o st is u se d in th e m o d e l T h e tim e fo r c o m p u tin g

a m o v e-g en e ra tin g h e u ristic w a s s et to th e ra th e r lo n g 2 0 s ec o n d s mdash g en era tin g a

m o v e w ith o u t u sin g p a tte rn r ec o g n itio n re q u ires p u ttin g to g eth e r v a rio u s ty p e s o f

in fo rm a tio n a n d a s k s fo r m a n y ch e c k in g p ro c ed u res T h e tim e fo r c a rry in g o u t

o n e m o v e (o n c e g e n erate d ) in th e m in d rsquos e y e w a s s et to tw o s ec o n d s T h is is

c o m p atib le w ith S a a rilu o m a rsquos (1 9 8 9 ) d ata w h ic h sh o w th a t a b lin d fo ld ed M a ste r

c an fo llo w a g a m e d icta ted a t tw o se c o n d s a m o v e F in ally th e tim e fo r ca rry in g

o u t a n ev a lu a tio n b y h eu ris tic is s e t to 1 0 s e co n d s T h is ra th e r s h o rt tim e m a y b e

ju stif ie d b y th e fa c t th a t p la y e rs ty p ic a lly co n s id e r o n ly o n e (s u b jec tiv e ) a sp e c t o f

th e p o sitio n (D e G ro o t 1 9 4 6 ) a n d th at m an y e v a lu atio n s c a n b e g ro u n d ed o n th e

b a sis o f c lea r m a teria l lo ss e s

T h e fu z zin e ss lev el o f th e s y ste m is e x p re ss ed in a rb itra ry u n its I t s ta rts w ith

th e v a lu e z e ro a n d it is in c re a se d w h e n a m o v e is c a rrie d o u t in th e m in d rsquos e y e

a n d w h e n tim e is s p e n t a p p ly in g a n h e u ris tic W h e n a te m p la te is fo u n d th e

PATTERN -R ECOGN IT ION AND SEA RCH 305

fu z z in es s lev el is d e cre a se d a s p a rt o f th e in fo rm atio n m ay b e sto re d in L T M

d ire c tly fre e in g c ap ac ity in w o rk in g m e m o ry a n d in th e m in d rsquos ey e

S im u la t io n s w ith th e ldquo C anon ica l M ode lrdquo

T h e sim u latio n s d e sc rib ed in th is s ec tio n a re s tra ig h tfo rw a rd U s in g th e

p a ra m e te r v alu e s d is cu sse d e a rlie r I le t th e p ro g ra m s ea rc h 1 0 0 0 ep iso d e s fo r

e ac h n e t s iz e S u m m a ry v alu e s fo r m e a n d ep th o f se a rc h t im e ra tio d e p th tim e

a n d fu z zin e s s a s w e ll a s fo r g e n e ra tio n an d s to p co n d itio n s w e re c o m p u ted fo r

e ac h n e t s iz e

M e a n D e p th o f S e a r ch R a te o f S e a rc h a n d F u z zin e ss A cc o rd in g to

S E A R C H m ea n d e p th o f s ea rc h fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f

c h u n k s (se e F ig 3 a) If w e as su m e a co n sta n t ra te o f le a rn in g n e w c h u n k s a s is

c o m m o n p ra ctic e in so m e c o g n itiv e a rch ite c tu res (c f N e w e ll 1 9 9 0 ) a n d if w e

a ss u m e th a t s k ille d p la y e rs h a v e sp e n t m o re p rac tice a n d stu d y tim e th a n

u n s k ille d p la y e rs th e n m e an d e p th fo llo w s a p o w e r fu n c tio n o f s k ill as w e ll T h is

p re d ic tio n w h ic h is a t v ar ia n c e w ith H o ld in g rsquos p re d ic tio n (1 9 8 5 p 1 8 2 ) o f a

lin ea r in c rea s e is p artly co n siste n t w ith C h a rn e ss rsquos (1 9 8 1 ) p ro p o s a l th a t d e p th o f

se a rc h is n o t l in e arly re la ted to s k ill b u t th at th e re is a ce ilin g a t h ig h s k ill le v e ls

T h e re su lt is a ls o c o m p atib le w ith th e w e a k lin e ar re la tio n fo u n d in e m p ir ic a l

stu d ie s (C h a rn e ss 1 9 8 1 G o b e t in p re ss ) b e tw e e n m e a n d e p th o f se a rch a n d sk ill

le v el b e c a u se re stric te d ra n g e s o f th e c u rv e c a n b e a p p ro x im a ted b y a lin e a r

fu n c tio n T h e a b so lu te v alu e s a re a lso q u ite r ea so n ab le th ey ris e f ro m lo w d ep th s

(le ss th a n 1 p ly ) w ith n o ch u n k s (co r res p o n d in g to th e n o v ic e le v el) to a ro u n d 2 5

p lies w ith a sm a ll n et (1 0 0 0 c h u n k s ) an d th e n to a ro u n d 4 p lie s w ith ex p ert le v e l

(a ro u n d 3 0 0 0 0 c h u n k s a s e s tim a te d b y s im u la tio n s o n th e re ca ll tas k ) T h e y th e n

slo w ly (s av e fo r a f ew ra n d o m v a ria tio n s ) in c re a se to m o re th an 5 p lie s w ith n e t

la rg er th an 1 0 0 0 0 0 c h u n k s w h ic h c o rre sp o n d s to G ran d m a ste r le v e l H o ld in g

(1 9 8 5 ) c o m p u te d m e a n d e p th o f se a rch fo r d e G ro o trsquos (1 9 4 6 ) d a ta a n d fo u n d th a t

TA BLE 3

T im e and ldquo Fuzz in ess rdquo Param e ters U sed in th e

S im ula t io n s

T im e fo r c a r ry in g o u t a m o v e 2 s

T im e fo r c o m p u t in g m o v e -g e n e r a tin g h e u r is tic 2 0 s

T im e fo r c o m p u t in g e v a lu a t io n 1 0 s

U p p e r l im it o f fu z z in e ss 5 0

In c r e a se o f fu z z in e s s p e r m o v e 1

In c re a se o f f u z z in e ss p e r s e c o n d 2

D e c re a s e in fu z z in e ss d u e to te m p la te 5

306 GOBET

E x p e rts a n d G ra n d m as ters h a d res p e ctiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 8 a n d

5 3 T h e reg res sio n e q u a tio n d e riv e d f ro m C h a rn e ss rsquos (1 9 8 1 ) d ata y ie ld a n

a v e rag e d e p th o f se a rc h o f a b o u t 2 3 p lies a t th e 1 3 0 0 E L O 1 le v e l o f 4 1 a t th e

E x p e rt le v e l (2 0 0 0 E L O ) a n d o f 5 7 a t th e G ra n d m a s te r le v el U n fo rtu n a tely n o

stu d y te ste d p la y e rs ra n g in g fro m n o v ic es to G ran d m a ste rs an d S E A R C H rsquos

p re d ic tio n o f a p o w e r la w o f p rac tic e c an n o t b e te ste d (y e t) I w ill re p o rt la te r

sim u la tio n s a d d re ssin g d a ta co lle c ted b y S a arilu o m a (1 9 9 0 ) w h e re In tern atio n a l

M a ste rs a n d G ra n d m a s te rs te n d e d to s e arc h le s s th a n M as te rs

T h e ra te o f s ea rc h a lso fo llo w s a p o w e r fu n ctio n o f th e n u m b e r o f c h u n k s (se e

F ig 3 b ) D e G ro o t (1 9 4 6 ) C h arn es s (1 9 8 1 ) a n d G o b e t ( in p res s) a ll f o u n d th a t

stro n g p la y er s te n d e d to s e arc h fa ste r F o r ex a m p le G o b e t ( in p re s s) fo u n d th a t

h is M a ste rs E x p e rts C la ss A a n d C la s s B p lay e rs re sp e c tiv ely se arch e d 4 8 4 1

3 2 an d 3 4 n o d e s p e r m in u te S E A R C H rsquos v a lu es a re h ig h e r b u t s til l p la u s ib le

F o r ex am p le W a g n e r a n d S c u rra h rsquos (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r

m in u te N o te a lso th a t a ll th e ex p erim e n ts m e n tio n e d e a rlier h a v e u se d v e rb a l

p ro to c o ls w h ic h m ay h av e s lo w e d d o w n th e ra te o f se a rc h (c f E ric ss o n amp

S im o n 1 9 8 0 ) F in a lly th e ra te o f se arch m a y h av e b e e n u n d e res tim a ted in th e

lite ra tu re b ec a u se th e r a te o f g e n e ratin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d

b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l t im e H o w e v e r to ta l t im e in c lu d es

tim e n o t sp e n t in s e arc h ( fo r e x a m p le w h a t D e G ro o t c a lls th e ldquo firs t p h a se rdquo)

T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a riab le th e le v e l o f fu zz in e ss a t

w h ic h a se a rc h is e n d e d is m o re d if fic u lt to ju d g e b ec a u se lit tle is k n o w n a b o u t

th e ro le o f fu z z in es s in c h es s th in k in g A g ain S E A R C H p ro p o se s th a t th is

v a riab le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s ee F ig 3 c ) W ith la rg e r

n e ts e p iso d es te n d to b e e n d e d w ith lo w er le v els o f fu z z in e s s T h is su g g es ts th at

in g e n e ra l s tro n g p la y ers s h o u ld b e m o re c o n fid e n t in th e ir c alc u la tio n s as th e y

a re n o t a t th e e d g e o f th eir p o s sib ilitie s N o te th a t th e ra te o f ch an g e is ra th e r h ig h

fo r th is p o w er law w h ic h s u g g e sts th at it sh o u ld b e p o ss ib le to d e te c t i t

e x p erim e n tally

G e n e ra tio n o f M o ve s H o w is m o v e g en e ra tio n af fec te d b y sk ill le v e l A s

sh o w n in F ig 4 a S E A R C H m a k es c le a r p re d ic tio n s W ith sm a ll n u m b e rs o f

c h u n k s th e tim e -c o n s u m in g p ro ce s s o f g en e ra tin g m o v es b y h e u ristic s is

e m p lo y e d T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y ch u n k s

w h ic h is in tu rn d o m in a te d b y te m p la te g e n eratio n

1 T h e E L O ra t in g i s a n in te r v a l sc a le th a t ra n k s c o m p e t it io n c h e ss p la y e rs I ts s ta n d a rd de v ia t io n

(2 0 0 p o in ts) is o f te n in te r p re te d a s a m e a su r e o f sk i ll c la s s in c h e ss G r a n d m a s te r s a re n o rm a lly ra te d

a b o v e 2 5 0 0 In te rn a t io n a l M a s te r s a b o v e 2 4 0 0 M a s te r s a b o v e 2 2 0 0 a n d E x p e rt s a b o v e 2 0 0 0

B e lo w c la sse s (A B e tc ) d iv id e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in ts

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

PATTERN -R ECOGN IT ION AND SEA RCH 297

(a ) s lo ts a llo w in fo rm a tio n ab o u t s tra te g ic o r tac tica l th e m e s a s w e ll a s a b o u t

e v a lu a tio n o f th e p o sitio n to b e en co d e d in L T M rap id ly (b ) lin k s b e tw e e n

te m p la tes a llo w fo r ldquo m e ta -se a rc h rdquo (c ) in fo rm a tio n s to re d b o th in th e c o re a n d in

th e slo ts o f th e te m p late c o m p en sa tes fo r d e c a y an d in te rfe re n c e in th e m in d rsquos

e y e as it m a y b e u se d to re in sta te fa d in g in fo rm a tio n T h is c o m p e n sa tio n

m ec h a n ism is p ar tic u la rly u se fu l w h e n p e rce p tu a l in fo rm a tio n fro m th e ex te rn a l

b o a rd is u n re liab le fo r ex a m p le b e ca u s e se v e ra l m o v e s h a v e b e en c arr ie d o u t in

th e m in d rsquos e y e

Em p ir ica l D a ta Sup po rtin g th e TT A ccoun t o f Sea rchand Pa tte rn R e cogn itio n

In th is se c tio n T T is q u alita tiv e ly ap p lie d to s o m e o f th e k ey d a ta f ro m e m p ir ic a l

stu d ie s o f ch e s s p ro b le m s o lv in g Q u a n tita tiv e a s se ss m e n t w ill b e th e to p ic o f

th e fo llo w in g se c tio n I h a v e sh o w n e lse w h e re (G o b e t 1 9 9 6 ) th at th e p re d ic tio n s

o f T T a re w e ll su p p o rted b y e m p ir ic a l d a ta fro m re se a rch o n m e m o ry a n d

p e rce p tio n

In c re a sin g th e n u m b e r o f c h u n k s a n d te m p la te s h a s tw o o p p o site ef fec ts w ith

re sp e c t to se a rch (G o b e t in p res s) O n th e o n e h a n d d e ep s e arc h is fac ilita te d as

c o m p are d w ith th e m o re co m p u ta tio n a lly e x p e n s iv e w e a k m e th o d s b e c au se

p a tte rn re c o g n itio n is a ra p id p ro c es s a n d b e ca u s e se q u e n c e s o f m o v es m a y b e

le arn e d an d su g g e ste d b y c h u n k s O n th e o th er h a n d th e n ee d fo r d e e p se a rc h

o fte n d isa p p e ar s b e ca u s e e v a lu atio n s su g g e ste d b y p a tte rn re c o g n itio n m a y b e

m o re re lia b le th a n e v a lu atio n s co m p u te d b y w e a k m eth o d s T h e s e tw o o p p o site

e ffe cts c a n e x p la in w h y th e sk ill d iffe re n c e s in a v e rag e d e p th o f se a rc h a re sm all

P a tte rn re co g n itio n a llo w s stro n g p la y e rs to b e h ig h ly s e le c tiv e in th e ir s ea rc h

T h is c a n b e s e en b o th in th e ra p id w a y M a s te rs ze ro in to th e k e y as p e cts o f a

p o s itio n (D e G ro o t 1 9 4 6 ) an d in th e w ay e y e m o v e m e n ts d iffe r a s a fu n c tio n o f

sk ill d u rin g th e firs t s ec o n d s o f th e p e rc ep tio n o f a p o sitio n (D e G ro o t amp G o b et

1 9 9 6 ) A d d itio n a l e v id e n ce is p ro v id e d b y S a a rilu o m a (1 9 9 0 ) w h o h a s sh o w n

th a t p la y e rs ch o o se ste re o ty p e d so lu tio n s in p ro b le m s w h e re fa ste r ( in th e

n u m b e r o f m o v es to r ea c h m a te) b u t u n c o m m o n so lu tio n s a re p re s en t T h e se d a ta

a d d s u p p o rt to T T b e c a u se p a ttern re co g n itio n lie s a t i ts c o re

F u r th er s tro n g e v id e n ce fo r th e ro le o f p atte rn re c o g n itio n is th a t M as te rs c a n

p la y s ev e ra l o p p o n en ts s im u lta n eo u sly a t a s tre n g th c lo se to th at in o n e -a g ain s t-

o n e p lay I t is in te re stin g th at in s im u lta n eo u s g a m e s th ey te n d to p la y ldquon o rm a lrdquo

m o v e s a n d re ly o n o p p o n e n ts rsquo e rro rs (G o b e t amp S im o n 1 9 9 6 c ) N o rm a l m o v es

m ay c o rre sp o n d to th e ty p e o f m o v e s su g g e ste d b y c h u n k s an d tem p la te s

A fea tu re o f c h es s ex p e rtise c a p tu re d u n iq u e ly b y T T is th e h ig h le v e ls a t

w h ic h ch e s s p lay e rs o rg a n is e th e ir k n o w le d g e D e G ro o t (1 9 4 6 ) p ro p o s e d th a t

p la y er s o rg an is e p o sitio n s a ro u n d la rg e ldquo c o m p le x e srdquo b ig g e r th a n th e c h u n k s th a t

w e re la te r p ro p o se d b y C h a se a n d S im o n (1 9 7 3 ) D e G ro o t a lso su g g es ted a s d id

C o o k e e t a l (1 9 9 3 ) th a t p la y e rs re p re s en t in fo rm a tio n a t a c o n c e p tu a l lev el In

p a rticu la r D e G ro o t (1 9 4 6 ) p ro p o se d th a t M a ste rsrsquo d e sc rip tio n s o f g am e s a re

298 GOBET

c en tred a ro u n d k ey p o sitio n s o f th e g a m e T T o ffe rs th eo retic al s tru c tu res

(te m p la te s) th a t co u ld a c c o u n t fo r p lay ers rsquo larg e c o m p le x es h ig h - le v e l re p re -

se n ta tio n s a n d k e y p o sitio n s T T a lso o ff ers m e ch a n ism s b as e d o n f req u en c y o f

o c c u rre n ce s e x p la in in g h o w th e s e h ig h - le v e l re p re se n ta tio n s a re d ev elo p e d a n d

m ec h a n ism s b a se d o n d isc rim in a tio n p ro c e sse s e x p la in in g h o w th ey c o u ld b e

a c ce ss e d ra p id ly

T T is a lso co m p a tib le w ith re su lts fro m e x p er im e n ts u s in g p o s itio n s fo r w h ic h

a cc e ss to k n o w le d g e is d iffic u lt In H o ld in g a n d R e y n o ld s rsquo (1 9 8 2 ) e x p e rim e n t

c h e ss s k ill d id n o t c o rr ela te w ith th e re c a ll o f s e m i-ra n d o m p o s itio n s sh o w n fo r a

fe w se co n d s b u t eff ec tiv en es s o f th e s ea rc h fo r th e b e st m o v e in th es e p o s itio n s

d id c o rr ela te w ith s k ill T T o f fer s a n ex p la n a tio n fo r th e fa c t th a t th e re w a s a

stro n g c o rre la tio n b e tw e en sk ill le v e l a n d q u a lity o f m o v e p ro p o se d P lay e rs

re c u rsiv e ly g e n e ra te a m o v e th ro u g h w ea k m e th o d s w h en n o c h u n k is

re c o g n ise d u n til o n e o f th e h a ltin g co n d itio n s (m en tio n e d e a rlier ) a p p lie s T h e n

g iv e n th eir la rg e r d ata b a se o f c h u n k s s tro n g p la y e rs a re m o re lik e ly th a n w e a k

p la y er s to f in d a u s efu l p a tte rn in p o sitio n s th a t h a v e b ee n n e w ly u p d ate d in th e

m in d rsquos e y e a n d th e re fo re a re m o re lik e ly to f in d g o o d m o v e s in th eir se a rch

I m en tio n e d e a rlier th at E ric ss o n a n d K in tsc h (1 9 9 5 ) p ro p o s ed m ec h a n ism s

(re trie v al s tru c tu re a n d ela b o ra tio n s o f L T M sc h e m a s ) th a t e n c o d e in fo rm a tio n

q u ic k ly a n d re lia b ly B y c o n tra st th e e n c o d in g c a p a c ity o f te m p la te s is r e la tiv ely

w e a k In p a rtic u la r T T p re d icts th at th e sa m e te m p la te m a y s o m e tim e s b e u se d to

e n c o d e s e v era l s im ilar p o sitio n s th u s in c re as in g th e ris k o f in terf ere n c e as se a rc h

p ro g re s se s A s a co n se q u e n ce a n d c o n trary to L T W M T rsquos p re d ic tio n s p lay e rs

sh o u ld o fte n re v isit p o sitio n s b y g e n era tin g m o v es in s tea d o f a cc e ss in g th e m

d ire ctly fro m m em o ry T h is is w h at p la y e rsmdash e v e n m a ste rs mdash d o (D e G ro o t

1 9 4 6 ) F in a lly T T m a y h a v e s o m e th in g to sa y a b o u t e rro rs in c h e ss K ro g iu s

(1 9 7 6 ) m e n tio n s th a t er ro rs o f te n o c c u r w h e n a m o v e h a s ca u s ed im p o rta n t

c h a n g es in th e p o s itio n T h is m a y b e d u e to p la y e rsrsquo in a b ility to re c o g n ise th a t a

p re v io u sly a d eq u ate te m p late h as b ec o m e in a d e q u a te

In s u m m a ry T T o ffe rs a g o o d q u alita tiv e a c co u n t o f s e v eral im p o rtan t c h e ss

p h e n o m en a I t is n o w tim e to tu rn to m o re o b je c tiv e q u an tita tiv e te sts o f th e

th eo ry

A COM PUTER M ODE L O F S EARCH IN CH ESS

In th e re m a in d e r o f th is p a p e r I p re s en t a c o m p u te r m o d e l c a lled S E A R C H

w h ic h im p le m e n ts T T in so m e d e ta il I f irs t d e s crib e th e im p le m en ta tio n o f

S E A R C H m a k in g cle a r w h a t a s p ec ts o f T T h a v e b e e n in c lu d ed a n d th en d isc u ss

its b e h a v io u r w ith r es p e ct to h u m a n d a ta

O ve rv iew o f M ode l

F u ll im p le m e n ta tio n o f T T a s a c h e ss-p la y in g c o m p u ter p ro g ram w o u ld b e a

m ajo r ta sk mdash th is d iffic u lty is d e m o n stra te d b y th e fa c t th a t n o c o m p le te co m p u te r

m o d e l o f ch e s s c o g n itio n in c lu d in g p e rc e p tio n m em o ry a n d p ro b le m so lv in g

PATTERN -R ECOGN IT ION AND SEA RCH 299

h a s e v e r b e e n d e v elo p e d I p u rs u e d a lim ited a im a co m p u te r m o d el th a t c o n tain s

so m e o f th e im p o rta n t p aram e te rs o f T T a n d th a t co m p u te s k e y b e h a v io u ra l

v a ria b le s T h is m o d el d o e s n o t c o n stitu te a co m p le te im p le m e n ta tio n o f th e

th e o ry (it d o e s n o t s ea rc h o r e v a lu a te c h e ss p o sitio n s) b u t is d e ta ile d en o u g h to

o ffe r a g o o d te st o f so m e a s p ec ts o f T T I t is s o b e rin g to n o tic e th a t e v e n th is

p a rtia l im p lem e n tatio n o f th e th e o ry is q u ite c o m p le x a n d re q u ire s m a n y

p a ra m e te rs T h is is th e p rice o f a v o id in g th e v ag u en e s s o f v e rb al th e o ris in g

The M a in P rob lem -so lv in g Loop

T h e m ain in te re st o f th e m o d el is in th e in te ra c tio n b etw ee n p atte rn re c o g n itio n

a n d s ea rc h T h e m o d e l g e n e ra tes in d e p en d en t ep is o d es fo llo w in g se v e ral ru les

fo r g e n eratin g m o v e s a n d ch o o sin g sto p co n d itio n s C o m p atib le w ith m o s t

h u m an p ro to co ls th e p ro g ra m c o n sid e rs o n ly o n e b ra n c h w ith in a n ep is o d e (th u s

th e re is n o b ra n c h in g p o in t w ith in a n e p iso d e) A s illu stra te d in F ig 1 th e m o d e l

is c lo se to th e d es crip tio n o f T T g iv en e a rlie r in th is p a p e r T h e v ario u s c o n d itio n s

a n d o p e ra tio n s in S E A R C H a re re p re se n te d as p ro b a b ilit ie s o r p ro b ab ility

d istr ib u tio n s an d n o t a s a ctu a l c h e ss m o v e s e v a lu atio n s o r s y m b o lic s tru c tu res

in S T M o r in th e m in d rsquos e y e

A tra c e o f S E A R C H is sh o w n in F ig 2 T h e an aly s is w ill c e n tre o n th e

fo llo w in g v a ria b les a s a fu n c tio n o f th e n u m b e r o f c h u n k s ra te o f g en e ra tin g a

m o v e le v el o f fu z zin e ss in th e m in d rsquos e y e w h en a n e p is o d e is e n d e d m e an d e p th

o f s ea rc h m eth o d s u se d fo r g en e ra tin g a m o v e a n d m eth o d s u se d fo r s to p p in g a n

e p iso d e

T h e c o n c ep t o f te m p la te is im p le m e n te d in tw o w a y s (a ) b y h ig h e r

p ro b a b ilitie s o f f in d in g (s eq u en c e s o f) m o v e s a n d ev a lu a tio n s th an w ith p la in

c h u n k s a n d (b ) b y a d e cre a se in th e le v e l o f fu zz in e ss m ad e p o s sib le b y th e L T M

re p re se n ta tio n o f th e c o re o f th e p o sitio n a n d o f s lo ts

T h e le v e l o f re lia b ility o f th e in fo rm a tio n in th e m in d rsquos ey e is c a p tu re d b y a

ldquo fu z zin e s srdquo p a ra m e te r e x p re ss ed in a rb itr ary u n its T h re e m a in c o g n itiv e

fe a tu res ar e c a p tu red b y th is p a ra m ete r w o rk in g m e m o ry c a p a c ity a b ility to

m ain ta in a v isu o -s p atia l im ag e a n d su b je ctiv e e s tim a te o f th e r isk o f m ak in g a n

e rro r T h e fu z z in es s p a ram e ter is th e n as su m e d to o rig in ate b o th fro m th e

h a rd w a re a n d th e so ftw a re o f th e sy s tem It m a y v a ry d u r in g th e life tim e o f a

p la y er b e c a u se o f b io lo g ic a l m a tu ra tio n o r a g e in g an d m a y b e a ffe c ted b y

e x p e rim e n ta l m a n ip u latio n s T h e re a re th ree re a so n s w h y S E A R C H en d s a

se a rc h th e lev el o f fu z z in e s s is to o h ig h a n e v a lu atio n is p ro p o se d o r n o m o v e is

p ro p o s e d T h e id e a o f ex p ec ta tio n le v e l is n o t e x p lic itly p re se n t in th e m o d el b u t

it is im p lic it in th e p ro b a b ility v alu e s o f f in d in g fe atu re s e n d in g th e s ea rc h o f a n

e p iso d e e ith er b y p a tte rn re c o g n itio n o r b y th e a p p lica tio n o f h e u ristic s

S e le ctio n o f th e n ex t b a se -m o v e (a k e y c o n c ern o f N ew e ll amp S im o n 1 9 6 5 a n d

W ag n e r amp S c u rra h 1 9 7 1 ) is n o t ad d res se d b y S E A R C H w h ic h in g e n e ra l lac k s

th e s em a n tic in fo rm a tio n n e c es sa ry fo r su c h a se le c tio n F in a lly m e ta -se a rc h

w ith te m p la te s is n o t d ire c tly im p le m e n te d in S E A R C H b u t it is im p lic itly

300 GOBET

300

FIG 1 F lo w c h a rt o f S E A R C H

PATTERN -R ECOGN IT ION AND SEA RCH 301

301

F IG 2 E x a m p le s o f e p is o d e s g e n e ra te d b y S E A R C H

302 GOBET

re p re se n te d b y th e re la tiv e ly h ig h p ro b ab ility o f f in d in g (s eq u e n c e s o f) m o v es

a n d e v a lu atio n s w ith tem p la tes as c o m p are d w ith ch u n k s

The M ode lrsquos P aram e te rs

S E A R C H h as m a n y p a ra m ete rs a n d it is o f c o u rs e n e c es sa ry to se t u p a f ew o f

th e m w ith in d e p e n d e n t d a ta in o rd er to re d u c e th e n u m b e r o f d e g re e s o f fre e d o m

in th e m o d e l W h e n p o ss ib le I h a v e u s e d sim u la tio n s w ith th e C H R E S T (D e

G ro o t amp G o b e t 1 9 9 6 G o b e t 1 9 9 3 ) an d C H U M P (G o b e t amp Ja n s en 1 9 9 4 )

p ro g ram s to se t p a ra m e te r v a lu es C H R E S T is a p ro g ra m im p le m e n tin g as p e cts

o f T T a n d s im u la tin g n u m e ro u s e x p er im e n ts o n p e rc ep tio n an d m e m o ry in ch e s s

a n d C H U M P is a p ro g ra m p la y in g (w e ak ) c h e ss b y p u re p a tte rn re co g n itio n

N u m b e r o f C h u n k s a n d T e m p la te s T ab le 1 sh o w s th e v a lu es th at w ill b e

u s ed w ith th e S E A R C H m o d e l fo r th e se p a ra m ete rs T o c h o o se th e v a lu e s re la te d

to th e n u m b e r o f ch u n k s a n d te m p la tes th e c u rre n t v e rsio n o f C H R E S T h a s b e e n

e m p lo y e d T h e p ro b a b ility o f f in d in g a tem p la te w a s e stim ate d b y ru n n in g

C H R E S T o n 5 0 p o s itio n s ran d o m ly tak e n fro m M as ters rsquo g am e s T h e firs t lin e (0

c h u n k ) w a s ad d e d to g e t p re d ic tio n s a t th e n o v ic e lev e l W ith n e ts o f 1 0 0 0 0 0

1 2 0 0 0 0 a n d 1 5 0 0 0 0 c h u n k s th e p ara m ete rs w ere e stim ate d w ith th e b e s t-fit t in g

fu n c tio n s av a ilab le ( th e ldquo n o v ice rdquo v alu e s w ere n o t u se d ) T h e n u m b er o f te m p la tes

is ro u g h ly a lin e ar fu n c tio n o f th e n u m b er o f c h u n k s (r 2 = 9 7 ) T h e p ro b a b ility

o f f in d in g a tem p la te is a p p ro x im a tely a lo g -fu n c tio n o f th e n u m b e r o f c h u n k s

(r 2 = 9 4 )

H e u r is tic s C h u n k s T e m p la tes a n d T h e ir R e la tio n to th e P ro b a b ility o f

F in d in g M o v e s a n d E v a lu a tio n s T ab le 2 g iv e s th e v a lu e s u s ed in th e

sim u la tio n s fo r th e p a ra m ete rs re la te d to h e u ristic s c h u n k s a n d te m p la te s

H e u ris tic s in c lu d e sim p le se a rc h te c h n iq u e s (e g ldquo ta k e a p ie c e b a c k rdquo o r ldquoc h e c k

th e K in g rdquo ) a s w ell a s m o re a b stra c t ru le s (e g ldquoo c c u p y th e c en tre rdquo ) T h eir m a in

c h a rac te ris tic in co m p a riso n w ith c h u n k s an d tem p la te s is th a t th ey are g e n e ra l

a n d re q u ire so m e co n sc io u s c o m p u tatio n in o rd e r to p ro d u ce a m o v e T h e

a ss u m p tio n u n d e rly in g T a b le 2 is th at th e p aram e ters re la ted to h e u ristic s s ta y

ro u g h ly c o n sta n t w h ile th e o th e r p aram e te rs v a ry as a lo g arith m ic fu n c tio n o f th e

n u m b e r o f c h u n k s in th e n e t (A lo g arith m ic fu n ctio n h a s b e e n c h o se n to in d ica te

th a t ch u n k s y ie ld a d im in ish in g re tu rn as th e ir n u m b e r in c re a se s) T h e

a ss u m p tio n th a t th e n u m b e r o f h e u ristic s is c o n sta n t ac ro s s s k ill le v e ls se e m s

re a so n a b le (p e rh a p s w ith th e e x ce p tio n o f th e n o v ic e le v e l) a s m o s t c h e ss

M a ste rs rsquo k n o w le d g e is v e ry sp ec ific to c erta in a sp e c ts o f th e g a m e (D e G ro o t

1 9 4 6 )

T h e fo llo w in g c o n s id era tio n s w e re m ad e in se ttin g th e v alu e s g iv e n in

T ab le 2 I t w a s d ee m e d p lau sib le th a t th e p ro b a b ility o f f in d in g so m e h e u ristic in

a p o s itio n b e h ig h ( 9 5 ) a s w e ll a s th e p ro b a b ility o f f in d in g s o m e c h u n k F in ally

PATTERN -R ECOGN IT ION AND SEA RCH 303

TA BLE 1

The V a lu es o f th e 14 N e ts U sed in th e S im u la tio ns

P ro b a b i li ty o f

re c o g n is in g a t le as t

P ro p o r t io n o f o n e te m p la te g iv e n a

N u m b e r o f c h u n k s N u m b e r o f te m p la te s te m p la te s p o s i t io n

0 0 0 0 0 0 0 0

1 0 0 2 0 0 0 0 0 0 0

2 6 8 0 5 0 0 2 1 8 0

5 0 0 3 3 6 0 0 7 1 4 0

1 0 0 1 1 1 0 0 0 1 0 2 4 0

2 0 0 0 3 2 6 5 0 1 3 3 0 0

3 0 0 0 1 4 9 3 0 1 6 3 6 0

4 0 0 0 5 7 7 4 0 1 9 4 6 0

5 0 0 0 6 1 1 4 2 0 2 3 4 0 0

7 2 0 4 4 2 1 3 6 0 3 0 4 8 0

8 0 0 1 0 2 2 8 5 0 2 9 5 4 0

1 0 0 0 0 0 2 7 6 5 0 2 8 5 1 0

1 2 0 0 0 0 3 3 5 7 0 2 8 5 4 0

1 5 0 0 0 0 4 2 4 5 0 2 8 5 6 0

T h e v a lu e s b e lo w 1 0 0 0 0 0 c h u n k s w e r e ta k e n f ro m s im u la t io n s w ith C H R E S T th e o the rs

e x t ra p o la te d S e e te x t f o r d e ta ils

TA BLE 2

H eur is t ic s C hun ks Tem pla tes and Their Re la tion to th e P ro bab ility of Fin d in g

M oves and Evalu ta tio ns

T y p e H e u r is tic s C h u n k s T e m p la te s

P ro b a b i li ty o f e v o k in g a n 9 5 g (n _ c h u n k s 9 5 )a se e T a b le 1

h e u ri s t ic a c h u n k o r a te m p la te

P ro b a b i li ty o f f in d in g a m o v e 5 0 g (n _ c h u n k s 5 0 ) g (n _ c h u n k s 9 0 )

g ive n th a t a n h e u r is tic a c h u n k

o r a te m p la te h a s b e e n e v o k e d

P ro b a b i li ty o f f in d in g a n e v a lu a tio n 1 5 g (n _ c h u n k s 0 5 ) g (n _ c h u n k s 5 0 )

g iv e n th a t a n h e u ri s t ic a c h u n k o r

a te m p la te h a s b e e n e v o k e d

aT h e fu n c tio n g i s d e f in e d a s

g (n _ c h un k s p ro b ) = p ro b 0 2 lo g1 0

(n _ c h un k s ) i f n _ c h u n k s gt 0

a n d

g (n _ c h u n k s p ro b ) = 0 i f n _ c h u n k s = 0

w h e re n _ c h u n k s i s th e n u m b e r o f c h u n k s in a g iv e n n e t a n d p ro b i s a c o n s ta n t

303

304 GOBET

th e p ro b a b ility o f re c o g n isin g a te m p la te in a p o sitio n is sm a lle r a n d is g iv e n in

T ab le 1

T h e p ro b a b ility o f f in d in g a m o v e g iv e n a h e u ristic is s e t to 5 0 in d ic atin g th a t

h e u ristic s m a y fa il to p ro d u ce a m o v e h a lf o f th e tim e T h is is b e c a u se so m e

h e u ristic s m ay n o t y ie ld a m o v e a n d b ec a u se so m e p ro p o se d m o v es m a y b e

ille g a l T h e p ro b a b ility o f f in d in g a m o v e g iv en a tem p la te is h ig h p a rtly

re fle ctin g th e ric h s em a n tic k n o w le d g e an d th e in te r-te m p la te lin k s a s su m e d to

c h a rac te rise te m p la te s F o r th e p ro b a b ility o f f in d in g a m o v e g iv e n th a t a ch u n k

h a s b e en re co g n ise d I u se d th e p ara m e te r p ro b in th e fu n ctio n g (s ee T a b le 2 ) so

th a t i t a p p ro x im a te s th e d ata p ro d u c ed b y th e C H U M P p ro g ram (G o b et amp Ja n se n

1 9 9 4 ) E v a lu a tio n s a re su p p o s ed to b e h a rd er to le arn a n d th e re fo re h a rd e r to u se

th a n m o v es H e n ce th e ir p ro b a b ilit ie s a re lo w e r th a n th e co r res p o n d in g p ro b -

a b ilit ie s w ith m o v es A g a in fo llo w in g d irec tly fro m th e th e o ry te m p la te s o ffe r

th e b e st so u rce o f ev alu a tio n s

W ith re sp e c t to th e n u m b e r o f se q u e n tia l m o v e s p ro p o s ed c o u n ted in p lie s

(i e m o v e s fo r W h ite o r B la ck ) i t is as su m e d th a t h e u ristic s g iv e a cc e ss to o n ly

o n e m o v e w h ile c h u n k s a n d te m p late s y ie ld se q u e n c es o f m o v e s w h o se n u m b e r

fo llo w s a g e o m e tric p ro b a b ility d is tr ib u tio n (th e c h o ice o f th is d is tr ib u tio n w as

in sp ire d b y sta tis tic s ta k e n fro m C H U M P ) T h e lo n g e s t s eq u e n c e ( ca ll i t k ) h as a

fre q u e n c y o f 1 th e s e co n d -lo n g e st a fre q u en cy o f 2 th e th ird -lo n g e st a fre q u e n c y

o f 4 a n d so o n u n til th e sh o rte st se q u e n c e w h o s e len g th is 1 m o v e an d w h o se

fre q u e n c y is 2 (k ndash 1 ) T h e m a x im u m se q u e n ce o f m o v es w a s se t to 1 8 F in a lly

S E A R C H atte m p ts to g e n e ra te a m o v e b y p a ttern re c o g n itio n ( ch u n k o r te m p la te )

fo u r tim e s b e fo re u sin g a n h e u ristic

T im e a n d F u zzin e ss P a ra m ete rs T h e tim e p a ram e ter s fo r th e re sp e c tiv e

o p e ra tio n s w e re s et u sin g p la u sib le v a lu e s (se e T a b le 3 ) M o v e g en era tio n b y

p a tte rn re c o g n itio n (c h u n k o r te m p late ) is as su m e d to b e v e ry sh o rt (a few

h u n d re d m illis e co n d s) n o tim e c o st is u se d in th e m o d e l T h e tim e fo r c o m p u tin g

a m o v e-g en e ra tin g h e u ristic w a s s et to th e ra th e r lo n g 2 0 s ec o n d s mdash g en era tin g a

m o v e w ith o u t u sin g p a tte rn r ec o g n itio n re q u ires p u ttin g to g eth e r v a rio u s ty p e s o f

in fo rm a tio n a n d a s k s fo r m a n y ch e c k in g p ro c ed u res T h e tim e fo r c a rry in g o u t

o n e m o v e (o n c e g e n erate d ) in th e m in d rsquos e y e w a s s et to tw o s ec o n d s T h is is

c o m p atib le w ith S a a rilu o m a rsquos (1 9 8 9 ) d ata w h ic h sh o w th a t a b lin d fo ld ed M a ste r

c an fo llo w a g a m e d icta ted a t tw o se c o n d s a m o v e F in ally th e tim e fo r ca rry in g

o u t a n ev a lu a tio n b y h eu ris tic is s e t to 1 0 s e co n d s T h is ra th e r s h o rt tim e m a y b e

ju stif ie d b y th e fa c t th a t p la y e rs ty p ic a lly co n s id e r o n ly o n e (s u b jec tiv e ) a sp e c t o f

th e p o sitio n (D e G ro o t 1 9 4 6 ) a n d th at m an y e v a lu atio n s c a n b e g ro u n d ed o n th e

b a sis o f c lea r m a teria l lo ss e s

T h e fu z zin e ss lev el o f th e s y ste m is e x p re ss ed in a rb itra ry u n its I t s ta rts w ith

th e v a lu e z e ro a n d it is in c re a se d w h e n a m o v e is c a rrie d o u t in th e m in d rsquos e y e

a n d w h e n tim e is s p e n t a p p ly in g a n h e u ris tic W h e n a te m p la te is fo u n d th e

PATTERN -R ECOGN IT ION AND SEA RCH 305

fu z z in es s lev el is d e cre a se d a s p a rt o f th e in fo rm atio n m ay b e sto re d in L T M

d ire c tly fre e in g c ap ac ity in w o rk in g m e m o ry a n d in th e m in d rsquos ey e

S im u la t io n s w ith th e ldquo C anon ica l M ode lrdquo

T h e sim u latio n s d e sc rib ed in th is s ec tio n a re s tra ig h tfo rw a rd U s in g th e

p a ra m e te r v alu e s d is cu sse d e a rlie r I le t th e p ro g ra m s ea rc h 1 0 0 0 ep iso d e s fo r

e ac h n e t s iz e S u m m a ry v alu e s fo r m e a n d ep th o f se a rc h t im e ra tio d e p th tim e

a n d fu z zin e s s a s w e ll a s fo r g e n e ra tio n an d s to p co n d itio n s w e re c o m p u ted fo r

e ac h n e t s iz e

M e a n D e p th o f S e a r ch R a te o f S e a rc h a n d F u z zin e ss A cc o rd in g to

S E A R C H m ea n d e p th o f s ea rc h fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f

c h u n k s (se e F ig 3 a) If w e as su m e a co n sta n t ra te o f le a rn in g n e w c h u n k s a s is

c o m m o n p ra ctic e in so m e c o g n itiv e a rch ite c tu res (c f N e w e ll 1 9 9 0 ) a n d if w e

a ss u m e th a t s k ille d p la y e rs h a v e sp e n t m o re p rac tice a n d stu d y tim e th a n

u n s k ille d p la y e rs th e n m e an d e p th fo llo w s a p o w e r fu n c tio n o f s k ill as w e ll T h is

p re d ic tio n w h ic h is a t v ar ia n c e w ith H o ld in g rsquos p re d ic tio n (1 9 8 5 p 1 8 2 ) o f a

lin ea r in c rea s e is p artly co n siste n t w ith C h a rn e ss rsquos (1 9 8 1 ) p ro p o s a l th a t d e p th o f

se a rc h is n o t l in e arly re la ted to s k ill b u t th at th e re is a ce ilin g a t h ig h s k ill le v e ls

T h e re su lt is a ls o c o m p atib le w ith th e w e a k lin e ar re la tio n fo u n d in e m p ir ic a l

stu d ie s (C h a rn e ss 1 9 8 1 G o b e t in p re ss ) b e tw e e n m e a n d e p th o f se a rch a n d sk ill

le v el b e c a u se re stric te d ra n g e s o f th e c u rv e c a n b e a p p ro x im a ted b y a lin e a r

fu n c tio n T h e a b so lu te v alu e s a re a lso q u ite r ea so n ab le th ey ris e f ro m lo w d ep th s

(le ss th a n 1 p ly ) w ith n o ch u n k s (co r res p o n d in g to th e n o v ic e le v el) to a ro u n d 2 5

p lies w ith a sm a ll n et (1 0 0 0 c h u n k s ) an d th e n to a ro u n d 4 p lie s w ith ex p ert le v e l

(a ro u n d 3 0 0 0 0 c h u n k s a s e s tim a te d b y s im u la tio n s o n th e re ca ll tas k ) T h e y th e n

slo w ly (s av e fo r a f ew ra n d o m v a ria tio n s ) in c re a se to m o re th an 5 p lie s w ith n e t

la rg er th an 1 0 0 0 0 0 c h u n k s w h ic h c o rre sp o n d s to G ran d m a ste r le v e l H o ld in g

(1 9 8 5 ) c o m p u te d m e a n d e p th o f se a rch fo r d e G ro o trsquos (1 9 4 6 ) d a ta a n d fo u n d th a t

TA BLE 3

T im e and ldquo Fuzz in ess rdquo Param e ters U sed in th e

S im ula t io n s

T im e fo r c a r ry in g o u t a m o v e 2 s

T im e fo r c o m p u t in g m o v e -g e n e r a tin g h e u r is tic 2 0 s

T im e fo r c o m p u t in g e v a lu a t io n 1 0 s

U p p e r l im it o f fu z z in e ss 5 0

In c r e a se o f fu z z in e s s p e r m o v e 1

In c re a se o f f u z z in e ss p e r s e c o n d 2

D e c re a s e in fu z z in e ss d u e to te m p la te 5

306 GOBET

E x p e rts a n d G ra n d m as ters h a d res p e ctiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 8 a n d

5 3 T h e reg res sio n e q u a tio n d e riv e d f ro m C h a rn e ss rsquos (1 9 8 1 ) d ata y ie ld a n

a v e rag e d e p th o f se a rc h o f a b o u t 2 3 p lies a t th e 1 3 0 0 E L O 1 le v e l o f 4 1 a t th e

E x p e rt le v e l (2 0 0 0 E L O ) a n d o f 5 7 a t th e G ra n d m a s te r le v el U n fo rtu n a tely n o

stu d y te ste d p la y e rs ra n g in g fro m n o v ic es to G ran d m a ste rs an d S E A R C H rsquos

p re d ic tio n o f a p o w e r la w o f p rac tic e c an n o t b e te ste d (y e t) I w ill re p o rt la te r

sim u la tio n s a d d re ssin g d a ta co lle c ted b y S a arilu o m a (1 9 9 0 ) w h e re In tern atio n a l

M a ste rs a n d G ra n d m a s te rs te n d e d to s e arc h le s s th a n M as te rs

T h e ra te o f s ea rc h a lso fo llo w s a p o w e r fu n ctio n o f th e n u m b e r o f c h u n k s (se e

F ig 3 b ) D e G ro o t (1 9 4 6 ) C h arn es s (1 9 8 1 ) a n d G o b e t ( in p res s) a ll f o u n d th a t

stro n g p la y er s te n d e d to s e arc h fa ste r F o r ex a m p le G o b e t ( in p re s s) fo u n d th a t

h is M a ste rs E x p e rts C la ss A a n d C la s s B p lay e rs re sp e c tiv ely se arch e d 4 8 4 1

3 2 an d 3 4 n o d e s p e r m in u te S E A R C H rsquos v a lu es a re h ig h e r b u t s til l p la u s ib le

F o r ex am p le W a g n e r a n d S c u rra h rsquos (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r

m in u te N o te a lso th a t a ll th e ex p erim e n ts m e n tio n e d e a rlier h a v e u se d v e rb a l

p ro to c o ls w h ic h m ay h av e s lo w e d d o w n th e ra te o f se a rc h (c f E ric ss o n amp

S im o n 1 9 8 0 ) F in a lly th e ra te o f se arch m a y h av e b e e n u n d e res tim a ted in th e

lite ra tu re b ec a u se th e r a te o f g e n e ratin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d

b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l t im e H o w e v e r to ta l t im e in c lu d es

tim e n o t sp e n t in s e arc h ( fo r e x a m p le w h a t D e G ro o t c a lls th e ldquo firs t p h a se rdquo)

T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a riab le th e le v e l o f fu zz in e ss a t

w h ic h a se a rc h is e n d e d is m o re d if fic u lt to ju d g e b ec a u se lit tle is k n o w n a b o u t

th e ro le o f fu z z in es s in c h es s th in k in g A g ain S E A R C H p ro p o se s th a t th is

v a riab le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s ee F ig 3 c ) W ith la rg e r

n e ts e p iso d es te n d to b e e n d e d w ith lo w er le v els o f fu z z in e s s T h is su g g es ts th at

in g e n e ra l s tro n g p la y ers s h o u ld b e m o re c o n fid e n t in th e ir c alc u la tio n s as th e y

a re n o t a t th e e d g e o f th eir p o s sib ilitie s N o te th a t th e ra te o f ch an g e is ra th e r h ig h

fo r th is p o w er law w h ic h s u g g e sts th at it sh o u ld b e p o ss ib le to d e te c t i t

e x p erim e n tally

G e n e ra tio n o f M o ve s H o w is m o v e g en e ra tio n af fec te d b y sk ill le v e l A s

sh o w n in F ig 4 a S E A R C H m a k es c le a r p re d ic tio n s W ith sm a ll n u m b e rs o f

c h u n k s th e tim e -c o n s u m in g p ro ce s s o f g en e ra tin g m o v es b y h e u ristic s is

e m p lo y e d T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y ch u n k s

w h ic h is in tu rn d o m in a te d b y te m p la te g e n eratio n

1 T h e E L O ra t in g i s a n in te r v a l sc a le th a t ra n k s c o m p e t it io n c h e ss p la y e rs I ts s ta n d a rd de v ia t io n

(2 0 0 p o in ts) is o f te n in te r p re te d a s a m e a su r e o f sk i ll c la s s in c h e ss G r a n d m a s te r s a re n o rm a lly ra te d

a b o v e 2 5 0 0 In te rn a t io n a l M a s te r s a b o v e 2 4 0 0 M a s te r s a b o v e 2 2 0 0 a n d E x p e rt s a b o v e 2 0 0 0

B e lo w c la sse s (A B e tc ) d iv id e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in ts

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

298 GOBET

c en tred a ro u n d k ey p o sitio n s o f th e g a m e T T o ffe rs th eo retic al s tru c tu res

(te m p la te s) th a t co u ld a c c o u n t fo r p lay ers rsquo larg e c o m p le x es h ig h - le v e l re p re -

se n ta tio n s a n d k e y p o sitio n s T T a lso o ff ers m e ch a n ism s b as e d o n f req u en c y o f

o c c u rre n ce s e x p la in in g h o w th e s e h ig h - le v e l re p re se n ta tio n s a re d ev elo p e d a n d

m ec h a n ism s b a se d o n d isc rim in a tio n p ro c e sse s e x p la in in g h o w th ey c o u ld b e

a c ce ss e d ra p id ly

T T is a lso co m p a tib le w ith re su lts fro m e x p er im e n ts u s in g p o s itio n s fo r w h ic h

a cc e ss to k n o w le d g e is d iffic u lt In H o ld in g a n d R e y n o ld s rsquo (1 9 8 2 ) e x p e rim e n t

c h e ss s k ill d id n o t c o rr ela te w ith th e re c a ll o f s e m i-ra n d o m p o s itio n s sh o w n fo r a

fe w se co n d s b u t eff ec tiv en es s o f th e s ea rc h fo r th e b e st m o v e in th es e p o s itio n s

d id c o rr ela te w ith s k ill T T o f fer s a n ex p la n a tio n fo r th e fa c t th a t th e re w a s a

stro n g c o rre la tio n b e tw e en sk ill le v e l a n d q u a lity o f m o v e p ro p o se d P lay e rs

re c u rsiv e ly g e n e ra te a m o v e th ro u g h w ea k m e th o d s w h en n o c h u n k is

re c o g n ise d u n til o n e o f th e h a ltin g co n d itio n s (m en tio n e d e a rlier ) a p p lie s T h e n

g iv e n th eir la rg e r d ata b a se o f c h u n k s s tro n g p la y e rs a re m o re lik e ly th a n w e a k

p la y er s to f in d a u s efu l p a tte rn in p o sitio n s th a t h a v e b ee n n e w ly u p d ate d in th e

m in d rsquos e y e a n d th e re fo re a re m o re lik e ly to f in d g o o d m o v e s in th eir se a rch

I m en tio n e d e a rlier th at E ric ss o n a n d K in tsc h (1 9 9 5 ) p ro p o s ed m ec h a n ism s

(re trie v al s tru c tu re a n d ela b o ra tio n s o f L T M sc h e m a s ) th a t e n c o d e in fo rm a tio n

q u ic k ly a n d re lia b ly B y c o n tra st th e e n c o d in g c a p a c ity o f te m p la te s is r e la tiv ely

w e a k In p a rtic u la r T T p re d icts th at th e sa m e te m p la te m a y s o m e tim e s b e u se d to

e n c o d e s e v era l s im ilar p o sitio n s th u s in c re as in g th e ris k o f in terf ere n c e as se a rc h

p ro g re s se s A s a co n se q u e n ce a n d c o n trary to L T W M T rsquos p re d ic tio n s p lay e rs

sh o u ld o fte n re v isit p o sitio n s b y g e n era tin g m o v es in s tea d o f a cc e ss in g th e m

d ire ctly fro m m em o ry T h is is w h at p la y e rsmdash e v e n m a ste rs mdash d o (D e G ro o t

1 9 4 6 ) F in a lly T T m a y h a v e s o m e th in g to sa y a b o u t e rro rs in c h e ss K ro g iu s

(1 9 7 6 ) m e n tio n s th a t er ro rs o f te n o c c u r w h e n a m o v e h a s ca u s ed im p o rta n t

c h a n g es in th e p o s itio n T h is m a y b e d u e to p la y e rsrsquo in a b ility to re c o g n ise th a t a

p re v io u sly a d eq u ate te m p late h as b ec o m e in a d e q u a te

In s u m m a ry T T o ffe rs a g o o d q u alita tiv e a c co u n t o f s e v eral im p o rtan t c h e ss

p h e n o m en a I t is n o w tim e to tu rn to m o re o b je c tiv e q u an tita tiv e te sts o f th e

th eo ry

A COM PUTER M ODE L O F S EARCH IN CH ESS

In th e re m a in d e r o f th is p a p e r I p re s en t a c o m p u te r m o d e l c a lled S E A R C H

w h ic h im p le m e n ts T T in so m e d e ta il I f irs t d e s crib e th e im p le m en ta tio n o f

S E A R C H m a k in g cle a r w h a t a s p ec ts o f T T h a v e b e e n in c lu d ed a n d th en d isc u ss

its b e h a v io u r w ith r es p e ct to h u m a n d a ta

O ve rv iew o f M ode l

F u ll im p le m e n ta tio n o f T T a s a c h e ss-p la y in g c o m p u ter p ro g ram w o u ld b e a

m ajo r ta sk mdash th is d iffic u lty is d e m o n stra te d b y th e fa c t th a t n o c o m p le te co m p u te r

m o d e l o f ch e s s c o g n itio n in c lu d in g p e rc e p tio n m em o ry a n d p ro b le m so lv in g

PATTERN -R ECOGN IT ION AND SEA RCH 299

h a s e v e r b e e n d e v elo p e d I p u rs u e d a lim ited a im a co m p u te r m o d el th a t c o n tain s

so m e o f th e im p o rta n t p aram e te rs o f T T a n d th a t co m p u te s k e y b e h a v io u ra l

v a ria b le s T h is m o d el d o e s n o t c o n stitu te a co m p le te im p le m e n ta tio n o f th e

th e o ry (it d o e s n o t s ea rc h o r e v a lu a te c h e ss p o sitio n s) b u t is d e ta ile d en o u g h to

o ffe r a g o o d te st o f so m e a s p ec ts o f T T I t is s o b e rin g to n o tic e th a t e v e n th is

p a rtia l im p lem e n tatio n o f th e th e o ry is q u ite c o m p le x a n d re q u ire s m a n y

p a ra m e te rs T h is is th e p rice o f a v o id in g th e v ag u en e s s o f v e rb al th e o ris in g

The M a in P rob lem -so lv in g Loop

T h e m ain in te re st o f th e m o d el is in th e in te ra c tio n b etw ee n p atte rn re c o g n itio n

a n d s ea rc h T h e m o d e l g e n e ra tes in d e p en d en t ep is o d es fo llo w in g se v e ral ru les

fo r g e n eratin g m o v e s a n d ch o o sin g sto p co n d itio n s C o m p atib le w ith m o s t

h u m an p ro to co ls th e p ro g ra m c o n sid e rs o n ly o n e b ra n c h w ith in a n ep is o d e (th u s

th e re is n o b ra n c h in g p o in t w ith in a n e p iso d e) A s illu stra te d in F ig 1 th e m o d e l

is c lo se to th e d es crip tio n o f T T g iv en e a rlie r in th is p a p e r T h e v ario u s c o n d itio n s

a n d o p e ra tio n s in S E A R C H a re re p re se n te d as p ro b a b ilit ie s o r p ro b ab ility

d istr ib u tio n s an d n o t a s a ctu a l c h e ss m o v e s e v a lu atio n s o r s y m b o lic s tru c tu res

in S T M o r in th e m in d rsquos e y e

A tra c e o f S E A R C H is sh o w n in F ig 2 T h e an aly s is w ill c e n tre o n th e

fo llo w in g v a ria b les a s a fu n c tio n o f th e n u m b e r o f c h u n k s ra te o f g en e ra tin g a

m o v e le v el o f fu z zin e ss in th e m in d rsquos e y e w h en a n e p is o d e is e n d e d m e an d e p th

o f s ea rc h m eth o d s u se d fo r g en e ra tin g a m o v e a n d m eth o d s u se d fo r s to p p in g a n

e p iso d e

T h e c o n c ep t o f te m p la te is im p le m e n te d in tw o w a y s (a ) b y h ig h e r

p ro b a b ilitie s o f f in d in g (s eq u en c e s o f) m o v e s a n d ev a lu a tio n s th an w ith p la in

c h u n k s a n d (b ) b y a d e cre a se in th e le v e l o f fu zz in e ss m ad e p o s sib le b y th e L T M

re p re se n ta tio n o f th e c o re o f th e p o sitio n a n d o f s lo ts

T h e le v e l o f re lia b ility o f th e in fo rm a tio n in th e m in d rsquos ey e is c a p tu re d b y a

ldquo fu z zin e s srdquo p a ra m e te r e x p re ss ed in a rb itr ary u n its T h re e m a in c o g n itiv e

fe a tu res ar e c a p tu red b y th is p a ra m ete r w o rk in g m e m o ry c a p a c ity a b ility to

m ain ta in a v isu o -s p atia l im ag e a n d su b je ctiv e e s tim a te o f th e r isk o f m ak in g a n

e rro r T h e fu z z in es s p a ram e ter is th e n as su m e d to o rig in ate b o th fro m th e

h a rd w a re a n d th e so ftw a re o f th e sy s tem It m a y v a ry d u r in g th e life tim e o f a

p la y er b e c a u se o f b io lo g ic a l m a tu ra tio n o r a g e in g an d m a y b e a ffe c ted b y

e x p e rim e n ta l m a n ip u latio n s T h e re a re th ree re a so n s w h y S E A R C H en d s a

se a rc h th e lev el o f fu z z in e s s is to o h ig h a n e v a lu atio n is p ro p o se d o r n o m o v e is

p ro p o s e d T h e id e a o f ex p ec ta tio n le v e l is n o t e x p lic itly p re se n t in th e m o d el b u t

it is im p lic it in th e p ro b a b ility v alu e s o f f in d in g fe atu re s e n d in g th e s ea rc h o f a n

e p iso d e e ith er b y p a tte rn re c o g n itio n o r b y th e a p p lica tio n o f h e u ristic s

S e le ctio n o f th e n ex t b a se -m o v e (a k e y c o n c ern o f N ew e ll amp S im o n 1 9 6 5 a n d

W ag n e r amp S c u rra h 1 9 7 1 ) is n o t ad d res se d b y S E A R C H w h ic h in g e n e ra l lac k s

th e s em a n tic in fo rm a tio n n e c es sa ry fo r su c h a se le c tio n F in a lly m e ta -se a rc h

w ith te m p la te s is n o t d ire c tly im p le m e n te d in S E A R C H b u t it is im p lic itly

300 GOBET

300

FIG 1 F lo w c h a rt o f S E A R C H

PATTERN -R ECOGN IT ION AND SEA RCH 301

301

F IG 2 E x a m p le s o f e p is o d e s g e n e ra te d b y S E A R C H

302 GOBET

re p re se n te d b y th e re la tiv e ly h ig h p ro b ab ility o f f in d in g (s eq u e n c e s o f) m o v es

a n d e v a lu atio n s w ith tem p la tes as c o m p are d w ith ch u n k s

The M ode lrsquos P aram e te rs

S E A R C H h as m a n y p a ra m ete rs a n d it is o f c o u rs e n e c es sa ry to se t u p a f ew o f

th e m w ith in d e p e n d e n t d a ta in o rd er to re d u c e th e n u m b e r o f d e g re e s o f fre e d o m

in th e m o d e l W h e n p o ss ib le I h a v e u s e d sim u la tio n s w ith th e C H R E S T (D e

G ro o t amp G o b e t 1 9 9 6 G o b e t 1 9 9 3 ) an d C H U M P (G o b e t amp Ja n s en 1 9 9 4 )

p ro g ram s to se t p a ra m e te r v a lu es C H R E S T is a p ro g ra m im p le m e n tin g as p e cts

o f T T a n d s im u la tin g n u m e ro u s e x p er im e n ts o n p e rc ep tio n an d m e m o ry in ch e s s

a n d C H U M P is a p ro g ra m p la y in g (w e ak ) c h e ss b y p u re p a tte rn re co g n itio n

N u m b e r o f C h u n k s a n d T e m p la te s T ab le 1 sh o w s th e v a lu es th at w ill b e

u s ed w ith th e S E A R C H m o d e l fo r th e se p a ra m ete rs T o c h o o se th e v a lu e s re la te d

to th e n u m b e r o f ch u n k s a n d te m p la tes th e c u rre n t v e rsio n o f C H R E S T h a s b e e n

e m p lo y e d T h e p ro b a b ility o f f in d in g a tem p la te w a s e stim ate d b y ru n n in g

C H R E S T o n 5 0 p o s itio n s ran d o m ly tak e n fro m M as ters rsquo g am e s T h e firs t lin e (0

c h u n k ) w a s ad d e d to g e t p re d ic tio n s a t th e n o v ic e lev e l W ith n e ts o f 1 0 0 0 0 0

1 2 0 0 0 0 a n d 1 5 0 0 0 0 c h u n k s th e p ara m ete rs w ere e stim ate d w ith th e b e s t-fit t in g

fu n c tio n s av a ilab le ( th e ldquo n o v ice rdquo v alu e s w ere n o t u se d ) T h e n u m b er o f te m p la tes

is ro u g h ly a lin e ar fu n c tio n o f th e n u m b er o f c h u n k s (r 2 = 9 7 ) T h e p ro b a b ility

o f f in d in g a tem p la te is a p p ro x im a tely a lo g -fu n c tio n o f th e n u m b e r o f c h u n k s

(r 2 = 9 4 )

H e u r is tic s C h u n k s T e m p la tes a n d T h e ir R e la tio n to th e P ro b a b ility o f

F in d in g M o v e s a n d E v a lu a tio n s T ab le 2 g iv e s th e v a lu e s u s ed in th e

sim u la tio n s fo r th e p a ra m ete rs re la te d to h e u ristic s c h u n k s a n d te m p la te s

H e u ris tic s in c lu d e sim p le se a rc h te c h n iq u e s (e g ldquo ta k e a p ie c e b a c k rdquo o r ldquoc h e c k

th e K in g rdquo ) a s w ell a s m o re a b stra c t ru le s (e g ldquoo c c u p y th e c en tre rdquo ) T h eir m a in

c h a rac te ris tic in co m p a riso n w ith c h u n k s an d tem p la te s is th a t th ey are g e n e ra l

a n d re q u ire so m e co n sc io u s c o m p u tatio n in o rd e r to p ro d u ce a m o v e T h e

a ss u m p tio n u n d e rly in g T a b le 2 is th at th e p aram e ters re la ted to h e u ristic s s ta y

ro u g h ly c o n sta n t w h ile th e o th e r p aram e te rs v a ry as a lo g arith m ic fu n c tio n o f th e

n u m b e r o f c h u n k s in th e n e t (A lo g arith m ic fu n ctio n h a s b e e n c h o se n to in d ica te

th a t ch u n k s y ie ld a d im in ish in g re tu rn as th e ir n u m b e r in c re a se s) T h e

a ss u m p tio n th a t th e n u m b e r o f h e u ristic s is c o n sta n t ac ro s s s k ill le v e ls se e m s

re a so n a b le (p e rh a p s w ith th e e x ce p tio n o f th e n o v ic e le v e l) a s m o s t c h e ss

M a ste rs rsquo k n o w le d g e is v e ry sp ec ific to c erta in a sp e c ts o f th e g a m e (D e G ro o t

1 9 4 6 )

T h e fo llo w in g c o n s id era tio n s w e re m ad e in se ttin g th e v alu e s g iv e n in

T ab le 2 I t w a s d ee m e d p lau sib le th a t th e p ro b a b ility o f f in d in g so m e h e u ristic in

a p o s itio n b e h ig h ( 9 5 ) a s w e ll a s th e p ro b a b ility o f f in d in g s o m e c h u n k F in ally

PATTERN -R ECOGN IT ION AND SEA RCH 303

TA BLE 1

The V a lu es o f th e 14 N e ts U sed in th e S im u la tio ns

P ro b a b i li ty o f

re c o g n is in g a t le as t

P ro p o r t io n o f o n e te m p la te g iv e n a

N u m b e r o f c h u n k s N u m b e r o f te m p la te s te m p la te s p o s i t io n

0 0 0 0 0 0 0 0

1 0 0 2 0 0 0 0 0 0 0

2 6 8 0 5 0 0 2 1 8 0

5 0 0 3 3 6 0 0 7 1 4 0

1 0 0 1 1 1 0 0 0 1 0 2 4 0

2 0 0 0 3 2 6 5 0 1 3 3 0 0

3 0 0 0 1 4 9 3 0 1 6 3 6 0

4 0 0 0 5 7 7 4 0 1 9 4 6 0

5 0 0 0 6 1 1 4 2 0 2 3 4 0 0

7 2 0 4 4 2 1 3 6 0 3 0 4 8 0

8 0 0 1 0 2 2 8 5 0 2 9 5 4 0

1 0 0 0 0 0 2 7 6 5 0 2 8 5 1 0

1 2 0 0 0 0 3 3 5 7 0 2 8 5 4 0

1 5 0 0 0 0 4 2 4 5 0 2 8 5 6 0

T h e v a lu e s b e lo w 1 0 0 0 0 0 c h u n k s w e r e ta k e n f ro m s im u la t io n s w ith C H R E S T th e o the rs

e x t ra p o la te d S e e te x t f o r d e ta ils

TA BLE 2

H eur is t ic s C hun ks Tem pla tes and Their Re la tion to th e P ro bab ility of Fin d in g

M oves and Evalu ta tio ns

T y p e H e u r is tic s C h u n k s T e m p la te s

P ro b a b i li ty o f e v o k in g a n 9 5 g (n _ c h u n k s 9 5 )a se e T a b le 1

h e u ri s t ic a c h u n k o r a te m p la te

P ro b a b i li ty o f f in d in g a m o v e 5 0 g (n _ c h u n k s 5 0 ) g (n _ c h u n k s 9 0 )

g ive n th a t a n h e u r is tic a c h u n k

o r a te m p la te h a s b e e n e v o k e d

P ro b a b i li ty o f f in d in g a n e v a lu a tio n 1 5 g (n _ c h u n k s 0 5 ) g (n _ c h u n k s 5 0 )

g iv e n th a t a n h e u ri s t ic a c h u n k o r

a te m p la te h a s b e e n e v o k e d

aT h e fu n c tio n g i s d e f in e d a s

g (n _ c h un k s p ro b ) = p ro b 0 2 lo g1 0

(n _ c h un k s ) i f n _ c h u n k s gt 0

a n d

g (n _ c h u n k s p ro b ) = 0 i f n _ c h u n k s = 0

w h e re n _ c h u n k s i s th e n u m b e r o f c h u n k s in a g iv e n n e t a n d p ro b i s a c o n s ta n t

303

304 GOBET

th e p ro b a b ility o f re c o g n isin g a te m p la te in a p o sitio n is sm a lle r a n d is g iv e n in

T ab le 1

T h e p ro b a b ility o f f in d in g a m o v e g iv e n a h e u ristic is s e t to 5 0 in d ic atin g th a t

h e u ristic s m a y fa il to p ro d u ce a m o v e h a lf o f th e tim e T h is is b e c a u se so m e

h e u ristic s m ay n o t y ie ld a m o v e a n d b ec a u se so m e p ro p o se d m o v es m a y b e

ille g a l T h e p ro b a b ility o f f in d in g a m o v e g iv en a tem p la te is h ig h p a rtly

re fle ctin g th e ric h s em a n tic k n o w le d g e an d th e in te r-te m p la te lin k s a s su m e d to

c h a rac te rise te m p la te s F o r th e p ro b a b ility o f f in d in g a m o v e g iv e n th a t a ch u n k

h a s b e en re co g n ise d I u se d th e p ara m e te r p ro b in th e fu n ctio n g (s ee T a b le 2 ) so

th a t i t a p p ro x im a te s th e d ata p ro d u c ed b y th e C H U M P p ro g ram (G o b et amp Ja n se n

1 9 9 4 ) E v a lu a tio n s a re su p p o s ed to b e h a rd er to le arn a n d th e re fo re h a rd e r to u se

th a n m o v es H e n ce th e ir p ro b a b ilit ie s a re lo w e r th a n th e co r res p o n d in g p ro b -

a b ilit ie s w ith m o v es A g a in fo llo w in g d irec tly fro m th e th e o ry te m p la te s o ffe r

th e b e st so u rce o f ev alu a tio n s

W ith re sp e c t to th e n u m b e r o f se q u e n tia l m o v e s p ro p o s ed c o u n ted in p lie s

(i e m o v e s fo r W h ite o r B la ck ) i t is as su m e d th a t h e u ristic s g iv e a cc e ss to o n ly

o n e m o v e w h ile c h u n k s a n d te m p late s y ie ld se q u e n c es o f m o v e s w h o se n u m b e r

fo llo w s a g e o m e tric p ro b a b ility d is tr ib u tio n (th e c h o ice o f th is d is tr ib u tio n w as

in sp ire d b y sta tis tic s ta k e n fro m C H U M P ) T h e lo n g e s t s eq u e n c e ( ca ll i t k ) h as a

fre q u e n c y o f 1 th e s e co n d -lo n g e st a fre q u en cy o f 2 th e th ird -lo n g e st a fre q u e n c y

o f 4 a n d so o n u n til th e sh o rte st se q u e n c e w h o s e len g th is 1 m o v e an d w h o se

fre q u e n c y is 2 (k ndash 1 ) T h e m a x im u m se q u e n ce o f m o v es w a s se t to 1 8 F in a lly

S E A R C H atte m p ts to g e n e ra te a m o v e b y p a ttern re c o g n itio n ( ch u n k o r te m p la te )

fo u r tim e s b e fo re u sin g a n h e u ristic

T im e a n d F u zzin e ss P a ra m ete rs T h e tim e p a ram e ter s fo r th e re sp e c tiv e

o p e ra tio n s w e re s et u sin g p la u sib le v a lu e s (se e T a b le 3 ) M o v e g en era tio n b y

p a tte rn re c o g n itio n (c h u n k o r te m p late ) is as su m e d to b e v e ry sh o rt (a few

h u n d re d m illis e co n d s) n o tim e c o st is u se d in th e m o d e l T h e tim e fo r c o m p u tin g

a m o v e-g en e ra tin g h e u ristic w a s s et to th e ra th e r lo n g 2 0 s ec o n d s mdash g en era tin g a

m o v e w ith o u t u sin g p a tte rn r ec o g n itio n re q u ires p u ttin g to g eth e r v a rio u s ty p e s o f

in fo rm a tio n a n d a s k s fo r m a n y ch e c k in g p ro c ed u res T h e tim e fo r c a rry in g o u t

o n e m o v e (o n c e g e n erate d ) in th e m in d rsquos e y e w a s s et to tw o s ec o n d s T h is is

c o m p atib le w ith S a a rilu o m a rsquos (1 9 8 9 ) d ata w h ic h sh o w th a t a b lin d fo ld ed M a ste r

c an fo llo w a g a m e d icta ted a t tw o se c o n d s a m o v e F in ally th e tim e fo r ca rry in g

o u t a n ev a lu a tio n b y h eu ris tic is s e t to 1 0 s e co n d s T h is ra th e r s h o rt tim e m a y b e

ju stif ie d b y th e fa c t th a t p la y e rs ty p ic a lly co n s id e r o n ly o n e (s u b jec tiv e ) a sp e c t o f

th e p o sitio n (D e G ro o t 1 9 4 6 ) a n d th at m an y e v a lu atio n s c a n b e g ro u n d ed o n th e

b a sis o f c lea r m a teria l lo ss e s

T h e fu z zin e ss lev el o f th e s y ste m is e x p re ss ed in a rb itra ry u n its I t s ta rts w ith

th e v a lu e z e ro a n d it is in c re a se d w h e n a m o v e is c a rrie d o u t in th e m in d rsquos e y e

a n d w h e n tim e is s p e n t a p p ly in g a n h e u ris tic W h e n a te m p la te is fo u n d th e

PATTERN -R ECOGN IT ION AND SEA RCH 305

fu z z in es s lev el is d e cre a se d a s p a rt o f th e in fo rm atio n m ay b e sto re d in L T M

d ire c tly fre e in g c ap ac ity in w o rk in g m e m o ry a n d in th e m in d rsquos ey e

S im u la t io n s w ith th e ldquo C anon ica l M ode lrdquo

T h e sim u latio n s d e sc rib ed in th is s ec tio n a re s tra ig h tfo rw a rd U s in g th e

p a ra m e te r v alu e s d is cu sse d e a rlie r I le t th e p ro g ra m s ea rc h 1 0 0 0 ep iso d e s fo r

e ac h n e t s iz e S u m m a ry v alu e s fo r m e a n d ep th o f se a rc h t im e ra tio d e p th tim e

a n d fu z zin e s s a s w e ll a s fo r g e n e ra tio n an d s to p co n d itio n s w e re c o m p u ted fo r

e ac h n e t s iz e

M e a n D e p th o f S e a r ch R a te o f S e a rc h a n d F u z zin e ss A cc o rd in g to

S E A R C H m ea n d e p th o f s ea rc h fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f

c h u n k s (se e F ig 3 a) If w e as su m e a co n sta n t ra te o f le a rn in g n e w c h u n k s a s is

c o m m o n p ra ctic e in so m e c o g n itiv e a rch ite c tu res (c f N e w e ll 1 9 9 0 ) a n d if w e

a ss u m e th a t s k ille d p la y e rs h a v e sp e n t m o re p rac tice a n d stu d y tim e th a n

u n s k ille d p la y e rs th e n m e an d e p th fo llo w s a p o w e r fu n c tio n o f s k ill as w e ll T h is

p re d ic tio n w h ic h is a t v ar ia n c e w ith H o ld in g rsquos p re d ic tio n (1 9 8 5 p 1 8 2 ) o f a

lin ea r in c rea s e is p artly co n siste n t w ith C h a rn e ss rsquos (1 9 8 1 ) p ro p o s a l th a t d e p th o f

se a rc h is n o t l in e arly re la ted to s k ill b u t th at th e re is a ce ilin g a t h ig h s k ill le v e ls

T h e re su lt is a ls o c o m p atib le w ith th e w e a k lin e ar re la tio n fo u n d in e m p ir ic a l

stu d ie s (C h a rn e ss 1 9 8 1 G o b e t in p re ss ) b e tw e e n m e a n d e p th o f se a rch a n d sk ill

le v el b e c a u se re stric te d ra n g e s o f th e c u rv e c a n b e a p p ro x im a ted b y a lin e a r

fu n c tio n T h e a b so lu te v alu e s a re a lso q u ite r ea so n ab le th ey ris e f ro m lo w d ep th s

(le ss th a n 1 p ly ) w ith n o ch u n k s (co r res p o n d in g to th e n o v ic e le v el) to a ro u n d 2 5

p lies w ith a sm a ll n et (1 0 0 0 c h u n k s ) an d th e n to a ro u n d 4 p lie s w ith ex p ert le v e l

(a ro u n d 3 0 0 0 0 c h u n k s a s e s tim a te d b y s im u la tio n s o n th e re ca ll tas k ) T h e y th e n

slo w ly (s av e fo r a f ew ra n d o m v a ria tio n s ) in c re a se to m o re th an 5 p lie s w ith n e t

la rg er th an 1 0 0 0 0 0 c h u n k s w h ic h c o rre sp o n d s to G ran d m a ste r le v e l H o ld in g

(1 9 8 5 ) c o m p u te d m e a n d e p th o f se a rch fo r d e G ro o trsquos (1 9 4 6 ) d a ta a n d fo u n d th a t

TA BLE 3

T im e and ldquo Fuzz in ess rdquo Param e ters U sed in th e

S im ula t io n s

T im e fo r c a r ry in g o u t a m o v e 2 s

T im e fo r c o m p u t in g m o v e -g e n e r a tin g h e u r is tic 2 0 s

T im e fo r c o m p u t in g e v a lu a t io n 1 0 s

U p p e r l im it o f fu z z in e ss 5 0

In c r e a se o f fu z z in e s s p e r m o v e 1

In c re a se o f f u z z in e ss p e r s e c o n d 2

D e c re a s e in fu z z in e ss d u e to te m p la te 5

306 GOBET

E x p e rts a n d G ra n d m as ters h a d res p e ctiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 8 a n d

5 3 T h e reg res sio n e q u a tio n d e riv e d f ro m C h a rn e ss rsquos (1 9 8 1 ) d ata y ie ld a n

a v e rag e d e p th o f se a rc h o f a b o u t 2 3 p lies a t th e 1 3 0 0 E L O 1 le v e l o f 4 1 a t th e

E x p e rt le v e l (2 0 0 0 E L O ) a n d o f 5 7 a t th e G ra n d m a s te r le v el U n fo rtu n a tely n o

stu d y te ste d p la y e rs ra n g in g fro m n o v ic es to G ran d m a ste rs an d S E A R C H rsquos

p re d ic tio n o f a p o w e r la w o f p rac tic e c an n o t b e te ste d (y e t) I w ill re p o rt la te r

sim u la tio n s a d d re ssin g d a ta co lle c ted b y S a arilu o m a (1 9 9 0 ) w h e re In tern atio n a l

M a ste rs a n d G ra n d m a s te rs te n d e d to s e arc h le s s th a n M as te rs

T h e ra te o f s ea rc h a lso fo llo w s a p o w e r fu n ctio n o f th e n u m b e r o f c h u n k s (se e

F ig 3 b ) D e G ro o t (1 9 4 6 ) C h arn es s (1 9 8 1 ) a n d G o b e t ( in p res s) a ll f o u n d th a t

stro n g p la y er s te n d e d to s e arc h fa ste r F o r ex a m p le G o b e t ( in p re s s) fo u n d th a t

h is M a ste rs E x p e rts C la ss A a n d C la s s B p lay e rs re sp e c tiv ely se arch e d 4 8 4 1

3 2 an d 3 4 n o d e s p e r m in u te S E A R C H rsquos v a lu es a re h ig h e r b u t s til l p la u s ib le

F o r ex am p le W a g n e r a n d S c u rra h rsquos (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r

m in u te N o te a lso th a t a ll th e ex p erim e n ts m e n tio n e d e a rlier h a v e u se d v e rb a l

p ro to c o ls w h ic h m ay h av e s lo w e d d o w n th e ra te o f se a rc h (c f E ric ss o n amp

S im o n 1 9 8 0 ) F in a lly th e ra te o f se arch m a y h av e b e e n u n d e res tim a ted in th e

lite ra tu re b ec a u se th e r a te o f g e n e ratin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d

b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l t im e H o w e v e r to ta l t im e in c lu d es

tim e n o t sp e n t in s e arc h ( fo r e x a m p le w h a t D e G ro o t c a lls th e ldquo firs t p h a se rdquo)

T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a riab le th e le v e l o f fu zz in e ss a t

w h ic h a se a rc h is e n d e d is m o re d if fic u lt to ju d g e b ec a u se lit tle is k n o w n a b o u t

th e ro le o f fu z z in es s in c h es s th in k in g A g ain S E A R C H p ro p o se s th a t th is

v a riab le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s ee F ig 3 c ) W ith la rg e r

n e ts e p iso d es te n d to b e e n d e d w ith lo w er le v els o f fu z z in e s s T h is su g g es ts th at

in g e n e ra l s tro n g p la y ers s h o u ld b e m o re c o n fid e n t in th e ir c alc u la tio n s as th e y

a re n o t a t th e e d g e o f th eir p o s sib ilitie s N o te th a t th e ra te o f ch an g e is ra th e r h ig h

fo r th is p o w er law w h ic h s u g g e sts th at it sh o u ld b e p o ss ib le to d e te c t i t

e x p erim e n tally

G e n e ra tio n o f M o ve s H o w is m o v e g en e ra tio n af fec te d b y sk ill le v e l A s

sh o w n in F ig 4 a S E A R C H m a k es c le a r p re d ic tio n s W ith sm a ll n u m b e rs o f

c h u n k s th e tim e -c o n s u m in g p ro ce s s o f g en e ra tin g m o v es b y h e u ristic s is

e m p lo y e d T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y ch u n k s

w h ic h is in tu rn d o m in a te d b y te m p la te g e n eratio n

1 T h e E L O ra t in g i s a n in te r v a l sc a le th a t ra n k s c o m p e t it io n c h e ss p la y e rs I ts s ta n d a rd de v ia t io n

(2 0 0 p o in ts) is o f te n in te r p re te d a s a m e a su r e o f sk i ll c la s s in c h e ss G r a n d m a s te r s a re n o rm a lly ra te d

a b o v e 2 5 0 0 In te rn a t io n a l M a s te r s a b o v e 2 4 0 0 M a s te r s a b o v e 2 2 0 0 a n d E x p e rt s a b o v e 2 0 0 0

B e lo w c la sse s (A B e tc ) d iv id e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in ts

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

PATTERN -R ECOGN IT ION AND SEA RCH 299

h a s e v e r b e e n d e v elo p e d I p u rs u e d a lim ited a im a co m p u te r m o d el th a t c o n tain s

so m e o f th e im p o rta n t p aram e te rs o f T T a n d th a t co m p u te s k e y b e h a v io u ra l

v a ria b le s T h is m o d el d o e s n o t c o n stitu te a co m p le te im p le m e n ta tio n o f th e

th e o ry (it d o e s n o t s ea rc h o r e v a lu a te c h e ss p o sitio n s) b u t is d e ta ile d en o u g h to

o ffe r a g o o d te st o f so m e a s p ec ts o f T T I t is s o b e rin g to n o tic e th a t e v e n th is

p a rtia l im p lem e n tatio n o f th e th e o ry is q u ite c o m p le x a n d re q u ire s m a n y

p a ra m e te rs T h is is th e p rice o f a v o id in g th e v ag u en e s s o f v e rb al th e o ris in g

The M a in P rob lem -so lv in g Loop

T h e m ain in te re st o f th e m o d el is in th e in te ra c tio n b etw ee n p atte rn re c o g n itio n

a n d s ea rc h T h e m o d e l g e n e ra tes in d e p en d en t ep is o d es fo llo w in g se v e ral ru les

fo r g e n eratin g m o v e s a n d ch o o sin g sto p co n d itio n s C o m p atib le w ith m o s t

h u m an p ro to co ls th e p ro g ra m c o n sid e rs o n ly o n e b ra n c h w ith in a n ep is o d e (th u s

th e re is n o b ra n c h in g p o in t w ith in a n e p iso d e) A s illu stra te d in F ig 1 th e m o d e l

is c lo se to th e d es crip tio n o f T T g iv en e a rlie r in th is p a p e r T h e v ario u s c o n d itio n s

a n d o p e ra tio n s in S E A R C H a re re p re se n te d as p ro b a b ilit ie s o r p ro b ab ility

d istr ib u tio n s an d n o t a s a ctu a l c h e ss m o v e s e v a lu atio n s o r s y m b o lic s tru c tu res

in S T M o r in th e m in d rsquos e y e

A tra c e o f S E A R C H is sh o w n in F ig 2 T h e an aly s is w ill c e n tre o n th e

fo llo w in g v a ria b les a s a fu n c tio n o f th e n u m b e r o f c h u n k s ra te o f g en e ra tin g a

m o v e le v el o f fu z zin e ss in th e m in d rsquos e y e w h en a n e p is o d e is e n d e d m e an d e p th

o f s ea rc h m eth o d s u se d fo r g en e ra tin g a m o v e a n d m eth o d s u se d fo r s to p p in g a n

e p iso d e

T h e c o n c ep t o f te m p la te is im p le m e n te d in tw o w a y s (a ) b y h ig h e r

p ro b a b ilitie s o f f in d in g (s eq u en c e s o f) m o v e s a n d ev a lu a tio n s th an w ith p la in

c h u n k s a n d (b ) b y a d e cre a se in th e le v e l o f fu zz in e ss m ad e p o s sib le b y th e L T M

re p re se n ta tio n o f th e c o re o f th e p o sitio n a n d o f s lo ts

T h e le v e l o f re lia b ility o f th e in fo rm a tio n in th e m in d rsquos ey e is c a p tu re d b y a

ldquo fu z zin e s srdquo p a ra m e te r e x p re ss ed in a rb itr ary u n its T h re e m a in c o g n itiv e

fe a tu res ar e c a p tu red b y th is p a ra m ete r w o rk in g m e m o ry c a p a c ity a b ility to

m ain ta in a v isu o -s p atia l im ag e a n d su b je ctiv e e s tim a te o f th e r isk o f m ak in g a n

e rro r T h e fu z z in es s p a ram e ter is th e n as su m e d to o rig in ate b o th fro m th e

h a rd w a re a n d th e so ftw a re o f th e sy s tem It m a y v a ry d u r in g th e life tim e o f a

p la y er b e c a u se o f b io lo g ic a l m a tu ra tio n o r a g e in g an d m a y b e a ffe c ted b y

e x p e rim e n ta l m a n ip u latio n s T h e re a re th ree re a so n s w h y S E A R C H en d s a

se a rc h th e lev el o f fu z z in e s s is to o h ig h a n e v a lu atio n is p ro p o se d o r n o m o v e is

p ro p o s e d T h e id e a o f ex p ec ta tio n le v e l is n o t e x p lic itly p re se n t in th e m o d el b u t

it is im p lic it in th e p ro b a b ility v alu e s o f f in d in g fe atu re s e n d in g th e s ea rc h o f a n

e p iso d e e ith er b y p a tte rn re c o g n itio n o r b y th e a p p lica tio n o f h e u ristic s

S e le ctio n o f th e n ex t b a se -m o v e (a k e y c o n c ern o f N ew e ll amp S im o n 1 9 6 5 a n d

W ag n e r amp S c u rra h 1 9 7 1 ) is n o t ad d res se d b y S E A R C H w h ic h in g e n e ra l lac k s

th e s em a n tic in fo rm a tio n n e c es sa ry fo r su c h a se le c tio n F in a lly m e ta -se a rc h

w ith te m p la te s is n o t d ire c tly im p le m e n te d in S E A R C H b u t it is im p lic itly

300 GOBET

300

FIG 1 F lo w c h a rt o f S E A R C H

PATTERN -R ECOGN IT ION AND SEA RCH 301

301

F IG 2 E x a m p le s o f e p is o d e s g e n e ra te d b y S E A R C H

302 GOBET

re p re se n te d b y th e re la tiv e ly h ig h p ro b ab ility o f f in d in g (s eq u e n c e s o f) m o v es

a n d e v a lu atio n s w ith tem p la tes as c o m p are d w ith ch u n k s

The M ode lrsquos P aram e te rs

S E A R C H h as m a n y p a ra m ete rs a n d it is o f c o u rs e n e c es sa ry to se t u p a f ew o f

th e m w ith in d e p e n d e n t d a ta in o rd er to re d u c e th e n u m b e r o f d e g re e s o f fre e d o m

in th e m o d e l W h e n p o ss ib le I h a v e u s e d sim u la tio n s w ith th e C H R E S T (D e

G ro o t amp G o b e t 1 9 9 6 G o b e t 1 9 9 3 ) an d C H U M P (G o b e t amp Ja n s en 1 9 9 4 )

p ro g ram s to se t p a ra m e te r v a lu es C H R E S T is a p ro g ra m im p le m e n tin g as p e cts

o f T T a n d s im u la tin g n u m e ro u s e x p er im e n ts o n p e rc ep tio n an d m e m o ry in ch e s s

a n d C H U M P is a p ro g ra m p la y in g (w e ak ) c h e ss b y p u re p a tte rn re co g n itio n

N u m b e r o f C h u n k s a n d T e m p la te s T ab le 1 sh o w s th e v a lu es th at w ill b e

u s ed w ith th e S E A R C H m o d e l fo r th e se p a ra m ete rs T o c h o o se th e v a lu e s re la te d

to th e n u m b e r o f ch u n k s a n d te m p la tes th e c u rre n t v e rsio n o f C H R E S T h a s b e e n

e m p lo y e d T h e p ro b a b ility o f f in d in g a tem p la te w a s e stim ate d b y ru n n in g

C H R E S T o n 5 0 p o s itio n s ran d o m ly tak e n fro m M as ters rsquo g am e s T h e firs t lin e (0

c h u n k ) w a s ad d e d to g e t p re d ic tio n s a t th e n o v ic e lev e l W ith n e ts o f 1 0 0 0 0 0

1 2 0 0 0 0 a n d 1 5 0 0 0 0 c h u n k s th e p ara m ete rs w ere e stim ate d w ith th e b e s t-fit t in g

fu n c tio n s av a ilab le ( th e ldquo n o v ice rdquo v alu e s w ere n o t u se d ) T h e n u m b er o f te m p la tes

is ro u g h ly a lin e ar fu n c tio n o f th e n u m b er o f c h u n k s (r 2 = 9 7 ) T h e p ro b a b ility

o f f in d in g a tem p la te is a p p ro x im a tely a lo g -fu n c tio n o f th e n u m b e r o f c h u n k s

(r 2 = 9 4 )

H e u r is tic s C h u n k s T e m p la tes a n d T h e ir R e la tio n to th e P ro b a b ility o f

F in d in g M o v e s a n d E v a lu a tio n s T ab le 2 g iv e s th e v a lu e s u s ed in th e

sim u la tio n s fo r th e p a ra m ete rs re la te d to h e u ristic s c h u n k s a n d te m p la te s

H e u ris tic s in c lu d e sim p le se a rc h te c h n iq u e s (e g ldquo ta k e a p ie c e b a c k rdquo o r ldquoc h e c k

th e K in g rdquo ) a s w ell a s m o re a b stra c t ru le s (e g ldquoo c c u p y th e c en tre rdquo ) T h eir m a in

c h a rac te ris tic in co m p a riso n w ith c h u n k s an d tem p la te s is th a t th ey are g e n e ra l

a n d re q u ire so m e co n sc io u s c o m p u tatio n in o rd e r to p ro d u ce a m o v e T h e

a ss u m p tio n u n d e rly in g T a b le 2 is th at th e p aram e ters re la ted to h e u ristic s s ta y

ro u g h ly c o n sta n t w h ile th e o th e r p aram e te rs v a ry as a lo g arith m ic fu n c tio n o f th e

n u m b e r o f c h u n k s in th e n e t (A lo g arith m ic fu n ctio n h a s b e e n c h o se n to in d ica te

th a t ch u n k s y ie ld a d im in ish in g re tu rn as th e ir n u m b e r in c re a se s) T h e

a ss u m p tio n th a t th e n u m b e r o f h e u ristic s is c o n sta n t ac ro s s s k ill le v e ls se e m s

re a so n a b le (p e rh a p s w ith th e e x ce p tio n o f th e n o v ic e le v e l) a s m o s t c h e ss

M a ste rs rsquo k n o w le d g e is v e ry sp ec ific to c erta in a sp e c ts o f th e g a m e (D e G ro o t

1 9 4 6 )

T h e fo llo w in g c o n s id era tio n s w e re m ad e in se ttin g th e v alu e s g iv e n in

T ab le 2 I t w a s d ee m e d p lau sib le th a t th e p ro b a b ility o f f in d in g so m e h e u ristic in

a p o s itio n b e h ig h ( 9 5 ) a s w e ll a s th e p ro b a b ility o f f in d in g s o m e c h u n k F in ally

PATTERN -R ECOGN IT ION AND SEA RCH 303

TA BLE 1

The V a lu es o f th e 14 N e ts U sed in th e S im u la tio ns

P ro b a b i li ty o f

re c o g n is in g a t le as t

P ro p o r t io n o f o n e te m p la te g iv e n a

N u m b e r o f c h u n k s N u m b e r o f te m p la te s te m p la te s p o s i t io n

0 0 0 0 0 0 0 0

1 0 0 2 0 0 0 0 0 0 0

2 6 8 0 5 0 0 2 1 8 0

5 0 0 3 3 6 0 0 7 1 4 0

1 0 0 1 1 1 0 0 0 1 0 2 4 0

2 0 0 0 3 2 6 5 0 1 3 3 0 0

3 0 0 0 1 4 9 3 0 1 6 3 6 0

4 0 0 0 5 7 7 4 0 1 9 4 6 0

5 0 0 0 6 1 1 4 2 0 2 3 4 0 0

7 2 0 4 4 2 1 3 6 0 3 0 4 8 0

8 0 0 1 0 2 2 8 5 0 2 9 5 4 0

1 0 0 0 0 0 2 7 6 5 0 2 8 5 1 0

1 2 0 0 0 0 3 3 5 7 0 2 8 5 4 0

1 5 0 0 0 0 4 2 4 5 0 2 8 5 6 0

T h e v a lu e s b e lo w 1 0 0 0 0 0 c h u n k s w e r e ta k e n f ro m s im u la t io n s w ith C H R E S T th e o the rs

e x t ra p o la te d S e e te x t f o r d e ta ils

TA BLE 2

H eur is t ic s C hun ks Tem pla tes and Their Re la tion to th e P ro bab ility of Fin d in g

M oves and Evalu ta tio ns

T y p e H e u r is tic s C h u n k s T e m p la te s

P ro b a b i li ty o f e v o k in g a n 9 5 g (n _ c h u n k s 9 5 )a se e T a b le 1

h e u ri s t ic a c h u n k o r a te m p la te

P ro b a b i li ty o f f in d in g a m o v e 5 0 g (n _ c h u n k s 5 0 ) g (n _ c h u n k s 9 0 )

g ive n th a t a n h e u r is tic a c h u n k

o r a te m p la te h a s b e e n e v o k e d

P ro b a b i li ty o f f in d in g a n e v a lu a tio n 1 5 g (n _ c h u n k s 0 5 ) g (n _ c h u n k s 5 0 )

g iv e n th a t a n h e u ri s t ic a c h u n k o r

a te m p la te h a s b e e n e v o k e d

aT h e fu n c tio n g i s d e f in e d a s

g (n _ c h un k s p ro b ) = p ro b 0 2 lo g1 0

(n _ c h un k s ) i f n _ c h u n k s gt 0

a n d

g (n _ c h u n k s p ro b ) = 0 i f n _ c h u n k s = 0

w h e re n _ c h u n k s i s th e n u m b e r o f c h u n k s in a g iv e n n e t a n d p ro b i s a c o n s ta n t

303

304 GOBET

th e p ro b a b ility o f re c o g n isin g a te m p la te in a p o sitio n is sm a lle r a n d is g iv e n in

T ab le 1

T h e p ro b a b ility o f f in d in g a m o v e g iv e n a h e u ristic is s e t to 5 0 in d ic atin g th a t

h e u ristic s m a y fa il to p ro d u ce a m o v e h a lf o f th e tim e T h is is b e c a u se so m e

h e u ristic s m ay n o t y ie ld a m o v e a n d b ec a u se so m e p ro p o se d m o v es m a y b e

ille g a l T h e p ro b a b ility o f f in d in g a m o v e g iv en a tem p la te is h ig h p a rtly

re fle ctin g th e ric h s em a n tic k n o w le d g e an d th e in te r-te m p la te lin k s a s su m e d to

c h a rac te rise te m p la te s F o r th e p ro b a b ility o f f in d in g a m o v e g iv e n th a t a ch u n k

h a s b e en re co g n ise d I u se d th e p ara m e te r p ro b in th e fu n ctio n g (s ee T a b le 2 ) so

th a t i t a p p ro x im a te s th e d ata p ro d u c ed b y th e C H U M P p ro g ram (G o b et amp Ja n se n

1 9 9 4 ) E v a lu a tio n s a re su p p o s ed to b e h a rd er to le arn a n d th e re fo re h a rd e r to u se

th a n m o v es H e n ce th e ir p ro b a b ilit ie s a re lo w e r th a n th e co r res p o n d in g p ro b -

a b ilit ie s w ith m o v es A g a in fo llo w in g d irec tly fro m th e th e o ry te m p la te s o ffe r

th e b e st so u rce o f ev alu a tio n s

W ith re sp e c t to th e n u m b e r o f se q u e n tia l m o v e s p ro p o s ed c o u n ted in p lie s

(i e m o v e s fo r W h ite o r B la ck ) i t is as su m e d th a t h e u ristic s g iv e a cc e ss to o n ly

o n e m o v e w h ile c h u n k s a n d te m p late s y ie ld se q u e n c es o f m o v e s w h o se n u m b e r

fo llo w s a g e o m e tric p ro b a b ility d is tr ib u tio n (th e c h o ice o f th is d is tr ib u tio n w as

in sp ire d b y sta tis tic s ta k e n fro m C H U M P ) T h e lo n g e s t s eq u e n c e ( ca ll i t k ) h as a

fre q u e n c y o f 1 th e s e co n d -lo n g e st a fre q u en cy o f 2 th e th ird -lo n g e st a fre q u e n c y

o f 4 a n d so o n u n til th e sh o rte st se q u e n c e w h o s e len g th is 1 m o v e an d w h o se

fre q u e n c y is 2 (k ndash 1 ) T h e m a x im u m se q u e n ce o f m o v es w a s se t to 1 8 F in a lly

S E A R C H atte m p ts to g e n e ra te a m o v e b y p a ttern re c o g n itio n ( ch u n k o r te m p la te )

fo u r tim e s b e fo re u sin g a n h e u ristic

T im e a n d F u zzin e ss P a ra m ete rs T h e tim e p a ram e ter s fo r th e re sp e c tiv e

o p e ra tio n s w e re s et u sin g p la u sib le v a lu e s (se e T a b le 3 ) M o v e g en era tio n b y

p a tte rn re c o g n itio n (c h u n k o r te m p late ) is as su m e d to b e v e ry sh o rt (a few

h u n d re d m illis e co n d s) n o tim e c o st is u se d in th e m o d e l T h e tim e fo r c o m p u tin g

a m o v e-g en e ra tin g h e u ristic w a s s et to th e ra th e r lo n g 2 0 s ec o n d s mdash g en era tin g a

m o v e w ith o u t u sin g p a tte rn r ec o g n itio n re q u ires p u ttin g to g eth e r v a rio u s ty p e s o f

in fo rm a tio n a n d a s k s fo r m a n y ch e c k in g p ro c ed u res T h e tim e fo r c a rry in g o u t

o n e m o v e (o n c e g e n erate d ) in th e m in d rsquos e y e w a s s et to tw o s ec o n d s T h is is

c o m p atib le w ith S a a rilu o m a rsquos (1 9 8 9 ) d ata w h ic h sh o w th a t a b lin d fo ld ed M a ste r

c an fo llo w a g a m e d icta ted a t tw o se c o n d s a m o v e F in ally th e tim e fo r ca rry in g

o u t a n ev a lu a tio n b y h eu ris tic is s e t to 1 0 s e co n d s T h is ra th e r s h o rt tim e m a y b e

ju stif ie d b y th e fa c t th a t p la y e rs ty p ic a lly co n s id e r o n ly o n e (s u b jec tiv e ) a sp e c t o f

th e p o sitio n (D e G ro o t 1 9 4 6 ) a n d th at m an y e v a lu atio n s c a n b e g ro u n d ed o n th e

b a sis o f c lea r m a teria l lo ss e s

T h e fu z zin e ss lev el o f th e s y ste m is e x p re ss ed in a rb itra ry u n its I t s ta rts w ith

th e v a lu e z e ro a n d it is in c re a se d w h e n a m o v e is c a rrie d o u t in th e m in d rsquos e y e

a n d w h e n tim e is s p e n t a p p ly in g a n h e u ris tic W h e n a te m p la te is fo u n d th e

PATTERN -R ECOGN IT ION AND SEA RCH 305

fu z z in es s lev el is d e cre a se d a s p a rt o f th e in fo rm atio n m ay b e sto re d in L T M

d ire c tly fre e in g c ap ac ity in w o rk in g m e m o ry a n d in th e m in d rsquos ey e

S im u la t io n s w ith th e ldquo C anon ica l M ode lrdquo

T h e sim u latio n s d e sc rib ed in th is s ec tio n a re s tra ig h tfo rw a rd U s in g th e

p a ra m e te r v alu e s d is cu sse d e a rlie r I le t th e p ro g ra m s ea rc h 1 0 0 0 ep iso d e s fo r

e ac h n e t s iz e S u m m a ry v alu e s fo r m e a n d ep th o f se a rc h t im e ra tio d e p th tim e

a n d fu z zin e s s a s w e ll a s fo r g e n e ra tio n an d s to p co n d itio n s w e re c o m p u ted fo r

e ac h n e t s iz e

M e a n D e p th o f S e a r ch R a te o f S e a rc h a n d F u z zin e ss A cc o rd in g to

S E A R C H m ea n d e p th o f s ea rc h fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f

c h u n k s (se e F ig 3 a) If w e as su m e a co n sta n t ra te o f le a rn in g n e w c h u n k s a s is

c o m m o n p ra ctic e in so m e c o g n itiv e a rch ite c tu res (c f N e w e ll 1 9 9 0 ) a n d if w e

a ss u m e th a t s k ille d p la y e rs h a v e sp e n t m o re p rac tice a n d stu d y tim e th a n

u n s k ille d p la y e rs th e n m e an d e p th fo llo w s a p o w e r fu n c tio n o f s k ill as w e ll T h is

p re d ic tio n w h ic h is a t v ar ia n c e w ith H o ld in g rsquos p re d ic tio n (1 9 8 5 p 1 8 2 ) o f a

lin ea r in c rea s e is p artly co n siste n t w ith C h a rn e ss rsquos (1 9 8 1 ) p ro p o s a l th a t d e p th o f

se a rc h is n o t l in e arly re la ted to s k ill b u t th at th e re is a ce ilin g a t h ig h s k ill le v e ls

T h e re su lt is a ls o c o m p atib le w ith th e w e a k lin e ar re la tio n fo u n d in e m p ir ic a l

stu d ie s (C h a rn e ss 1 9 8 1 G o b e t in p re ss ) b e tw e e n m e a n d e p th o f se a rch a n d sk ill

le v el b e c a u se re stric te d ra n g e s o f th e c u rv e c a n b e a p p ro x im a ted b y a lin e a r

fu n c tio n T h e a b so lu te v alu e s a re a lso q u ite r ea so n ab le th ey ris e f ro m lo w d ep th s

(le ss th a n 1 p ly ) w ith n o ch u n k s (co r res p o n d in g to th e n o v ic e le v el) to a ro u n d 2 5

p lies w ith a sm a ll n et (1 0 0 0 c h u n k s ) an d th e n to a ro u n d 4 p lie s w ith ex p ert le v e l

(a ro u n d 3 0 0 0 0 c h u n k s a s e s tim a te d b y s im u la tio n s o n th e re ca ll tas k ) T h e y th e n

slo w ly (s av e fo r a f ew ra n d o m v a ria tio n s ) in c re a se to m o re th an 5 p lie s w ith n e t

la rg er th an 1 0 0 0 0 0 c h u n k s w h ic h c o rre sp o n d s to G ran d m a ste r le v e l H o ld in g

(1 9 8 5 ) c o m p u te d m e a n d e p th o f se a rch fo r d e G ro o trsquos (1 9 4 6 ) d a ta a n d fo u n d th a t

TA BLE 3

T im e and ldquo Fuzz in ess rdquo Param e ters U sed in th e

S im ula t io n s

T im e fo r c a r ry in g o u t a m o v e 2 s

T im e fo r c o m p u t in g m o v e -g e n e r a tin g h e u r is tic 2 0 s

T im e fo r c o m p u t in g e v a lu a t io n 1 0 s

U p p e r l im it o f fu z z in e ss 5 0

In c r e a se o f fu z z in e s s p e r m o v e 1

In c re a se o f f u z z in e ss p e r s e c o n d 2

D e c re a s e in fu z z in e ss d u e to te m p la te 5

306 GOBET

E x p e rts a n d G ra n d m as ters h a d res p e ctiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 8 a n d

5 3 T h e reg res sio n e q u a tio n d e riv e d f ro m C h a rn e ss rsquos (1 9 8 1 ) d ata y ie ld a n

a v e rag e d e p th o f se a rc h o f a b o u t 2 3 p lies a t th e 1 3 0 0 E L O 1 le v e l o f 4 1 a t th e

E x p e rt le v e l (2 0 0 0 E L O ) a n d o f 5 7 a t th e G ra n d m a s te r le v el U n fo rtu n a tely n o

stu d y te ste d p la y e rs ra n g in g fro m n o v ic es to G ran d m a ste rs an d S E A R C H rsquos

p re d ic tio n o f a p o w e r la w o f p rac tic e c an n o t b e te ste d (y e t) I w ill re p o rt la te r

sim u la tio n s a d d re ssin g d a ta co lle c ted b y S a arilu o m a (1 9 9 0 ) w h e re In tern atio n a l

M a ste rs a n d G ra n d m a s te rs te n d e d to s e arc h le s s th a n M as te rs

T h e ra te o f s ea rc h a lso fo llo w s a p o w e r fu n ctio n o f th e n u m b e r o f c h u n k s (se e

F ig 3 b ) D e G ro o t (1 9 4 6 ) C h arn es s (1 9 8 1 ) a n d G o b e t ( in p res s) a ll f o u n d th a t

stro n g p la y er s te n d e d to s e arc h fa ste r F o r ex a m p le G o b e t ( in p re s s) fo u n d th a t

h is M a ste rs E x p e rts C la ss A a n d C la s s B p lay e rs re sp e c tiv ely se arch e d 4 8 4 1

3 2 an d 3 4 n o d e s p e r m in u te S E A R C H rsquos v a lu es a re h ig h e r b u t s til l p la u s ib le

F o r ex am p le W a g n e r a n d S c u rra h rsquos (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r

m in u te N o te a lso th a t a ll th e ex p erim e n ts m e n tio n e d e a rlier h a v e u se d v e rb a l

p ro to c o ls w h ic h m ay h av e s lo w e d d o w n th e ra te o f se a rc h (c f E ric ss o n amp

S im o n 1 9 8 0 ) F in a lly th e ra te o f se arch m a y h av e b e e n u n d e res tim a ted in th e

lite ra tu re b ec a u se th e r a te o f g e n e ratin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d

b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l t im e H o w e v e r to ta l t im e in c lu d es

tim e n o t sp e n t in s e arc h ( fo r e x a m p le w h a t D e G ro o t c a lls th e ldquo firs t p h a se rdquo)

T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a riab le th e le v e l o f fu zz in e ss a t

w h ic h a se a rc h is e n d e d is m o re d if fic u lt to ju d g e b ec a u se lit tle is k n o w n a b o u t

th e ro le o f fu z z in es s in c h es s th in k in g A g ain S E A R C H p ro p o se s th a t th is

v a riab le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s ee F ig 3 c ) W ith la rg e r

n e ts e p iso d es te n d to b e e n d e d w ith lo w er le v els o f fu z z in e s s T h is su g g es ts th at

in g e n e ra l s tro n g p la y ers s h o u ld b e m o re c o n fid e n t in th e ir c alc u la tio n s as th e y

a re n o t a t th e e d g e o f th eir p o s sib ilitie s N o te th a t th e ra te o f ch an g e is ra th e r h ig h

fo r th is p o w er law w h ic h s u g g e sts th at it sh o u ld b e p o ss ib le to d e te c t i t

e x p erim e n tally

G e n e ra tio n o f M o ve s H o w is m o v e g en e ra tio n af fec te d b y sk ill le v e l A s

sh o w n in F ig 4 a S E A R C H m a k es c le a r p re d ic tio n s W ith sm a ll n u m b e rs o f

c h u n k s th e tim e -c o n s u m in g p ro ce s s o f g en e ra tin g m o v es b y h e u ristic s is

e m p lo y e d T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y ch u n k s

w h ic h is in tu rn d o m in a te d b y te m p la te g e n eratio n

1 T h e E L O ra t in g i s a n in te r v a l sc a le th a t ra n k s c o m p e t it io n c h e ss p la y e rs I ts s ta n d a rd de v ia t io n

(2 0 0 p o in ts) is o f te n in te r p re te d a s a m e a su r e o f sk i ll c la s s in c h e ss G r a n d m a s te r s a re n o rm a lly ra te d

a b o v e 2 5 0 0 In te rn a t io n a l M a s te r s a b o v e 2 4 0 0 M a s te r s a b o v e 2 2 0 0 a n d E x p e rt s a b o v e 2 0 0 0

B e lo w c la sse s (A B e tc ) d iv id e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in ts

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

300 GOBET

300

FIG 1 F lo w c h a rt o f S E A R C H

PATTERN -R ECOGN IT ION AND SEA RCH 301

301

F IG 2 E x a m p le s o f e p is o d e s g e n e ra te d b y S E A R C H

302 GOBET

re p re se n te d b y th e re la tiv e ly h ig h p ro b ab ility o f f in d in g (s eq u e n c e s o f) m o v es

a n d e v a lu atio n s w ith tem p la tes as c o m p are d w ith ch u n k s

The M ode lrsquos P aram e te rs

S E A R C H h as m a n y p a ra m ete rs a n d it is o f c o u rs e n e c es sa ry to se t u p a f ew o f

th e m w ith in d e p e n d e n t d a ta in o rd er to re d u c e th e n u m b e r o f d e g re e s o f fre e d o m

in th e m o d e l W h e n p o ss ib le I h a v e u s e d sim u la tio n s w ith th e C H R E S T (D e

G ro o t amp G o b e t 1 9 9 6 G o b e t 1 9 9 3 ) an d C H U M P (G o b e t amp Ja n s en 1 9 9 4 )

p ro g ram s to se t p a ra m e te r v a lu es C H R E S T is a p ro g ra m im p le m e n tin g as p e cts

o f T T a n d s im u la tin g n u m e ro u s e x p er im e n ts o n p e rc ep tio n an d m e m o ry in ch e s s

a n d C H U M P is a p ro g ra m p la y in g (w e ak ) c h e ss b y p u re p a tte rn re co g n itio n

N u m b e r o f C h u n k s a n d T e m p la te s T ab le 1 sh o w s th e v a lu es th at w ill b e

u s ed w ith th e S E A R C H m o d e l fo r th e se p a ra m ete rs T o c h o o se th e v a lu e s re la te d

to th e n u m b e r o f ch u n k s a n d te m p la tes th e c u rre n t v e rsio n o f C H R E S T h a s b e e n

e m p lo y e d T h e p ro b a b ility o f f in d in g a tem p la te w a s e stim ate d b y ru n n in g

C H R E S T o n 5 0 p o s itio n s ran d o m ly tak e n fro m M as ters rsquo g am e s T h e firs t lin e (0

c h u n k ) w a s ad d e d to g e t p re d ic tio n s a t th e n o v ic e lev e l W ith n e ts o f 1 0 0 0 0 0

1 2 0 0 0 0 a n d 1 5 0 0 0 0 c h u n k s th e p ara m ete rs w ere e stim ate d w ith th e b e s t-fit t in g

fu n c tio n s av a ilab le ( th e ldquo n o v ice rdquo v alu e s w ere n o t u se d ) T h e n u m b er o f te m p la tes

is ro u g h ly a lin e ar fu n c tio n o f th e n u m b er o f c h u n k s (r 2 = 9 7 ) T h e p ro b a b ility

o f f in d in g a tem p la te is a p p ro x im a tely a lo g -fu n c tio n o f th e n u m b e r o f c h u n k s

(r 2 = 9 4 )

H e u r is tic s C h u n k s T e m p la tes a n d T h e ir R e la tio n to th e P ro b a b ility o f

F in d in g M o v e s a n d E v a lu a tio n s T ab le 2 g iv e s th e v a lu e s u s ed in th e

sim u la tio n s fo r th e p a ra m ete rs re la te d to h e u ristic s c h u n k s a n d te m p la te s

H e u ris tic s in c lu d e sim p le se a rc h te c h n iq u e s (e g ldquo ta k e a p ie c e b a c k rdquo o r ldquoc h e c k

th e K in g rdquo ) a s w ell a s m o re a b stra c t ru le s (e g ldquoo c c u p y th e c en tre rdquo ) T h eir m a in

c h a rac te ris tic in co m p a riso n w ith c h u n k s an d tem p la te s is th a t th ey are g e n e ra l

a n d re q u ire so m e co n sc io u s c o m p u tatio n in o rd e r to p ro d u ce a m o v e T h e

a ss u m p tio n u n d e rly in g T a b le 2 is th at th e p aram e ters re la ted to h e u ristic s s ta y

ro u g h ly c o n sta n t w h ile th e o th e r p aram e te rs v a ry as a lo g arith m ic fu n c tio n o f th e

n u m b e r o f c h u n k s in th e n e t (A lo g arith m ic fu n ctio n h a s b e e n c h o se n to in d ica te

th a t ch u n k s y ie ld a d im in ish in g re tu rn as th e ir n u m b e r in c re a se s) T h e

a ss u m p tio n th a t th e n u m b e r o f h e u ristic s is c o n sta n t ac ro s s s k ill le v e ls se e m s

re a so n a b le (p e rh a p s w ith th e e x ce p tio n o f th e n o v ic e le v e l) a s m o s t c h e ss

M a ste rs rsquo k n o w le d g e is v e ry sp ec ific to c erta in a sp e c ts o f th e g a m e (D e G ro o t

1 9 4 6 )

T h e fo llo w in g c o n s id era tio n s w e re m ad e in se ttin g th e v alu e s g iv e n in

T ab le 2 I t w a s d ee m e d p lau sib le th a t th e p ro b a b ility o f f in d in g so m e h e u ristic in

a p o s itio n b e h ig h ( 9 5 ) a s w e ll a s th e p ro b a b ility o f f in d in g s o m e c h u n k F in ally

PATTERN -R ECOGN IT ION AND SEA RCH 303

TA BLE 1

The V a lu es o f th e 14 N e ts U sed in th e S im u la tio ns

P ro b a b i li ty o f

re c o g n is in g a t le as t

P ro p o r t io n o f o n e te m p la te g iv e n a

N u m b e r o f c h u n k s N u m b e r o f te m p la te s te m p la te s p o s i t io n

0 0 0 0 0 0 0 0

1 0 0 2 0 0 0 0 0 0 0

2 6 8 0 5 0 0 2 1 8 0

5 0 0 3 3 6 0 0 7 1 4 0

1 0 0 1 1 1 0 0 0 1 0 2 4 0

2 0 0 0 3 2 6 5 0 1 3 3 0 0

3 0 0 0 1 4 9 3 0 1 6 3 6 0

4 0 0 0 5 7 7 4 0 1 9 4 6 0

5 0 0 0 6 1 1 4 2 0 2 3 4 0 0

7 2 0 4 4 2 1 3 6 0 3 0 4 8 0

8 0 0 1 0 2 2 8 5 0 2 9 5 4 0

1 0 0 0 0 0 2 7 6 5 0 2 8 5 1 0

1 2 0 0 0 0 3 3 5 7 0 2 8 5 4 0

1 5 0 0 0 0 4 2 4 5 0 2 8 5 6 0

T h e v a lu e s b e lo w 1 0 0 0 0 0 c h u n k s w e r e ta k e n f ro m s im u la t io n s w ith C H R E S T th e o the rs

e x t ra p o la te d S e e te x t f o r d e ta ils

TA BLE 2

H eur is t ic s C hun ks Tem pla tes and Their Re la tion to th e P ro bab ility of Fin d in g

M oves and Evalu ta tio ns

T y p e H e u r is tic s C h u n k s T e m p la te s

P ro b a b i li ty o f e v o k in g a n 9 5 g (n _ c h u n k s 9 5 )a se e T a b le 1

h e u ri s t ic a c h u n k o r a te m p la te

P ro b a b i li ty o f f in d in g a m o v e 5 0 g (n _ c h u n k s 5 0 ) g (n _ c h u n k s 9 0 )

g ive n th a t a n h e u r is tic a c h u n k

o r a te m p la te h a s b e e n e v o k e d

P ro b a b i li ty o f f in d in g a n e v a lu a tio n 1 5 g (n _ c h u n k s 0 5 ) g (n _ c h u n k s 5 0 )

g iv e n th a t a n h e u ri s t ic a c h u n k o r

a te m p la te h a s b e e n e v o k e d

aT h e fu n c tio n g i s d e f in e d a s

g (n _ c h un k s p ro b ) = p ro b 0 2 lo g1 0

(n _ c h un k s ) i f n _ c h u n k s gt 0

a n d

g (n _ c h u n k s p ro b ) = 0 i f n _ c h u n k s = 0

w h e re n _ c h u n k s i s th e n u m b e r o f c h u n k s in a g iv e n n e t a n d p ro b i s a c o n s ta n t

303

304 GOBET

th e p ro b a b ility o f re c o g n isin g a te m p la te in a p o sitio n is sm a lle r a n d is g iv e n in

T ab le 1

T h e p ro b a b ility o f f in d in g a m o v e g iv e n a h e u ristic is s e t to 5 0 in d ic atin g th a t

h e u ristic s m a y fa il to p ro d u ce a m o v e h a lf o f th e tim e T h is is b e c a u se so m e

h e u ristic s m ay n o t y ie ld a m o v e a n d b ec a u se so m e p ro p o se d m o v es m a y b e

ille g a l T h e p ro b a b ility o f f in d in g a m o v e g iv en a tem p la te is h ig h p a rtly

re fle ctin g th e ric h s em a n tic k n o w le d g e an d th e in te r-te m p la te lin k s a s su m e d to

c h a rac te rise te m p la te s F o r th e p ro b a b ility o f f in d in g a m o v e g iv e n th a t a ch u n k

h a s b e en re co g n ise d I u se d th e p ara m e te r p ro b in th e fu n ctio n g (s ee T a b le 2 ) so

th a t i t a p p ro x im a te s th e d ata p ro d u c ed b y th e C H U M P p ro g ram (G o b et amp Ja n se n

1 9 9 4 ) E v a lu a tio n s a re su p p o s ed to b e h a rd er to le arn a n d th e re fo re h a rd e r to u se

th a n m o v es H e n ce th e ir p ro b a b ilit ie s a re lo w e r th a n th e co r res p o n d in g p ro b -

a b ilit ie s w ith m o v es A g a in fo llo w in g d irec tly fro m th e th e o ry te m p la te s o ffe r

th e b e st so u rce o f ev alu a tio n s

W ith re sp e c t to th e n u m b e r o f se q u e n tia l m o v e s p ro p o s ed c o u n ted in p lie s

(i e m o v e s fo r W h ite o r B la ck ) i t is as su m e d th a t h e u ristic s g iv e a cc e ss to o n ly

o n e m o v e w h ile c h u n k s a n d te m p late s y ie ld se q u e n c es o f m o v e s w h o se n u m b e r

fo llo w s a g e o m e tric p ro b a b ility d is tr ib u tio n (th e c h o ice o f th is d is tr ib u tio n w as

in sp ire d b y sta tis tic s ta k e n fro m C H U M P ) T h e lo n g e s t s eq u e n c e ( ca ll i t k ) h as a

fre q u e n c y o f 1 th e s e co n d -lo n g e st a fre q u en cy o f 2 th e th ird -lo n g e st a fre q u e n c y

o f 4 a n d so o n u n til th e sh o rte st se q u e n c e w h o s e len g th is 1 m o v e an d w h o se

fre q u e n c y is 2 (k ndash 1 ) T h e m a x im u m se q u e n ce o f m o v es w a s se t to 1 8 F in a lly

S E A R C H atte m p ts to g e n e ra te a m o v e b y p a ttern re c o g n itio n ( ch u n k o r te m p la te )

fo u r tim e s b e fo re u sin g a n h e u ristic

T im e a n d F u zzin e ss P a ra m ete rs T h e tim e p a ram e ter s fo r th e re sp e c tiv e

o p e ra tio n s w e re s et u sin g p la u sib le v a lu e s (se e T a b le 3 ) M o v e g en era tio n b y

p a tte rn re c o g n itio n (c h u n k o r te m p late ) is as su m e d to b e v e ry sh o rt (a few

h u n d re d m illis e co n d s) n o tim e c o st is u se d in th e m o d e l T h e tim e fo r c o m p u tin g

a m o v e-g en e ra tin g h e u ristic w a s s et to th e ra th e r lo n g 2 0 s ec o n d s mdash g en era tin g a

m o v e w ith o u t u sin g p a tte rn r ec o g n itio n re q u ires p u ttin g to g eth e r v a rio u s ty p e s o f

in fo rm a tio n a n d a s k s fo r m a n y ch e c k in g p ro c ed u res T h e tim e fo r c a rry in g o u t

o n e m o v e (o n c e g e n erate d ) in th e m in d rsquos e y e w a s s et to tw o s ec o n d s T h is is

c o m p atib le w ith S a a rilu o m a rsquos (1 9 8 9 ) d ata w h ic h sh o w th a t a b lin d fo ld ed M a ste r

c an fo llo w a g a m e d icta ted a t tw o se c o n d s a m o v e F in ally th e tim e fo r ca rry in g

o u t a n ev a lu a tio n b y h eu ris tic is s e t to 1 0 s e co n d s T h is ra th e r s h o rt tim e m a y b e

ju stif ie d b y th e fa c t th a t p la y e rs ty p ic a lly co n s id e r o n ly o n e (s u b jec tiv e ) a sp e c t o f

th e p o sitio n (D e G ro o t 1 9 4 6 ) a n d th at m an y e v a lu atio n s c a n b e g ro u n d ed o n th e

b a sis o f c lea r m a teria l lo ss e s

T h e fu z zin e ss lev el o f th e s y ste m is e x p re ss ed in a rb itra ry u n its I t s ta rts w ith

th e v a lu e z e ro a n d it is in c re a se d w h e n a m o v e is c a rrie d o u t in th e m in d rsquos e y e

a n d w h e n tim e is s p e n t a p p ly in g a n h e u ris tic W h e n a te m p la te is fo u n d th e

PATTERN -R ECOGN IT ION AND SEA RCH 305

fu z z in es s lev el is d e cre a se d a s p a rt o f th e in fo rm atio n m ay b e sto re d in L T M

d ire c tly fre e in g c ap ac ity in w o rk in g m e m o ry a n d in th e m in d rsquos ey e

S im u la t io n s w ith th e ldquo C anon ica l M ode lrdquo

T h e sim u latio n s d e sc rib ed in th is s ec tio n a re s tra ig h tfo rw a rd U s in g th e

p a ra m e te r v alu e s d is cu sse d e a rlie r I le t th e p ro g ra m s ea rc h 1 0 0 0 ep iso d e s fo r

e ac h n e t s iz e S u m m a ry v alu e s fo r m e a n d ep th o f se a rc h t im e ra tio d e p th tim e

a n d fu z zin e s s a s w e ll a s fo r g e n e ra tio n an d s to p co n d itio n s w e re c o m p u ted fo r

e ac h n e t s iz e

M e a n D e p th o f S e a r ch R a te o f S e a rc h a n d F u z zin e ss A cc o rd in g to

S E A R C H m ea n d e p th o f s ea rc h fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f

c h u n k s (se e F ig 3 a) If w e as su m e a co n sta n t ra te o f le a rn in g n e w c h u n k s a s is

c o m m o n p ra ctic e in so m e c o g n itiv e a rch ite c tu res (c f N e w e ll 1 9 9 0 ) a n d if w e

a ss u m e th a t s k ille d p la y e rs h a v e sp e n t m o re p rac tice a n d stu d y tim e th a n

u n s k ille d p la y e rs th e n m e an d e p th fo llo w s a p o w e r fu n c tio n o f s k ill as w e ll T h is

p re d ic tio n w h ic h is a t v ar ia n c e w ith H o ld in g rsquos p re d ic tio n (1 9 8 5 p 1 8 2 ) o f a

lin ea r in c rea s e is p artly co n siste n t w ith C h a rn e ss rsquos (1 9 8 1 ) p ro p o s a l th a t d e p th o f

se a rc h is n o t l in e arly re la ted to s k ill b u t th at th e re is a ce ilin g a t h ig h s k ill le v e ls

T h e re su lt is a ls o c o m p atib le w ith th e w e a k lin e ar re la tio n fo u n d in e m p ir ic a l

stu d ie s (C h a rn e ss 1 9 8 1 G o b e t in p re ss ) b e tw e e n m e a n d e p th o f se a rch a n d sk ill

le v el b e c a u se re stric te d ra n g e s o f th e c u rv e c a n b e a p p ro x im a ted b y a lin e a r

fu n c tio n T h e a b so lu te v alu e s a re a lso q u ite r ea so n ab le th ey ris e f ro m lo w d ep th s

(le ss th a n 1 p ly ) w ith n o ch u n k s (co r res p o n d in g to th e n o v ic e le v el) to a ro u n d 2 5

p lies w ith a sm a ll n et (1 0 0 0 c h u n k s ) an d th e n to a ro u n d 4 p lie s w ith ex p ert le v e l

(a ro u n d 3 0 0 0 0 c h u n k s a s e s tim a te d b y s im u la tio n s o n th e re ca ll tas k ) T h e y th e n

slo w ly (s av e fo r a f ew ra n d o m v a ria tio n s ) in c re a se to m o re th an 5 p lie s w ith n e t

la rg er th an 1 0 0 0 0 0 c h u n k s w h ic h c o rre sp o n d s to G ran d m a ste r le v e l H o ld in g

(1 9 8 5 ) c o m p u te d m e a n d e p th o f se a rch fo r d e G ro o trsquos (1 9 4 6 ) d a ta a n d fo u n d th a t

TA BLE 3

T im e and ldquo Fuzz in ess rdquo Param e ters U sed in th e

S im ula t io n s

T im e fo r c a r ry in g o u t a m o v e 2 s

T im e fo r c o m p u t in g m o v e -g e n e r a tin g h e u r is tic 2 0 s

T im e fo r c o m p u t in g e v a lu a t io n 1 0 s

U p p e r l im it o f fu z z in e ss 5 0

In c r e a se o f fu z z in e s s p e r m o v e 1

In c re a se o f f u z z in e ss p e r s e c o n d 2

D e c re a s e in fu z z in e ss d u e to te m p la te 5

306 GOBET

E x p e rts a n d G ra n d m as ters h a d res p e ctiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 8 a n d

5 3 T h e reg res sio n e q u a tio n d e riv e d f ro m C h a rn e ss rsquos (1 9 8 1 ) d ata y ie ld a n

a v e rag e d e p th o f se a rc h o f a b o u t 2 3 p lies a t th e 1 3 0 0 E L O 1 le v e l o f 4 1 a t th e

E x p e rt le v e l (2 0 0 0 E L O ) a n d o f 5 7 a t th e G ra n d m a s te r le v el U n fo rtu n a tely n o

stu d y te ste d p la y e rs ra n g in g fro m n o v ic es to G ran d m a ste rs an d S E A R C H rsquos

p re d ic tio n o f a p o w e r la w o f p rac tic e c an n o t b e te ste d (y e t) I w ill re p o rt la te r

sim u la tio n s a d d re ssin g d a ta co lle c ted b y S a arilu o m a (1 9 9 0 ) w h e re In tern atio n a l

M a ste rs a n d G ra n d m a s te rs te n d e d to s e arc h le s s th a n M as te rs

T h e ra te o f s ea rc h a lso fo llo w s a p o w e r fu n ctio n o f th e n u m b e r o f c h u n k s (se e

F ig 3 b ) D e G ro o t (1 9 4 6 ) C h arn es s (1 9 8 1 ) a n d G o b e t ( in p res s) a ll f o u n d th a t

stro n g p la y er s te n d e d to s e arc h fa ste r F o r ex a m p le G o b e t ( in p re s s) fo u n d th a t

h is M a ste rs E x p e rts C la ss A a n d C la s s B p lay e rs re sp e c tiv ely se arch e d 4 8 4 1

3 2 an d 3 4 n o d e s p e r m in u te S E A R C H rsquos v a lu es a re h ig h e r b u t s til l p la u s ib le

F o r ex am p le W a g n e r a n d S c u rra h rsquos (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r

m in u te N o te a lso th a t a ll th e ex p erim e n ts m e n tio n e d e a rlier h a v e u se d v e rb a l

p ro to c o ls w h ic h m ay h av e s lo w e d d o w n th e ra te o f se a rc h (c f E ric ss o n amp

S im o n 1 9 8 0 ) F in a lly th e ra te o f se arch m a y h av e b e e n u n d e res tim a ted in th e

lite ra tu re b ec a u se th e r a te o f g e n e ratin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d

b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l t im e H o w e v e r to ta l t im e in c lu d es

tim e n o t sp e n t in s e arc h ( fo r e x a m p le w h a t D e G ro o t c a lls th e ldquo firs t p h a se rdquo)

T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a riab le th e le v e l o f fu zz in e ss a t

w h ic h a se a rc h is e n d e d is m o re d if fic u lt to ju d g e b ec a u se lit tle is k n o w n a b o u t

th e ro le o f fu z z in es s in c h es s th in k in g A g ain S E A R C H p ro p o se s th a t th is

v a riab le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s ee F ig 3 c ) W ith la rg e r

n e ts e p iso d es te n d to b e e n d e d w ith lo w er le v els o f fu z z in e s s T h is su g g es ts th at

in g e n e ra l s tro n g p la y ers s h o u ld b e m o re c o n fid e n t in th e ir c alc u la tio n s as th e y

a re n o t a t th e e d g e o f th eir p o s sib ilitie s N o te th a t th e ra te o f ch an g e is ra th e r h ig h

fo r th is p o w er law w h ic h s u g g e sts th at it sh o u ld b e p o ss ib le to d e te c t i t

e x p erim e n tally

G e n e ra tio n o f M o ve s H o w is m o v e g en e ra tio n af fec te d b y sk ill le v e l A s

sh o w n in F ig 4 a S E A R C H m a k es c le a r p re d ic tio n s W ith sm a ll n u m b e rs o f

c h u n k s th e tim e -c o n s u m in g p ro ce s s o f g en e ra tin g m o v es b y h e u ristic s is

e m p lo y e d T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y ch u n k s

w h ic h is in tu rn d o m in a te d b y te m p la te g e n eratio n

1 T h e E L O ra t in g i s a n in te r v a l sc a le th a t ra n k s c o m p e t it io n c h e ss p la y e rs I ts s ta n d a rd de v ia t io n

(2 0 0 p o in ts) is o f te n in te r p re te d a s a m e a su r e o f sk i ll c la s s in c h e ss G r a n d m a s te r s a re n o rm a lly ra te d

a b o v e 2 5 0 0 In te rn a t io n a l M a s te r s a b o v e 2 4 0 0 M a s te r s a b o v e 2 2 0 0 a n d E x p e rt s a b o v e 2 0 0 0

B e lo w c la sse s (A B e tc ) d iv id e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in ts

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

PATTERN -R ECOGN IT ION AND SEA RCH 301

301

F IG 2 E x a m p le s o f e p is o d e s g e n e ra te d b y S E A R C H

302 GOBET

re p re se n te d b y th e re la tiv e ly h ig h p ro b ab ility o f f in d in g (s eq u e n c e s o f) m o v es

a n d e v a lu atio n s w ith tem p la tes as c o m p are d w ith ch u n k s

The M ode lrsquos P aram e te rs

S E A R C H h as m a n y p a ra m ete rs a n d it is o f c o u rs e n e c es sa ry to se t u p a f ew o f

th e m w ith in d e p e n d e n t d a ta in o rd er to re d u c e th e n u m b e r o f d e g re e s o f fre e d o m

in th e m o d e l W h e n p o ss ib le I h a v e u s e d sim u la tio n s w ith th e C H R E S T (D e

G ro o t amp G o b e t 1 9 9 6 G o b e t 1 9 9 3 ) an d C H U M P (G o b e t amp Ja n s en 1 9 9 4 )

p ro g ram s to se t p a ra m e te r v a lu es C H R E S T is a p ro g ra m im p le m e n tin g as p e cts

o f T T a n d s im u la tin g n u m e ro u s e x p er im e n ts o n p e rc ep tio n an d m e m o ry in ch e s s

a n d C H U M P is a p ro g ra m p la y in g (w e ak ) c h e ss b y p u re p a tte rn re co g n itio n

N u m b e r o f C h u n k s a n d T e m p la te s T ab le 1 sh o w s th e v a lu es th at w ill b e

u s ed w ith th e S E A R C H m o d e l fo r th e se p a ra m ete rs T o c h o o se th e v a lu e s re la te d

to th e n u m b e r o f ch u n k s a n d te m p la tes th e c u rre n t v e rsio n o f C H R E S T h a s b e e n

e m p lo y e d T h e p ro b a b ility o f f in d in g a tem p la te w a s e stim ate d b y ru n n in g

C H R E S T o n 5 0 p o s itio n s ran d o m ly tak e n fro m M as ters rsquo g am e s T h e firs t lin e (0

c h u n k ) w a s ad d e d to g e t p re d ic tio n s a t th e n o v ic e lev e l W ith n e ts o f 1 0 0 0 0 0

1 2 0 0 0 0 a n d 1 5 0 0 0 0 c h u n k s th e p ara m ete rs w ere e stim ate d w ith th e b e s t-fit t in g

fu n c tio n s av a ilab le ( th e ldquo n o v ice rdquo v alu e s w ere n o t u se d ) T h e n u m b er o f te m p la tes

is ro u g h ly a lin e ar fu n c tio n o f th e n u m b er o f c h u n k s (r 2 = 9 7 ) T h e p ro b a b ility

o f f in d in g a tem p la te is a p p ro x im a tely a lo g -fu n c tio n o f th e n u m b e r o f c h u n k s

(r 2 = 9 4 )

H e u r is tic s C h u n k s T e m p la tes a n d T h e ir R e la tio n to th e P ro b a b ility o f

F in d in g M o v e s a n d E v a lu a tio n s T ab le 2 g iv e s th e v a lu e s u s ed in th e

sim u la tio n s fo r th e p a ra m ete rs re la te d to h e u ristic s c h u n k s a n d te m p la te s

H e u ris tic s in c lu d e sim p le se a rc h te c h n iq u e s (e g ldquo ta k e a p ie c e b a c k rdquo o r ldquoc h e c k

th e K in g rdquo ) a s w ell a s m o re a b stra c t ru le s (e g ldquoo c c u p y th e c en tre rdquo ) T h eir m a in

c h a rac te ris tic in co m p a riso n w ith c h u n k s an d tem p la te s is th a t th ey are g e n e ra l

a n d re q u ire so m e co n sc io u s c o m p u tatio n in o rd e r to p ro d u ce a m o v e T h e

a ss u m p tio n u n d e rly in g T a b le 2 is th at th e p aram e ters re la ted to h e u ristic s s ta y

ro u g h ly c o n sta n t w h ile th e o th e r p aram e te rs v a ry as a lo g arith m ic fu n c tio n o f th e

n u m b e r o f c h u n k s in th e n e t (A lo g arith m ic fu n ctio n h a s b e e n c h o se n to in d ica te

th a t ch u n k s y ie ld a d im in ish in g re tu rn as th e ir n u m b e r in c re a se s) T h e

a ss u m p tio n th a t th e n u m b e r o f h e u ristic s is c o n sta n t ac ro s s s k ill le v e ls se e m s

re a so n a b le (p e rh a p s w ith th e e x ce p tio n o f th e n o v ic e le v e l) a s m o s t c h e ss

M a ste rs rsquo k n o w le d g e is v e ry sp ec ific to c erta in a sp e c ts o f th e g a m e (D e G ro o t

1 9 4 6 )

T h e fo llo w in g c o n s id era tio n s w e re m ad e in se ttin g th e v alu e s g iv e n in

T ab le 2 I t w a s d ee m e d p lau sib le th a t th e p ro b a b ility o f f in d in g so m e h e u ristic in

a p o s itio n b e h ig h ( 9 5 ) a s w e ll a s th e p ro b a b ility o f f in d in g s o m e c h u n k F in ally

PATTERN -R ECOGN IT ION AND SEA RCH 303

TA BLE 1

The V a lu es o f th e 14 N e ts U sed in th e S im u la tio ns

P ro b a b i li ty o f

re c o g n is in g a t le as t

P ro p o r t io n o f o n e te m p la te g iv e n a

N u m b e r o f c h u n k s N u m b e r o f te m p la te s te m p la te s p o s i t io n

0 0 0 0 0 0 0 0

1 0 0 2 0 0 0 0 0 0 0

2 6 8 0 5 0 0 2 1 8 0

5 0 0 3 3 6 0 0 7 1 4 0

1 0 0 1 1 1 0 0 0 1 0 2 4 0

2 0 0 0 3 2 6 5 0 1 3 3 0 0

3 0 0 0 1 4 9 3 0 1 6 3 6 0

4 0 0 0 5 7 7 4 0 1 9 4 6 0

5 0 0 0 6 1 1 4 2 0 2 3 4 0 0

7 2 0 4 4 2 1 3 6 0 3 0 4 8 0

8 0 0 1 0 2 2 8 5 0 2 9 5 4 0

1 0 0 0 0 0 2 7 6 5 0 2 8 5 1 0

1 2 0 0 0 0 3 3 5 7 0 2 8 5 4 0

1 5 0 0 0 0 4 2 4 5 0 2 8 5 6 0

T h e v a lu e s b e lo w 1 0 0 0 0 0 c h u n k s w e r e ta k e n f ro m s im u la t io n s w ith C H R E S T th e o the rs

e x t ra p o la te d S e e te x t f o r d e ta ils

TA BLE 2

H eur is t ic s C hun ks Tem pla tes and Their Re la tion to th e P ro bab ility of Fin d in g

M oves and Evalu ta tio ns

T y p e H e u r is tic s C h u n k s T e m p la te s

P ro b a b i li ty o f e v o k in g a n 9 5 g (n _ c h u n k s 9 5 )a se e T a b le 1

h e u ri s t ic a c h u n k o r a te m p la te

P ro b a b i li ty o f f in d in g a m o v e 5 0 g (n _ c h u n k s 5 0 ) g (n _ c h u n k s 9 0 )

g ive n th a t a n h e u r is tic a c h u n k

o r a te m p la te h a s b e e n e v o k e d

P ro b a b i li ty o f f in d in g a n e v a lu a tio n 1 5 g (n _ c h u n k s 0 5 ) g (n _ c h u n k s 5 0 )

g iv e n th a t a n h e u ri s t ic a c h u n k o r

a te m p la te h a s b e e n e v o k e d

aT h e fu n c tio n g i s d e f in e d a s

g (n _ c h un k s p ro b ) = p ro b 0 2 lo g1 0

(n _ c h un k s ) i f n _ c h u n k s gt 0

a n d

g (n _ c h u n k s p ro b ) = 0 i f n _ c h u n k s = 0

w h e re n _ c h u n k s i s th e n u m b e r o f c h u n k s in a g iv e n n e t a n d p ro b i s a c o n s ta n t

303

304 GOBET

th e p ro b a b ility o f re c o g n isin g a te m p la te in a p o sitio n is sm a lle r a n d is g iv e n in

T ab le 1

T h e p ro b a b ility o f f in d in g a m o v e g iv e n a h e u ristic is s e t to 5 0 in d ic atin g th a t

h e u ristic s m a y fa il to p ro d u ce a m o v e h a lf o f th e tim e T h is is b e c a u se so m e

h e u ristic s m ay n o t y ie ld a m o v e a n d b ec a u se so m e p ro p o se d m o v es m a y b e

ille g a l T h e p ro b a b ility o f f in d in g a m o v e g iv en a tem p la te is h ig h p a rtly

re fle ctin g th e ric h s em a n tic k n o w le d g e an d th e in te r-te m p la te lin k s a s su m e d to

c h a rac te rise te m p la te s F o r th e p ro b a b ility o f f in d in g a m o v e g iv e n th a t a ch u n k

h a s b e en re co g n ise d I u se d th e p ara m e te r p ro b in th e fu n ctio n g (s ee T a b le 2 ) so

th a t i t a p p ro x im a te s th e d ata p ro d u c ed b y th e C H U M P p ro g ram (G o b et amp Ja n se n

1 9 9 4 ) E v a lu a tio n s a re su p p o s ed to b e h a rd er to le arn a n d th e re fo re h a rd e r to u se

th a n m o v es H e n ce th e ir p ro b a b ilit ie s a re lo w e r th a n th e co r res p o n d in g p ro b -

a b ilit ie s w ith m o v es A g a in fo llo w in g d irec tly fro m th e th e o ry te m p la te s o ffe r

th e b e st so u rce o f ev alu a tio n s

W ith re sp e c t to th e n u m b e r o f se q u e n tia l m o v e s p ro p o s ed c o u n ted in p lie s

(i e m o v e s fo r W h ite o r B la ck ) i t is as su m e d th a t h e u ristic s g iv e a cc e ss to o n ly

o n e m o v e w h ile c h u n k s a n d te m p late s y ie ld se q u e n c es o f m o v e s w h o se n u m b e r

fo llo w s a g e o m e tric p ro b a b ility d is tr ib u tio n (th e c h o ice o f th is d is tr ib u tio n w as

in sp ire d b y sta tis tic s ta k e n fro m C H U M P ) T h e lo n g e s t s eq u e n c e ( ca ll i t k ) h as a

fre q u e n c y o f 1 th e s e co n d -lo n g e st a fre q u en cy o f 2 th e th ird -lo n g e st a fre q u e n c y

o f 4 a n d so o n u n til th e sh o rte st se q u e n c e w h o s e len g th is 1 m o v e an d w h o se

fre q u e n c y is 2 (k ndash 1 ) T h e m a x im u m se q u e n ce o f m o v es w a s se t to 1 8 F in a lly

S E A R C H atte m p ts to g e n e ra te a m o v e b y p a ttern re c o g n itio n ( ch u n k o r te m p la te )

fo u r tim e s b e fo re u sin g a n h e u ristic

T im e a n d F u zzin e ss P a ra m ete rs T h e tim e p a ram e ter s fo r th e re sp e c tiv e

o p e ra tio n s w e re s et u sin g p la u sib le v a lu e s (se e T a b le 3 ) M o v e g en era tio n b y

p a tte rn re c o g n itio n (c h u n k o r te m p late ) is as su m e d to b e v e ry sh o rt (a few

h u n d re d m illis e co n d s) n o tim e c o st is u se d in th e m o d e l T h e tim e fo r c o m p u tin g

a m o v e-g en e ra tin g h e u ristic w a s s et to th e ra th e r lo n g 2 0 s ec o n d s mdash g en era tin g a

m o v e w ith o u t u sin g p a tte rn r ec o g n itio n re q u ires p u ttin g to g eth e r v a rio u s ty p e s o f

in fo rm a tio n a n d a s k s fo r m a n y ch e c k in g p ro c ed u res T h e tim e fo r c a rry in g o u t

o n e m o v e (o n c e g e n erate d ) in th e m in d rsquos e y e w a s s et to tw o s ec o n d s T h is is

c o m p atib le w ith S a a rilu o m a rsquos (1 9 8 9 ) d ata w h ic h sh o w th a t a b lin d fo ld ed M a ste r

c an fo llo w a g a m e d icta ted a t tw o se c o n d s a m o v e F in ally th e tim e fo r ca rry in g

o u t a n ev a lu a tio n b y h eu ris tic is s e t to 1 0 s e co n d s T h is ra th e r s h o rt tim e m a y b e

ju stif ie d b y th e fa c t th a t p la y e rs ty p ic a lly co n s id e r o n ly o n e (s u b jec tiv e ) a sp e c t o f

th e p o sitio n (D e G ro o t 1 9 4 6 ) a n d th at m an y e v a lu atio n s c a n b e g ro u n d ed o n th e

b a sis o f c lea r m a teria l lo ss e s

T h e fu z zin e ss lev el o f th e s y ste m is e x p re ss ed in a rb itra ry u n its I t s ta rts w ith

th e v a lu e z e ro a n d it is in c re a se d w h e n a m o v e is c a rrie d o u t in th e m in d rsquos e y e

a n d w h e n tim e is s p e n t a p p ly in g a n h e u ris tic W h e n a te m p la te is fo u n d th e

PATTERN -R ECOGN IT ION AND SEA RCH 305

fu z z in es s lev el is d e cre a se d a s p a rt o f th e in fo rm atio n m ay b e sto re d in L T M

d ire c tly fre e in g c ap ac ity in w o rk in g m e m o ry a n d in th e m in d rsquos ey e

S im u la t io n s w ith th e ldquo C anon ica l M ode lrdquo

T h e sim u latio n s d e sc rib ed in th is s ec tio n a re s tra ig h tfo rw a rd U s in g th e

p a ra m e te r v alu e s d is cu sse d e a rlie r I le t th e p ro g ra m s ea rc h 1 0 0 0 ep iso d e s fo r

e ac h n e t s iz e S u m m a ry v alu e s fo r m e a n d ep th o f se a rc h t im e ra tio d e p th tim e

a n d fu z zin e s s a s w e ll a s fo r g e n e ra tio n an d s to p co n d itio n s w e re c o m p u ted fo r

e ac h n e t s iz e

M e a n D e p th o f S e a r ch R a te o f S e a rc h a n d F u z zin e ss A cc o rd in g to

S E A R C H m ea n d e p th o f s ea rc h fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f

c h u n k s (se e F ig 3 a) If w e as su m e a co n sta n t ra te o f le a rn in g n e w c h u n k s a s is

c o m m o n p ra ctic e in so m e c o g n itiv e a rch ite c tu res (c f N e w e ll 1 9 9 0 ) a n d if w e

a ss u m e th a t s k ille d p la y e rs h a v e sp e n t m o re p rac tice a n d stu d y tim e th a n

u n s k ille d p la y e rs th e n m e an d e p th fo llo w s a p o w e r fu n c tio n o f s k ill as w e ll T h is

p re d ic tio n w h ic h is a t v ar ia n c e w ith H o ld in g rsquos p re d ic tio n (1 9 8 5 p 1 8 2 ) o f a

lin ea r in c rea s e is p artly co n siste n t w ith C h a rn e ss rsquos (1 9 8 1 ) p ro p o s a l th a t d e p th o f

se a rc h is n o t l in e arly re la ted to s k ill b u t th at th e re is a ce ilin g a t h ig h s k ill le v e ls

T h e re su lt is a ls o c o m p atib le w ith th e w e a k lin e ar re la tio n fo u n d in e m p ir ic a l

stu d ie s (C h a rn e ss 1 9 8 1 G o b e t in p re ss ) b e tw e e n m e a n d e p th o f se a rch a n d sk ill

le v el b e c a u se re stric te d ra n g e s o f th e c u rv e c a n b e a p p ro x im a ted b y a lin e a r

fu n c tio n T h e a b so lu te v alu e s a re a lso q u ite r ea so n ab le th ey ris e f ro m lo w d ep th s

(le ss th a n 1 p ly ) w ith n o ch u n k s (co r res p o n d in g to th e n o v ic e le v el) to a ro u n d 2 5

p lies w ith a sm a ll n et (1 0 0 0 c h u n k s ) an d th e n to a ro u n d 4 p lie s w ith ex p ert le v e l

(a ro u n d 3 0 0 0 0 c h u n k s a s e s tim a te d b y s im u la tio n s o n th e re ca ll tas k ) T h e y th e n

slo w ly (s av e fo r a f ew ra n d o m v a ria tio n s ) in c re a se to m o re th an 5 p lie s w ith n e t

la rg er th an 1 0 0 0 0 0 c h u n k s w h ic h c o rre sp o n d s to G ran d m a ste r le v e l H o ld in g

(1 9 8 5 ) c o m p u te d m e a n d e p th o f se a rch fo r d e G ro o trsquos (1 9 4 6 ) d a ta a n d fo u n d th a t

TA BLE 3

T im e and ldquo Fuzz in ess rdquo Param e ters U sed in th e

S im ula t io n s

T im e fo r c a r ry in g o u t a m o v e 2 s

T im e fo r c o m p u t in g m o v e -g e n e r a tin g h e u r is tic 2 0 s

T im e fo r c o m p u t in g e v a lu a t io n 1 0 s

U p p e r l im it o f fu z z in e ss 5 0

In c r e a se o f fu z z in e s s p e r m o v e 1

In c re a se o f f u z z in e ss p e r s e c o n d 2

D e c re a s e in fu z z in e ss d u e to te m p la te 5

306 GOBET

E x p e rts a n d G ra n d m as ters h a d res p e ctiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 8 a n d

5 3 T h e reg res sio n e q u a tio n d e riv e d f ro m C h a rn e ss rsquos (1 9 8 1 ) d ata y ie ld a n

a v e rag e d e p th o f se a rc h o f a b o u t 2 3 p lies a t th e 1 3 0 0 E L O 1 le v e l o f 4 1 a t th e

E x p e rt le v e l (2 0 0 0 E L O ) a n d o f 5 7 a t th e G ra n d m a s te r le v el U n fo rtu n a tely n o

stu d y te ste d p la y e rs ra n g in g fro m n o v ic es to G ran d m a ste rs an d S E A R C H rsquos

p re d ic tio n o f a p o w e r la w o f p rac tic e c an n o t b e te ste d (y e t) I w ill re p o rt la te r

sim u la tio n s a d d re ssin g d a ta co lle c ted b y S a arilu o m a (1 9 9 0 ) w h e re In tern atio n a l

M a ste rs a n d G ra n d m a s te rs te n d e d to s e arc h le s s th a n M as te rs

T h e ra te o f s ea rc h a lso fo llo w s a p o w e r fu n ctio n o f th e n u m b e r o f c h u n k s (se e

F ig 3 b ) D e G ro o t (1 9 4 6 ) C h arn es s (1 9 8 1 ) a n d G o b e t ( in p res s) a ll f o u n d th a t

stro n g p la y er s te n d e d to s e arc h fa ste r F o r ex a m p le G o b e t ( in p re s s) fo u n d th a t

h is M a ste rs E x p e rts C la ss A a n d C la s s B p lay e rs re sp e c tiv ely se arch e d 4 8 4 1

3 2 an d 3 4 n o d e s p e r m in u te S E A R C H rsquos v a lu es a re h ig h e r b u t s til l p la u s ib le

F o r ex am p le W a g n e r a n d S c u rra h rsquos (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r

m in u te N o te a lso th a t a ll th e ex p erim e n ts m e n tio n e d e a rlier h a v e u se d v e rb a l

p ro to c o ls w h ic h m ay h av e s lo w e d d o w n th e ra te o f se a rc h (c f E ric ss o n amp

S im o n 1 9 8 0 ) F in a lly th e ra te o f se arch m a y h av e b e e n u n d e res tim a ted in th e

lite ra tu re b ec a u se th e r a te o f g e n e ratin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d

b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l t im e H o w e v e r to ta l t im e in c lu d es

tim e n o t sp e n t in s e arc h ( fo r e x a m p le w h a t D e G ro o t c a lls th e ldquo firs t p h a se rdquo)

T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a riab le th e le v e l o f fu zz in e ss a t

w h ic h a se a rc h is e n d e d is m o re d if fic u lt to ju d g e b ec a u se lit tle is k n o w n a b o u t

th e ro le o f fu z z in es s in c h es s th in k in g A g ain S E A R C H p ro p o se s th a t th is

v a riab le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s ee F ig 3 c ) W ith la rg e r

n e ts e p iso d es te n d to b e e n d e d w ith lo w er le v els o f fu z z in e s s T h is su g g es ts th at

in g e n e ra l s tro n g p la y ers s h o u ld b e m o re c o n fid e n t in th e ir c alc u la tio n s as th e y

a re n o t a t th e e d g e o f th eir p o s sib ilitie s N o te th a t th e ra te o f ch an g e is ra th e r h ig h

fo r th is p o w er law w h ic h s u g g e sts th at it sh o u ld b e p o ss ib le to d e te c t i t

e x p erim e n tally

G e n e ra tio n o f M o ve s H o w is m o v e g en e ra tio n af fec te d b y sk ill le v e l A s

sh o w n in F ig 4 a S E A R C H m a k es c le a r p re d ic tio n s W ith sm a ll n u m b e rs o f

c h u n k s th e tim e -c o n s u m in g p ro ce s s o f g en e ra tin g m o v es b y h e u ristic s is

e m p lo y e d T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y ch u n k s

w h ic h is in tu rn d o m in a te d b y te m p la te g e n eratio n

1 T h e E L O ra t in g i s a n in te r v a l sc a le th a t ra n k s c o m p e t it io n c h e ss p la y e rs I ts s ta n d a rd de v ia t io n

(2 0 0 p o in ts) is o f te n in te r p re te d a s a m e a su r e o f sk i ll c la s s in c h e ss G r a n d m a s te r s a re n o rm a lly ra te d

a b o v e 2 5 0 0 In te rn a t io n a l M a s te r s a b o v e 2 4 0 0 M a s te r s a b o v e 2 2 0 0 a n d E x p e rt s a b o v e 2 0 0 0

B e lo w c la sse s (A B e tc ) d iv id e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in ts

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

302 GOBET

re p re se n te d b y th e re la tiv e ly h ig h p ro b ab ility o f f in d in g (s eq u e n c e s o f) m o v es

a n d e v a lu atio n s w ith tem p la tes as c o m p are d w ith ch u n k s

The M ode lrsquos P aram e te rs

S E A R C H h as m a n y p a ra m ete rs a n d it is o f c o u rs e n e c es sa ry to se t u p a f ew o f

th e m w ith in d e p e n d e n t d a ta in o rd er to re d u c e th e n u m b e r o f d e g re e s o f fre e d o m

in th e m o d e l W h e n p o ss ib le I h a v e u s e d sim u la tio n s w ith th e C H R E S T (D e

G ro o t amp G o b e t 1 9 9 6 G o b e t 1 9 9 3 ) an d C H U M P (G o b e t amp Ja n s en 1 9 9 4 )

p ro g ram s to se t p a ra m e te r v a lu es C H R E S T is a p ro g ra m im p le m e n tin g as p e cts

o f T T a n d s im u la tin g n u m e ro u s e x p er im e n ts o n p e rc ep tio n an d m e m o ry in ch e s s

a n d C H U M P is a p ro g ra m p la y in g (w e ak ) c h e ss b y p u re p a tte rn re co g n itio n

N u m b e r o f C h u n k s a n d T e m p la te s T ab le 1 sh o w s th e v a lu es th at w ill b e

u s ed w ith th e S E A R C H m o d e l fo r th e se p a ra m ete rs T o c h o o se th e v a lu e s re la te d

to th e n u m b e r o f ch u n k s a n d te m p la tes th e c u rre n t v e rsio n o f C H R E S T h a s b e e n

e m p lo y e d T h e p ro b a b ility o f f in d in g a tem p la te w a s e stim ate d b y ru n n in g

C H R E S T o n 5 0 p o s itio n s ran d o m ly tak e n fro m M as ters rsquo g am e s T h e firs t lin e (0

c h u n k ) w a s ad d e d to g e t p re d ic tio n s a t th e n o v ic e lev e l W ith n e ts o f 1 0 0 0 0 0

1 2 0 0 0 0 a n d 1 5 0 0 0 0 c h u n k s th e p ara m ete rs w ere e stim ate d w ith th e b e s t-fit t in g

fu n c tio n s av a ilab le ( th e ldquo n o v ice rdquo v alu e s w ere n o t u se d ) T h e n u m b er o f te m p la tes

is ro u g h ly a lin e ar fu n c tio n o f th e n u m b er o f c h u n k s (r 2 = 9 7 ) T h e p ro b a b ility

o f f in d in g a tem p la te is a p p ro x im a tely a lo g -fu n c tio n o f th e n u m b e r o f c h u n k s

(r 2 = 9 4 )

H e u r is tic s C h u n k s T e m p la tes a n d T h e ir R e la tio n to th e P ro b a b ility o f

F in d in g M o v e s a n d E v a lu a tio n s T ab le 2 g iv e s th e v a lu e s u s ed in th e

sim u la tio n s fo r th e p a ra m ete rs re la te d to h e u ristic s c h u n k s a n d te m p la te s

H e u ris tic s in c lu d e sim p le se a rc h te c h n iq u e s (e g ldquo ta k e a p ie c e b a c k rdquo o r ldquoc h e c k

th e K in g rdquo ) a s w ell a s m o re a b stra c t ru le s (e g ldquoo c c u p y th e c en tre rdquo ) T h eir m a in

c h a rac te ris tic in co m p a riso n w ith c h u n k s an d tem p la te s is th a t th ey are g e n e ra l

a n d re q u ire so m e co n sc io u s c o m p u tatio n in o rd e r to p ro d u ce a m o v e T h e

a ss u m p tio n u n d e rly in g T a b le 2 is th at th e p aram e ters re la ted to h e u ristic s s ta y

ro u g h ly c o n sta n t w h ile th e o th e r p aram e te rs v a ry as a lo g arith m ic fu n c tio n o f th e

n u m b e r o f c h u n k s in th e n e t (A lo g arith m ic fu n ctio n h a s b e e n c h o se n to in d ica te

th a t ch u n k s y ie ld a d im in ish in g re tu rn as th e ir n u m b e r in c re a se s) T h e

a ss u m p tio n th a t th e n u m b e r o f h e u ristic s is c o n sta n t ac ro s s s k ill le v e ls se e m s

re a so n a b le (p e rh a p s w ith th e e x ce p tio n o f th e n o v ic e le v e l) a s m o s t c h e ss

M a ste rs rsquo k n o w le d g e is v e ry sp ec ific to c erta in a sp e c ts o f th e g a m e (D e G ro o t

1 9 4 6 )

T h e fo llo w in g c o n s id era tio n s w e re m ad e in se ttin g th e v alu e s g iv e n in

T ab le 2 I t w a s d ee m e d p lau sib le th a t th e p ro b a b ility o f f in d in g so m e h e u ristic in

a p o s itio n b e h ig h ( 9 5 ) a s w e ll a s th e p ro b a b ility o f f in d in g s o m e c h u n k F in ally

PATTERN -R ECOGN IT ION AND SEA RCH 303

TA BLE 1

The V a lu es o f th e 14 N e ts U sed in th e S im u la tio ns

P ro b a b i li ty o f

re c o g n is in g a t le as t

P ro p o r t io n o f o n e te m p la te g iv e n a

N u m b e r o f c h u n k s N u m b e r o f te m p la te s te m p la te s p o s i t io n

0 0 0 0 0 0 0 0

1 0 0 2 0 0 0 0 0 0 0

2 6 8 0 5 0 0 2 1 8 0

5 0 0 3 3 6 0 0 7 1 4 0

1 0 0 1 1 1 0 0 0 1 0 2 4 0

2 0 0 0 3 2 6 5 0 1 3 3 0 0

3 0 0 0 1 4 9 3 0 1 6 3 6 0

4 0 0 0 5 7 7 4 0 1 9 4 6 0

5 0 0 0 6 1 1 4 2 0 2 3 4 0 0

7 2 0 4 4 2 1 3 6 0 3 0 4 8 0

8 0 0 1 0 2 2 8 5 0 2 9 5 4 0

1 0 0 0 0 0 2 7 6 5 0 2 8 5 1 0

1 2 0 0 0 0 3 3 5 7 0 2 8 5 4 0

1 5 0 0 0 0 4 2 4 5 0 2 8 5 6 0

T h e v a lu e s b e lo w 1 0 0 0 0 0 c h u n k s w e r e ta k e n f ro m s im u la t io n s w ith C H R E S T th e o the rs

e x t ra p o la te d S e e te x t f o r d e ta ils

TA BLE 2

H eur is t ic s C hun ks Tem pla tes and Their Re la tion to th e P ro bab ility of Fin d in g

M oves and Evalu ta tio ns

T y p e H e u r is tic s C h u n k s T e m p la te s

P ro b a b i li ty o f e v o k in g a n 9 5 g (n _ c h u n k s 9 5 )a se e T a b le 1

h e u ri s t ic a c h u n k o r a te m p la te

P ro b a b i li ty o f f in d in g a m o v e 5 0 g (n _ c h u n k s 5 0 ) g (n _ c h u n k s 9 0 )

g ive n th a t a n h e u r is tic a c h u n k

o r a te m p la te h a s b e e n e v o k e d

P ro b a b i li ty o f f in d in g a n e v a lu a tio n 1 5 g (n _ c h u n k s 0 5 ) g (n _ c h u n k s 5 0 )

g iv e n th a t a n h e u ri s t ic a c h u n k o r

a te m p la te h a s b e e n e v o k e d

aT h e fu n c tio n g i s d e f in e d a s

g (n _ c h un k s p ro b ) = p ro b 0 2 lo g1 0

(n _ c h un k s ) i f n _ c h u n k s gt 0

a n d

g (n _ c h u n k s p ro b ) = 0 i f n _ c h u n k s = 0

w h e re n _ c h u n k s i s th e n u m b e r o f c h u n k s in a g iv e n n e t a n d p ro b i s a c o n s ta n t

303

304 GOBET

th e p ro b a b ility o f re c o g n isin g a te m p la te in a p o sitio n is sm a lle r a n d is g iv e n in

T ab le 1

T h e p ro b a b ility o f f in d in g a m o v e g iv e n a h e u ristic is s e t to 5 0 in d ic atin g th a t

h e u ristic s m a y fa il to p ro d u ce a m o v e h a lf o f th e tim e T h is is b e c a u se so m e

h e u ristic s m ay n o t y ie ld a m o v e a n d b ec a u se so m e p ro p o se d m o v es m a y b e

ille g a l T h e p ro b a b ility o f f in d in g a m o v e g iv en a tem p la te is h ig h p a rtly

re fle ctin g th e ric h s em a n tic k n o w le d g e an d th e in te r-te m p la te lin k s a s su m e d to

c h a rac te rise te m p la te s F o r th e p ro b a b ility o f f in d in g a m o v e g iv e n th a t a ch u n k

h a s b e en re co g n ise d I u se d th e p ara m e te r p ro b in th e fu n ctio n g (s ee T a b le 2 ) so

th a t i t a p p ro x im a te s th e d ata p ro d u c ed b y th e C H U M P p ro g ram (G o b et amp Ja n se n

1 9 9 4 ) E v a lu a tio n s a re su p p o s ed to b e h a rd er to le arn a n d th e re fo re h a rd e r to u se

th a n m o v es H e n ce th e ir p ro b a b ilit ie s a re lo w e r th a n th e co r res p o n d in g p ro b -

a b ilit ie s w ith m o v es A g a in fo llo w in g d irec tly fro m th e th e o ry te m p la te s o ffe r

th e b e st so u rce o f ev alu a tio n s

W ith re sp e c t to th e n u m b e r o f se q u e n tia l m o v e s p ro p o s ed c o u n ted in p lie s

(i e m o v e s fo r W h ite o r B la ck ) i t is as su m e d th a t h e u ristic s g iv e a cc e ss to o n ly

o n e m o v e w h ile c h u n k s a n d te m p late s y ie ld se q u e n c es o f m o v e s w h o se n u m b e r

fo llo w s a g e o m e tric p ro b a b ility d is tr ib u tio n (th e c h o ice o f th is d is tr ib u tio n w as

in sp ire d b y sta tis tic s ta k e n fro m C H U M P ) T h e lo n g e s t s eq u e n c e ( ca ll i t k ) h as a

fre q u e n c y o f 1 th e s e co n d -lo n g e st a fre q u en cy o f 2 th e th ird -lo n g e st a fre q u e n c y

o f 4 a n d so o n u n til th e sh o rte st se q u e n c e w h o s e len g th is 1 m o v e an d w h o se

fre q u e n c y is 2 (k ndash 1 ) T h e m a x im u m se q u e n ce o f m o v es w a s se t to 1 8 F in a lly

S E A R C H atte m p ts to g e n e ra te a m o v e b y p a ttern re c o g n itio n ( ch u n k o r te m p la te )

fo u r tim e s b e fo re u sin g a n h e u ristic

T im e a n d F u zzin e ss P a ra m ete rs T h e tim e p a ram e ter s fo r th e re sp e c tiv e

o p e ra tio n s w e re s et u sin g p la u sib le v a lu e s (se e T a b le 3 ) M o v e g en era tio n b y

p a tte rn re c o g n itio n (c h u n k o r te m p late ) is as su m e d to b e v e ry sh o rt (a few

h u n d re d m illis e co n d s) n o tim e c o st is u se d in th e m o d e l T h e tim e fo r c o m p u tin g

a m o v e-g en e ra tin g h e u ristic w a s s et to th e ra th e r lo n g 2 0 s ec o n d s mdash g en era tin g a

m o v e w ith o u t u sin g p a tte rn r ec o g n itio n re q u ires p u ttin g to g eth e r v a rio u s ty p e s o f

in fo rm a tio n a n d a s k s fo r m a n y ch e c k in g p ro c ed u res T h e tim e fo r c a rry in g o u t

o n e m o v e (o n c e g e n erate d ) in th e m in d rsquos e y e w a s s et to tw o s ec o n d s T h is is

c o m p atib le w ith S a a rilu o m a rsquos (1 9 8 9 ) d ata w h ic h sh o w th a t a b lin d fo ld ed M a ste r

c an fo llo w a g a m e d icta ted a t tw o se c o n d s a m o v e F in ally th e tim e fo r ca rry in g

o u t a n ev a lu a tio n b y h eu ris tic is s e t to 1 0 s e co n d s T h is ra th e r s h o rt tim e m a y b e

ju stif ie d b y th e fa c t th a t p la y e rs ty p ic a lly co n s id e r o n ly o n e (s u b jec tiv e ) a sp e c t o f

th e p o sitio n (D e G ro o t 1 9 4 6 ) a n d th at m an y e v a lu atio n s c a n b e g ro u n d ed o n th e

b a sis o f c lea r m a teria l lo ss e s

T h e fu z zin e ss lev el o f th e s y ste m is e x p re ss ed in a rb itra ry u n its I t s ta rts w ith

th e v a lu e z e ro a n d it is in c re a se d w h e n a m o v e is c a rrie d o u t in th e m in d rsquos e y e

a n d w h e n tim e is s p e n t a p p ly in g a n h e u ris tic W h e n a te m p la te is fo u n d th e

PATTERN -R ECOGN IT ION AND SEA RCH 305

fu z z in es s lev el is d e cre a se d a s p a rt o f th e in fo rm atio n m ay b e sto re d in L T M

d ire c tly fre e in g c ap ac ity in w o rk in g m e m o ry a n d in th e m in d rsquos ey e

S im u la t io n s w ith th e ldquo C anon ica l M ode lrdquo

T h e sim u latio n s d e sc rib ed in th is s ec tio n a re s tra ig h tfo rw a rd U s in g th e

p a ra m e te r v alu e s d is cu sse d e a rlie r I le t th e p ro g ra m s ea rc h 1 0 0 0 ep iso d e s fo r

e ac h n e t s iz e S u m m a ry v alu e s fo r m e a n d ep th o f se a rc h t im e ra tio d e p th tim e

a n d fu z zin e s s a s w e ll a s fo r g e n e ra tio n an d s to p co n d itio n s w e re c o m p u ted fo r

e ac h n e t s iz e

M e a n D e p th o f S e a r ch R a te o f S e a rc h a n d F u z zin e ss A cc o rd in g to

S E A R C H m ea n d e p th o f s ea rc h fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f

c h u n k s (se e F ig 3 a) If w e as su m e a co n sta n t ra te o f le a rn in g n e w c h u n k s a s is

c o m m o n p ra ctic e in so m e c o g n itiv e a rch ite c tu res (c f N e w e ll 1 9 9 0 ) a n d if w e

a ss u m e th a t s k ille d p la y e rs h a v e sp e n t m o re p rac tice a n d stu d y tim e th a n

u n s k ille d p la y e rs th e n m e an d e p th fo llo w s a p o w e r fu n c tio n o f s k ill as w e ll T h is

p re d ic tio n w h ic h is a t v ar ia n c e w ith H o ld in g rsquos p re d ic tio n (1 9 8 5 p 1 8 2 ) o f a

lin ea r in c rea s e is p artly co n siste n t w ith C h a rn e ss rsquos (1 9 8 1 ) p ro p o s a l th a t d e p th o f

se a rc h is n o t l in e arly re la ted to s k ill b u t th at th e re is a ce ilin g a t h ig h s k ill le v e ls

T h e re su lt is a ls o c o m p atib le w ith th e w e a k lin e ar re la tio n fo u n d in e m p ir ic a l

stu d ie s (C h a rn e ss 1 9 8 1 G o b e t in p re ss ) b e tw e e n m e a n d e p th o f se a rch a n d sk ill

le v el b e c a u se re stric te d ra n g e s o f th e c u rv e c a n b e a p p ro x im a ted b y a lin e a r

fu n c tio n T h e a b so lu te v alu e s a re a lso q u ite r ea so n ab le th ey ris e f ro m lo w d ep th s

(le ss th a n 1 p ly ) w ith n o ch u n k s (co r res p o n d in g to th e n o v ic e le v el) to a ro u n d 2 5

p lies w ith a sm a ll n et (1 0 0 0 c h u n k s ) an d th e n to a ro u n d 4 p lie s w ith ex p ert le v e l

(a ro u n d 3 0 0 0 0 c h u n k s a s e s tim a te d b y s im u la tio n s o n th e re ca ll tas k ) T h e y th e n

slo w ly (s av e fo r a f ew ra n d o m v a ria tio n s ) in c re a se to m o re th an 5 p lie s w ith n e t

la rg er th an 1 0 0 0 0 0 c h u n k s w h ic h c o rre sp o n d s to G ran d m a ste r le v e l H o ld in g

(1 9 8 5 ) c o m p u te d m e a n d e p th o f se a rch fo r d e G ro o trsquos (1 9 4 6 ) d a ta a n d fo u n d th a t

TA BLE 3

T im e and ldquo Fuzz in ess rdquo Param e ters U sed in th e

S im ula t io n s

T im e fo r c a r ry in g o u t a m o v e 2 s

T im e fo r c o m p u t in g m o v e -g e n e r a tin g h e u r is tic 2 0 s

T im e fo r c o m p u t in g e v a lu a t io n 1 0 s

U p p e r l im it o f fu z z in e ss 5 0

In c r e a se o f fu z z in e s s p e r m o v e 1

In c re a se o f f u z z in e ss p e r s e c o n d 2

D e c re a s e in fu z z in e ss d u e to te m p la te 5

306 GOBET

E x p e rts a n d G ra n d m as ters h a d res p e ctiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 8 a n d

5 3 T h e reg res sio n e q u a tio n d e riv e d f ro m C h a rn e ss rsquos (1 9 8 1 ) d ata y ie ld a n

a v e rag e d e p th o f se a rc h o f a b o u t 2 3 p lies a t th e 1 3 0 0 E L O 1 le v e l o f 4 1 a t th e

E x p e rt le v e l (2 0 0 0 E L O ) a n d o f 5 7 a t th e G ra n d m a s te r le v el U n fo rtu n a tely n o

stu d y te ste d p la y e rs ra n g in g fro m n o v ic es to G ran d m a ste rs an d S E A R C H rsquos

p re d ic tio n o f a p o w e r la w o f p rac tic e c an n o t b e te ste d (y e t) I w ill re p o rt la te r

sim u la tio n s a d d re ssin g d a ta co lle c ted b y S a arilu o m a (1 9 9 0 ) w h e re In tern atio n a l

M a ste rs a n d G ra n d m a s te rs te n d e d to s e arc h le s s th a n M as te rs

T h e ra te o f s ea rc h a lso fo llo w s a p o w e r fu n ctio n o f th e n u m b e r o f c h u n k s (se e

F ig 3 b ) D e G ro o t (1 9 4 6 ) C h arn es s (1 9 8 1 ) a n d G o b e t ( in p res s) a ll f o u n d th a t

stro n g p la y er s te n d e d to s e arc h fa ste r F o r ex a m p le G o b e t ( in p re s s) fo u n d th a t

h is M a ste rs E x p e rts C la ss A a n d C la s s B p lay e rs re sp e c tiv ely se arch e d 4 8 4 1

3 2 an d 3 4 n o d e s p e r m in u te S E A R C H rsquos v a lu es a re h ig h e r b u t s til l p la u s ib le

F o r ex am p le W a g n e r a n d S c u rra h rsquos (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r

m in u te N o te a lso th a t a ll th e ex p erim e n ts m e n tio n e d e a rlier h a v e u se d v e rb a l

p ro to c o ls w h ic h m ay h av e s lo w e d d o w n th e ra te o f se a rc h (c f E ric ss o n amp

S im o n 1 9 8 0 ) F in a lly th e ra te o f se arch m a y h av e b e e n u n d e res tim a ted in th e

lite ra tu re b ec a u se th e r a te o f g e n e ratin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d

b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l t im e H o w e v e r to ta l t im e in c lu d es

tim e n o t sp e n t in s e arc h ( fo r e x a m p le w h a t D e G ro o t c a lls th e ldquo firs t p h a se rdquo)

T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a riab le th e le v e l o f fu zz in e ss a t

w h ic h a se a rc h is e n d e d is m o re d if fic u lt to ju d g e b ec a u se lit tle is k n o w n a b o u t

th e ro le o f fu z z in es s in c h es s th in k in g A g ain S E A R C H p ro p o se s th a t th is

v a riab le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s ee F ig 3 c ) W ith la rg e r

n e ts e p iso d es te n d to b e e n d e d w ith lo w er le v els o f fu z z in e s s T h is su g g es ts th at

in g e n e ra l s tro n g p la y ers s h o u ld b e m o re c o n fid e n t in th e ir c alc u la tio n s as th e y

a re n o t a t th e e d g e o f th eir p o s sib ilitie s N o te th a t th e ra te o f ch an g e is ra th e r h ig h

fo r th is p o w er law w h ic h s u g g e sts th at it sh o u ld b e p o ss ib le to d e te c t i t

e x p erim e n tally

G e n e ra tio n o f M o ve s H o w is m o v e g en e ra tio n af fec te d b y sk ill le v e l A s

sh o w n in F ig 4 a S E A R C H m a k es c le a r p re d ic tio n s W ith sm a ll n u m b e rs o f

c h u n k s th e tim e -c o n s u m in g p ro ce s s o f g en e ra tin g m o v es b y h e u ristic s is

e m p lo y e d T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y ch u n k s

w h ic h is in tu rn d o m in a te d b y te m p la te g e n eratio n

1 T h e E L O ra t in g i s a n in te r v a l sc a le th a t ra n k s c o m p e t it io n c h e ss p la y e rs I ts s ta n d a rd de v ia t io n

(2 0 0 p o in ts) is o f te n in te r p re te d a s a m e a su r e o f sk i ll c la s s in c h e ss G r a n d m a s te r s a re n o rm a lly ra te d

a b o v e 2 5 0 0 In te rn a t io n a l M a s te r s a b o v e 2 4 0 0 M a s te r s a b o v e 2 2 0 0 a n d E x p e rt s a b o v e 2 0 0 0

B e lo w c la sse s (A B e tc ) d iv id e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in ts

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

PATTERN -R ECOGN IT ION AND SEA RCH 303

TA BLE 1

The V a lu es o f th e 14 N e ts U sed in th e S im u la tio ns

P ro b a b i li ty o f

re c o g n is in g a t le as t

P ro p o r t io n o f o n e te m p la te g iv e n a

N u m b e r o f c h u n k s N u m b e r o f te m p la te s te m p la te s p o s i t io n

0 0 0 0 0 0 0 0

1 0 0 2 0 0 0 0 0 0 0

2 6 8 0 5 0 0 2 1 8 0

5 0 0 3 3 6 0 0 7 1 4 0

1 0 0 1 1 1 0 0 0 1 0 2 4 0

2 0 0 0 3 2 6 5 0 1 3 3 0 0

3 0 0 0 1 4 9 3 0 1 6 3 6 0

4 0 0 0 5 7 7 4 0 1 9 4 6 0

5 0 0 0 6 1 1 4 2 0 2 3 4 0 0

7 2 0 4 4 2 1 3 6 0 3 0 4 8 0

8 0 0 1 0 2 2 8 5 0 2 9 5 4 0

1 0 0 0 0 0 2 7 6 5 0 2 8 5 1 0

1 2 0 0 0 0 3 3 5 7 0 2 8 5 4 0

1 5 0 0 0 0 4 2 4 5 0 2 8 5 6 0

T h e v a lu e s b e lo w 1 0 0 0 0 0 c h u n k s w e r e ta k e n f ro m s im u la t io n s w ith C H R E S T th e o the rs

e x t ra p o la te d S e e te x t f o r d e ta ils

TA BLE 2

H eur is t ic s C hun ks Tem pla tes and Their Re la tion to th e P ro bab ility of Fin d in g

M oves and Evalu ta tio ns

T y p e H e u r is tic s C h u n k s T e m p la te s

P ro b a b i li ty o f e v o k in g a n 9 5 g (n _ c h u n k s 9 5 )a se e T a b le 1

h e u ri s t ic a c h u n k o r a te m p la te

P ro b a b i li ty o f f in d in g a m o v e 5 0 g (n _ c h u n k s 5 0 ) g (n _ c h u n k s 9 0 )

g ive n th a t a n h e u r is tic a c h u n k

o r a te m p la te h a s b e e n e v o k e d

P ro b a b i li ty o f f in d in g a n e v a lu a tio n 1 5 g (n _ c h u n k s 0 5 ) g (n _ c h u n k s 5 0 )

g iv e n th a t a n h e u ri s t ic a c h u n k o r

a te m p la te h a s b e e n e v o k e d

aT h e fu n c tio n g i s d e f in e d a s

g (n _ c h un k s p ro b ) = p ro b 0 2 lo g1 0

(n _ c h un k s ) i f n _ c h u n k s gt 0

a n d

g (n _ c h u n k s p ro b ) = 0 i f n _ c h u n k s = 0

w h e re n _ c h u n k s i s th e n u m b e r o f c h u n k s in a g iv e n n e t a n d p ro b i s a c o n s ta n t

303

304 GOBET

th e p ro b a b ility o f re c o g n isin g a te m p la te in a p o sitio n is sm a lle r a n d is g iv e n in

T ab le 1

T h e p ro b a b ility o f f in d in g a m o v e g iv e n a h e u ristic is s e t to 5 0 in d ic atin g th a t

h e u ristic s m a y fa il to p ro d u ce a m o v e h a lf o f th e tim e T h is is b e c a u se so m e

h e u ristic s m ay n o t y ie ld a m o v e a n d b ec a u se so m e p ro p o se d m o v es m a y b e

ille g a l T h e p ro b a b ility o f f in d in g a m o v e g iv en a tem p la te is h ig h p a rtly

re fle ctin g th e ric h s em a n tic k n o w le d g e an d th e in te r-te m p la te lin k s a s su m e d to

c h a rac te rise te m p la te s F o r th e p ro b a b ility o f f in d in g a m o v e g iv e n th a t a ch u n k

h a s b e en re co g n ise d I u se d th e p ara m e te r p ro b in th e fu n ctio n g (s ee T a b le 2 ) so

th a t i t a p p ro x im a te s th e d ata p ro d u c ed b y th e C H U M P p ro g ram (G o b et amp Ja n se n

1 9 9 4 ) E v a lu a tio n s a re su p p o s ed to b e h a rd er to le arn a n d th e re fo re h a rd e r to u se

th a n m o v es H e n ce th e ir p ro b a b ilit ie s a re lo w e r th a n th e co r res p o n d in g p ro b -

a b ilit ie s w ith m o v es A g a in fo llo w in g d irec tly fro m th e th e o ry te m p la te s o ffe r

th e b e st so u rce o f ev alu a tio n s

W ith re sp e c t to th e n u m b e r o f se q u e n tia l m o v e s p ro p o s ed c o u n ted in p lie s

(i e m o v e s fo r W h ite o r B la ck ) i t is as su m e d th a t h e u ristic s g iv e a cc e ss to o n ly

o n e m o v e w h ile c h u n k s a n d te m p late s y ie ld se q u e n c es o f m o v e s w h o se n u m b e r

fo llo w s a g e o m e tric p ro b a b ility d is tr ib u tio n (th e c h o ice o f th is d is tr ib u tio n w as

in sp ire d b y sta tis tic s ta k e n fro m C H U M P ) T h e lo n g e s t s eq u e n c e ( ca ll i t k ) h as a

fre q u e n c y o f 1 th e s e co n d -lo n g e st a fre q u en cy o f 2 th e th ird -lo n g e st a fre q u e n c y

o f 4 a n d so o n u n til th e sh o rte st se q u e n c e w h o s e len g th is 1 m o v e an d w h o se

fre q u e n c y is 2 (k ndash 1 ) T h e m a x im u m se q u e n ce o f m o v es w a s se t to 1 8 F in a lly

S E A R C H atte m p ts to g e n e ra te a m o v e b y p a ttern re c o g n itio n ( ch u n k o r te m p la te )

fo u r tim e s b e fo re u sin g a n h e u ristic

T im e a n d F u zzin e ss P a ra m ete rs T h e tim e p a ram e ter s fo r th e re sp e c tiv e

o p e ra tio n s w e re s et u sin g p la u sib le v a lu e s (se e T a b le 3 ) M o v e g en era tio n b y

p a tte rn re c o g n itio n (c h u n k o r te m p late ) is as su m e d to b e v e ry sh o rt (a few

h u n d re d m illis e co n d s) n o tim e c o st is u se d in th e m o d e l T h e tim e fo r c o m p u tin g

a m o v e-g en e ra tin g h e u ristic w a s s et to th e ra th e r lo n g 2 0 s ec o n d s mdash g en era tin g a

m o v e w ith o u t u sin g p a tte rn r ec o g n itio n re q u ires p u ttin g to g eth e r v a rio u s ty p e s o f

in fo rm a tio n a n d a s k s fo r m a n y ch e c k in g p ro c ed u res T h e tim e fo r c a rry in g o u t

o n e m o v e (o n c e g e n erate d ) in th e m in d rsquos e y e w a s s et to tw o s ec o n d s T h is is

c o m p atib le w ith S a a rilu o m a rsquos (1 9 8 9 ) d ata w h ic h sh o w th a t a b lin d fo ld ed M a ste r

c an fo llo w a g a m e d icta ted a t tw o se c o n d s a m o v e F in ally th e tim e fo r ca rry in g

o u t a n ev a lu a tio n b y h eu ris tic is s e t to 1 0 s e co n d s T h is ra th e r s h o rt tim e m a y b e

ju stif ie d b y th e fa c t th a t p la y e rs ty p ic a lly co n s id e r o n ly o n e (s u b jec tiv e ) a sp e c t o f

th e p o sitio n (D e G ro o t 1 9 4 6 ) a n d th at m an y e v a lu atio n s c a n b e g ro u n d ed o n th e

b a sis o f c lea r m a teria l lo ss e s

T h e fu z zin e ss lev el o f th e s y ste m is e x p re ss ed in a rb itra ry u n its I t s ta rts w ith

th e v a lu e z e ro a n d it is in c re a se d w h e n a m o v e is c a rrie d o u t in th e m in d rsquos e y e

a n d w h e n tim e is s p e n t a p p ly in g a n h e u ris tic W h e n a te m p la te is fo u n d th e

PATTERN -R ECOGN IT ION AND SEA RCH 305

fu z z in es s lev el is d e cre a se d a s p a rt o f th e in fo rm atio n m ay b e sto re d in L T M

d ire c tly fre e in g c ap ac ity in w o rk in g m e m o ry a n d in th e m in d rsquos ey e

S im u la t io n s w ith th e ldquo C anon ica l M ode lrdquo

T h e sim u latio n s d e sc rib ed in th is s ec tio n a re s tra ig h tfo rw a rd U s in g th e

p a ra m e te r v alu e s d is cu sse d e a rlie r I le t th e p ro g ra m s ea rc h 1 0 0 0 ep iso d e s fo r

e ac h n e t s iz e S u m m a ry v alu e s fo r m e a n d ep th o f se a rc h t im e ra tio d e p th tim e

a n d fu z zin e s s a s w e ll a s fo r g e n e ra tio n an d s to p co n d itio n s w e re c o m p u ted fo r

e ac h n e t s iz e

M e a n D e p th o f S e a r ch R a te o f S e a rc h a n d F u z zin e ss A cc o rd in g to

S E A R C H m ea n d e p th o f s ea rc h fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f

c h u n k s (se e F ig 3 a) If w e as su m e a co n sta n t ra te o f le a rn in g n e w c h u n k s a s is

c o m m o n p ra ctic e in so m e c o g n itiv e a rch ite c tu res (c f N e w e ll 1 9 9 0 ) a n d if w e

a ss u m e th a t s k ille d p la y e rs h a v e sp e n t m o re p rac tice a n d stu d y tim e th a n

u n s k ille d p la y e rs th e n m e an d e p th fo llo w s a p o w e r fu n c tio n o f s k ill as w e ll T h is

p re d ic tio n w h ic h is a t v ar ia n c e w ith H o ld in g rsquos p re d ic tio n (1 9 8 5 p 1 8 2 ) o f a

lin ea r in c rea s e is p artly co n siste n t w ith C h a rn e ss rsquos (1 9 8 1 ) p ro p o s a l th a t d e p th o f

se a rc h is n o t l in e arly re la ted to s k ill b u t th at th e re is a ce ilin g a t h ig h s k ill le v e ls

T h e re su lt is a ls o c o m p atib le w ith th e w e a k lin e ar re la tio n fo u n d in e m p ir ic a l

stu d ie s (C h a rn e ss 1 9 8 1 G o b e t in p re ss ) b e tw e e n m e a n d e p th o f se a rch a n d sk ill

le v el b e c a u se re stric te d ra n g e s o f th e c u rv e c a n b e a p p ro x im a ted b y a lin e a r

fu n c tio n T h e a b so lu te v alu e s a re a lso q u ite r ea so n ab le th ey ris e f ro m lo w d ep th s

(le ss th a n 1 p ly ) w ith n o ch u n k s (co r res p o n d in g to th e n o v ic e le v el) to a ro u n d 2 5

p lies w ith a sm a ll n et (1 0 0 0 c h u n k s ) an d th e n to a ro u n d 4 p lie s w ith ex p ert le v e l

(a ro u n d 3 0 0 0 0 c h u n k s a s e s tim a te d b y s im u la tio n s o n th e re ca ll tas k ) T h e y th e n

slo w ly (s av e fo r a f ew ra n d o m v a ria tio n s ) in c re a se to m o re th an 5 p lie s w ith n e t

la rg er th an 1 0 0 0 0 0 c h u n k s w h ic h c o rre sp o n d s to G ran d m a ste r le v e l H o ld in g

(1 9 8 5 ) c o m p u te d m e a n d e p th o f se a rch fo r d e G ro o trsquos (1 9 4 6 ) d a ta a n d fo u n d th a t

TA BLE 3

T im e and ldquo Fuzz in ess rdquo Param e ters U sed in th e

S im ula t io n s

T im e fo r c a r ry in g o u t a m o v e 2 s

T im e fo r c o m p u t in g m o v e -g e n e r a tin g h e u r is tic 2 0 s

T im e fo r c o m p u t in g e v a lu a t io n 1 0 s

U p p e r l im it o f fu z z in e ss 5 0

In c r e a se o f fu z z in e s s p e r m o v e 1

In c re a se o f f u z z in e ss p e r s e c o n d 2

D e c re a s e in fu z z in e ss d u e to te m p la te 5

306 GOBET

E x p e rts a n d G ra n d m as ters h a d res p e ctiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 8 a n d

5 3 T h e reg res sio n e q u a tio n d e riv e d f ro m C h a rn e ss rsquos (1 9 8 1 ) d ata y ie ld a n

a v e rag e d e p th o f se a rc h o f a b o u t 2 3 p lies a t th e 1 3 0 0 E L O 1 le v e l o f 4 1 a t th e

E x p e rt le v e l (2 0 0 0 E L O ) a n d o f 5 7 a t th e G ra n d m a s te r le v el U n fo rtu n a tely n o

stu d y te ste d p la y e rs ra n g in g fro m n o v ic es to G ran d m a ste rs an d S E A R C H rsquos

p re d ic tio n o f a p o w e r la w o f p rac tic e c an n o t b e te ste d (y e t) I w ill re p o rt la te r

sim u la tio n s a d d re ssin g d a ta co lle c ted b y S a arilu o m a (1 9 9 0 ) w h e re In tern atio n a l

M a ste rs a n d G ra n d m a s te rs te n d e d to s e arc h le s s th a n M as te rs

T h e ra te o f s ea rc h a lso fo llo w s a p o w e r fu n ctio n o f th e n u m b e r o f c h u n k s (se e

F ig 3 b ) D e G ro o t (1 9 4 6 ) C h arn es s (1 9 8 1 ) a n d G o b e t ( in p res s) a ll f o u n d th a t

stro n g p la y er s te n d e d to s e arc h fa ste r F o r ex a m p le G o b e t ( in p re s s) fo u n d th a t

h is M a ste rs E x p e rts C la ss A a n d C la s s B p lay e rs re sp e c tiv ely se arch e d 4 8 4 1

3 2 an d 3 4 n o d e s p e r m in u te S E A R C H rsquos v a lu es a re h ig h e r b u t s til l p la u s ib le

F o r ex am p le W a g n e r a n d S c u rra h rsquos (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r

m in u te N o te a lso th a t a ll th e ex p erim e n ts m e n tio n e d e a rlier h a v e u se d v e rb a l

p ro to c o ls w h ic h m ay h av e s lo w e d d o w n th e ra te o f se a rc h (c f E ric ss o n amp

S im o n 1 9 8 0 ) F in a lly th e ra te o f se arch m a y h av e b e e n u n d e res tim a ted in th e

lite ra tu re b ec a u se th e r a te o f g e n e ratin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d

b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l t im e H o w e v e r to ta l t im e in c lu d es

tim e n o t sp e n t in s e arc h ( fo r e x a m p le w h a t D e G ro o t c a lls th e ldquo firs t p h a se rdquo)

T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a riab le th e le v e l o f fu zz in e ss a t

w h ic h a se a rc h is e n d e d is m o re d if fic u lt to ju d g e b ec a u se lit tle is k n o w n a b o u t

th e ro le o f fu z z in es s in c h es s th in k in g A g ain S E A R C H p ro p o se s th a t th is

v a riab le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s ee F ig 3 c ) W ith la rg e r

n e ts e p iso d es te n d to b e e n d e d w ith lo w er le v els o f fu z z in e s s T h is su g g es ts th at

in g e n e ra l s tro n g p la y ers s h o u ld b e m o re c o n fid e n t in th e ir c alc u la tio n s as th e y

a re n o t a t th e e d g e o f th eir p o s sib ilitie s N o te th a t th e ra te o f ch an g e is ra th e r h ig h

fo r th is p o w er law w h ic h s u g g e sts th at it sh o u ld b e p o ss ib le to d e te c t i t

e x p erim e n tally

G e n e ra tio n o f M o ve s H o w is m o v e g en e ra tio n af fec te d b y sk ill le v e l A s

sh o w n in F ig 4 a S E A R C H m a k es c le a r p re d ic tio n s W ith sm a ll n u m b e rs o f

c h u n k s th e tim e -c o n s u m in g p ro ce s s o f g en e ra tin g m o v es b y h e u ristic s is

e m p lo y e d T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y ch u n k s

w h ic h is in tu rn d o m in a te d b y te m p la te g e n eratio n

1 T h e E L O ra t in g i s a n in te r v a l sc a le th a t ra n k s c o m p e t it io n c h e ss p la y e rs I ts s ta n d a rd de v ia t io n

(2 0 0 p o in ts) is o f te n in te r p re te d a s a m e a su r e o f sk i ll c la s s in c h e ss G r a n d m a s te r s a re n o rm a lly ra te d

a b o v e 2 5 0 0 In te rn a t io n a l M a s te r s a b o v e 2 4 0 0 M a s te r s a b o v e 2 2 0 0 a n d E x p e rt s a b o v e 2 0 0 0

B e lo w c la sse s (A B e tc ) d iv id e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in ts

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

304 GOBET

th e p ro b a b ility o f re c o g n isin g a te m p la te in a p o sitio n is sm a lle r a n d is g iv e n in

T ab le 1

T h e p ro b a b ility o f f in d in g a m o v e g iv e n a h e u ristic is s e t to 5 0 in d ic atin g th a t

h e u ristic s m a y fa il to p ro d u ce a m o v e h a lf o f th e tim e T h is is b e c a u se so m e

h e u ristic s m ay n o t y ie ld a m o v e a n d b ec a u se so m e p ro p o se d m o v es m a y b e

ille g a l T h e p ro b a b ility o f f in d in g a m o v e g iv en a tem p la te is h ig h p a rtly

re fle ctin g th e ric h s em a n tic k n o w le d g e an d th e in te r-te m p la te lin k s a s su m e d to

c h a rac te rise te m p la te s F o r th e p ro b a b ility o f f in d in g a m o v e g iv e n th a t a ch u n k

h a s b e en re co g n ise d I u se d th e p ara m e te r p ro b in th e fu n ctio n g (s ee T a b le 2 ) so

th a t i t a p p ro x im a te s th e d ata p ro d u c ed b y th e C H U M P p ro g ram (G o b et amp Ja n se n

1 9 9 4 ) E v a lu a tio n s a re su p p o s ed to b e h a rd er to le arn a n d th e re fo re h a rd e r to u se

th a n m o v es H e n ce th e ir p ro b a b ilit ie s a re lo w e r th a n th e co r res p o n d in g p ro b -

a b ilit ie s w ith m o v es A g a in fo llo w in g d irec tly fro m th e th e o ry te m p la te s o ffe r

th e b e st so u rce o f ev alu a tio n s

W ith re sp e c t to th e n u m b e r o f se q u e n tia l m o v e s p ro p o s ed c o u n ted in p lie s

(i e m o v e s fo r W h ite o r B la ck ) i t is as su m e d th a t h e u ristic s g iv e a cc e ss to o n ly

o n e m o v e w h ile c h u n k s a n d te m p late s y ie ld se q u e n c es o f m o v e s w h o se n u m b e r

fo llo w s a g e o m e tric p ro b a b ility d is tr ib u tio n (th e c h o ice o f th is d is tr ib u tio n w as

in sp ire d b y sta tis tic s ta k e n fro m C H U M P ) T h e lo n g e s t s eq u e n c e ( ca ll i t k ) h as a

fre q u e n c y o f 1 th e s e co n d -lo n g e st a fre q u en cy o f 2 th e th ird -lo n g e st a fre q u e n c y

o f 4 a n d so o n u n til th e sh o rte st se q u e n c e w h o s e len g th is 1 m o v e an d w h o se

fre q u e n c y is 2 (k ndash 1 ) T h e m a x im u m se q u e n ce o f m o v es w a s se t to 1 8 F in a lly

S E A R C H atte m p ts to g e n e ra te a m o v e b y p a ttern re c o g n itio n ( ch u n k o r te m p la te )

fo u r tim e s b e fo re u sin g a n h e u ristic

T im e a n d F u zzin e ss P a ra m ete rs T h e tim e p a ram e ter s fo r th e re sp e c tiv e

o p e ra tio n s w e re s et u sin g p la u sib le v a lu e s (se e T a b le 3 ) M o v e g en era tio n b y

p a tte rn re c o g n itio n (c h u n k o r te m p late ) is as su m e d to b e v e ry sh o rt (a few

h u n d re d m illis e co n d s) n o tim e c o st is u se d in th e m o d e l T h e tim e fo r c o m p u tin g

a m o v e-g en e ra tin g h e u ristic w a s s et to th e ra th e r lo n g 2 0 s ec o n d s mdash g en era tin g a

m o v e w ith o u t u sin g p a tte rn r ec o g n itio n re q u ires p u ttin g to g eth e r v a rio u s ty p e s o f

in fo rm a tio n a n d a s k s fo r m a n y ch e c k in g p ro c ed u res T h e tim e fo r c a rry in g o u t

o n e m o v e (o n c e g e n erate d ) in th e m in d rsquos e y e w a s s et to tw o s ec o n d s T h is is

c o m p atib le w ith S a a rilu o m a rsquos (1 9 8 9 ) d ata w h ic h sh o w th a t a b lin d fo ld ed M a ste r

c an fo llo w a g a m e d icta ted a t tw o se c o n d s a m o v e F in ally th e tim e fo r ca rry in g

o u t a n ev a lu a tio n b y h eu ris tic is s e t to 1 0 s e co n d s T h is ra th e r s h o rt tim e m a y b e

ju stif ie d b y th e fa c t th a t p la y e rs ty p ic a lly co n s id e r o n ly o n e (s u b jec tiv e ) a sp e c t o f

th e p o sitio n (D e G ro o t 1 9 4 6 ) a n d th at m an y e v a lu atio n s c a n b e g ro u n d ed o n th e

b a sis o f c lea r m a teria l lo ss e s

T h e fu z zin e ss lev el o f th e s y ste m is e x p re ss ed in a rb itra ry u n its I t s ta rts w ith

th e v a lu e z e ro a n d it is in c re a se d w h e n a m o v e is c a rrie d o u t in th e m in d rsquos e y e

a n d w h e n tim e is s p e n t a p p ly in g a n h e u ris tic W h e n a te m p la te is fo u n d th e

PATTERN -R ECOGN IT ION AND SEA RCH 305

fu z z in es s lev el is d e cre a se d a s p a rt o f th e in fo rm atio n m ay b e sto re d in L T M

d ire c tly fre e in g c ap ac ity in w o rk in g m e m o ry a n d in th e m in d rsquos ey e

S im u la t io n s w ith th e ldquo C anon ica l M ode lrdquo

T h e sim u latio n s d e sc rib ed in th is s ec tio n a re s tra ig h tfo rw a rd U s in g th e

p a ra m e te r v alu e s d is cu sse d e a rlie r I le t th e p ro g ra m s ea rc h 1 0 0 0 ep iso d e s fo r

e ac h n e t s iz e S u m m a ry v alu e s fo r m e a n d ep th o f se a rc h t im e ra tio d e p th tim e

a n d fu z zin e s s a s w e ll a s fo r g e n e ra tio n an d s to p co n d itio n s w e re c o m p u ted fo r

e ac h n e t s iz e

M e a n D e p th o f S e a r ch R a te o f S e a rc h a n d F u z zin e ss A cc o rd in g to

S E A R C H m ea n d e p th o f s ea rc h fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f

c h u n k s (se e F ig 3 a) If w e as su m e a co n sta n t ra te o f le a rn in g n e w c h u n k s a s is

c o m m o n p ra ctic e in so m e c o g n itiv e a rch ite c tu res (c f N e w e ll 1 9 9 0 ) a n d if w e

a ss u m e th a t s k ille d p la y e rs h a v e sp e n t m o re p rac tice a n d stu d y tim e th a n

u n s k ille d p la y e rs th e n m e an d e p th fo llo w s a p o w e r fu n c tio n o f s k ill as w e ll T h is

p re d ic tio n w h ic h is a t v ar ia n c e w ith H o ld in g rsquos p re d ic tio n (1 9 8 5 p 1 8 2 ) o f a

lin ea r in c rea s e is p artly co n siste n t w ith C h a rn e ss rsquos (1 9 8 1 ) p ro p o s a l th a t d e p th o f

se a rc h is n o t l in e arly re la ted to s k ill b u t th at th e re is a ce ilin g a t h ig h s k ill le v e ls

T h e re su lt is a ls o c o m p atib le w ith th e w e a k lin e ar re la tio n fo u n d in e m p ir ic a l

stu d ie s (C h a rn e ss 1 9 8 1 G o b e t in p re ss ) b e tw e e n m e a n d e p th o f se a rch a n d sk ill

le v el b e c a u se re stric te d ra n g e s o f th e c u rv e c a n b e a p p ro x im a ted b y a lin e a r

fu n c tio n T h e a b so lu te v alu e s a re a lso q u ite r ea so n ab le th ey ris e f ro m lo w d ep th s

(le ss th a n 1 p ly ) w ith n o ch u n k s (co r res p o n d in g to th e n o v ic e le v el) to a ro u n d 2 5

p lies w ith a sm a ll n et (1 0 0 0 c h u n k s ) an d th e n to a ro u n d 4 p lie s w ith ex p ert le v e l

(a ro u n d 3 0 0 0 0 c h u n k s a s e s tim a te d b y s im u la tio n s o n th e re ca ll tas k ) T h e y th e n

slo w ly (s av e fo r a f ew ra n d o m v a ria tio n s ) in c re a se to m o re th an 5 p lie s w ith n e t

la rg er th an 1 0 0 0 0 0 c h u n k s w h ic h c o rre sp o n d s to G ran d m a ste r le v e l H o ld in g

(1 9 8 5 ) c o m p u te d m e a n d e p th o f se a rch fo r d e G ro o trsquos (1 9 4 6 ) d a ta a n d fo u n d th a t

TA BLE 3

T im e and ldquo Fuzz in ess rdquo Param e ters U sed in th e

S im ula t io n s

T im e fo r c a r ry in g o u t a m o v e 2 s

T im e fo r c o m p u t in g m o v e -g e n e r a tin g h e u r is tic 2 0 s

T im e fo r c o m p u t in g e v a lu a t io n 1 0 s

U p p e r l im it o f fu z z in e ss 5 0

In c r e a se o f fu z z in e s s p e r m o v e 1

In c re a se o f f u z z in e ss p e r s e c o n d 2

D e c re a s e in fu z z in e ss d u e to te m p la te 5

306 GOBET

E x p e rts a n d G ra n d m as ters h a d res p e ctiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 8 a n d

5 3 T h e reg res sio n e q u a tio n d e riv e d f ro m C h a rn e ss rsquos (1 9 8 1 ) d ata y ie ld a n

a v e rag e d e p th o f se a rc h o f a b o u t 2 3 p lies a t th e 1 3 0 0 E L O 1 le v e l o f 4 1 a t th e

E x p e rt le v e l (2 0 0 0 E L O ) a n d o f 5 7 a t th e G ra n d m a s te r le v el U n fo rtu n a tely n o

stu d y te ste d p la y e rs ra n g in g fro m n o v ic es to G ran d m a ste rs an d S E A R C H rsquos

p re d ic tio n o f a p o w e r la w o f p rac tic e c an n o t b e te ste d (y e t) I w ill re p o rt la te r

sim u la tio n s a d d re ssin g d a ta co lle c ted b y S a arilu o m a (1 9 9 0 ) w h e re In tern atio n a l

M a ste rs a n d G ra n d m a s te rs te n d e d to s e arc h le s s th a n M as te rs

T h e ra te o f s ea rc h a lso fo llo w s a p o w e r fu n ctio n o f th e n u m b e r o f c h u n k s (se e

F ig 3 b ) D e G ro o t (1 9 4 6 ) C h arn es s (1 9 8 1 ) a n d G o b e t ( in p res s) a ll f o u n d th a t

stro n g p la y er s te n d e d to s e arc h fa ste r F o r ex a m p le G o b e t ( in p re s s) fo u n d th a t

h is M a ste rs E x p e rts C la ss A a n d C la s s B p lay e rs re sp e c tiv ely se arch e d 4 8 4 1

3 2 an d 3 4 n o d e s p e r m in u te S E A R C H rsquos v a lu es a re h ig h e r b u t s til l p la u s ib le

F o r ex am p le W a g n e r a n d S c u rra h rsquos (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r

m in u te N o te a lso th a t a ll th e ex p erim e n ts m e n tio n e d e a rlier h a v e u se d v e rb a l

p ro to c o ls w h ic h m ay h av e s lo w e d d o w n th e ra te o f se a rc h (c f E ric ss o n amp

S im o n 1 9 8 0 ) F in a lly th e ra te o f se arch m a y h av e b e e n u n d e res tim a ted in th e

lite ra tu re b ec a u se th e r a te o f g e n e ratin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d

b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l t im e H o w e v e r to ta l t im e in c lu d es

tim e n o t sp e n t in s e arc h ( fo r e x a m p le w h a t D e G ro o t c a lls th e ldquo firs t p h a se rdquo)

T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a riab le th e le v e l o f fu zz in e ss a t

w h ic h a se a rc h is e n d e d is m o re d if fic u lt to ju d g e b ec a u se lit tle is k n o w n a b o u t

th e ro le o f fu z z in es s in c h es s th in k in g A g ain S E A R C H p ro p o se s th a t th is

v a riab le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s ee F ig 3 c ) W ith la rg e r

n e ts e p iso d es te n d to b e e n d e d w ith lo w er le v els o f fu z z in e s s T h is su g g es ts th at

in g e n e ra l s tro n g p la y ers s h o u ld b e m o re c o n fid e n t in th e ir c alc u la tio n s as th e y

a re n o t a t th e e d g e o f th eir p o s sib ilitie s N o te th a t th e ra te o f ch an g e is ra th e r h ig h

fo r th is p o w er law w h ic h s u g g e sts th at it sh o u ld b e p o ss ib le to d e te c t i t

e x p erim e n tally

G e n e ra tio n o f M o ve s H o w is m o v e g en e ra tio n af fec te d b y sk ill le v e l A s

sh o w n in F ig 4 a S E A R C H m a k es c le a r p re d ic tio n s W ith sm a ll n u m b e rs o f

c h u n k s th e tim e -c o n s u m in g p ro ce s s o f g en e ra tin g m o v es b y h e u ristic s is

e m p lo y e d T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y ch u n k s

w h ic h is in tu rn d o m in a te d b y te m p la te g e n eratio n

1 T h e E L O ra t in g i s a n in te r v a l sc a le th a t ra n k s c o m p e t it io n c h e ss p la y e rs I ts s ta n d a rd de v ia t io n

(2 0 0 p o in ts) is o f te n in te r p re te d a s a m e a su r e o f sk i ll c la s s in c h e ss G r a n d m a s te r s a re n o rm a lly ra te d

a b o v e 2 5 0 0 In te rn a t io n a l M a s te r s a b o v e 2 4 0 0 M a s te r s a b o v e 2 2 0 0 a n d E x p e rt s a b o v e 2 0 0 0

B e lo w c la sse s (A B e tc ) d iv id e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in ts

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

PATTERN -R ECOGN IT ION AND SEA RCH 305

fu z z in es s lev el is d e cre a se d a s p a rt o f th e in fo rm atio n m ay b e sto re d in L T M

d ire c tly fre e in g c ap ac ity in w o rk in g m e m o ry a n d in th e m in d rsquos ey e

S im u la t io n s w ith th e ldquo C anon ica l M ode lrdquo

T h e sim u latio n s d e sc rib ed in th is s ec tio n a re s tra ig h tfo rw a rd U s in g th e

p a ra m e te r v alu e s d is cu sse d e a rlie r I le t th e p ro g ra m s ea rc h 1 0 0 0 ep iso d e s fo r

e ac h n e t s iz e S u m m a ry v alu e s fo r m e a n d ep th o f se a rc h t im e ra tio d e p th tim e

a n d fu z zin e s s a s w e ll a s fo r g e n e ra tio n an d s to p co n d itio n s w e re c o m p u ted fo r

e ac h n e t s iz e

M e a n D e p th o f S e a r ch R a te o f S e a rc h a n d F u z zin e ss A cc o rd in g to

S E A R C H m ea n d e p th o f s ea rc h fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f

c h u n k s (se e F ig 3 a) If w e as su m e a co n sta n t ra te o f le a rn in g n e w c h u n k s a s is

c o m m o n p ra ctic e in so m e c o g n itiv e a rch ite c tu res (c f N e w e ll 1 9 9 0 ) a n d if w e

a ss u m e th a t s k ille d p la y e rs h a v e sp e n t m o re p rac tice a n d stu d y tim e th a n

u n s k ille d p la y e rs th e n m e an d e p th fo llo w s a p o w e r fu n c tio n o f s k ill as w e ll T h is

p re d ic tio n w h ic h is a t v ar ia n c e w ith H o ld in g rsquos p re d ic tio n (1 9 8 5 p 1 8 2 ) o f a

lin ea r in c rea s e is p artly co n siste n t w ith C h a rn e ss rsquos (1 9 8 1 ) p ro p o s a l th a t d e p th o f

se a rc h is n o t l in e arly re la ted to s k ill b u t th at th e re is a ce ilin g a t h ig h s k ill le v e ls

T h e re su lt is a ls o c o m p atib le w ith th e w e a k lin e ar re la tio n fo u n d in e m p ir ic a l

stu d ie s (C h a rn e ss 1 9 8 1 G o b e t in p re ss ) b e tw e e n m e a n d e p th o f se a rch a n d sk ill

le v el b e c a u se re stric te d ra n g e s o f th e c u rv e c a n b e a p p ro x im a ted b y a lin e a r

fu n c tio n T h e a b so lu te v alu e s a re a lso q u ite r ea so n ab le th ey ris e f ro m lo w d ep th s

(le ss th a n 1 p ly ) w ith n o ch u n k s (co r res p o n d in g to th e n o v ic e le v el) to a ro u n d 2 5

p lies w ith a sm a ll n et (1 0 0 0 c h u n k s ) an d th e n to a ro u n d 4 p lie s w ith ex p ert le v e l

(a ro u n d 3 0 0 0 0 c h u n k s a s e s tim a te d b y s im u la tio n s o n th e re ca ll tas k ) T h e y th e n

slo w ly (s av e fo r a f ew ra n d o m v a ria tio n s ) in c re a se to m o re th an 5 p lie s w ith n e t

la rg er th an 1 0 0 0 0 0 c h u n k s w h ic h c o rre sp o n d s to G ran d m a ste r le v e l H o ld in g

(1 9 8 5 ) c o m p u te d m e a n d e p th o f se a rch fo r d e G ro o trsquos (1 9 4 6 ) d a ta a n d fo u n d th a t

TA BLE 3

T im e and ldquo Fuzz in ess rdquo Param e ters U sed in th e

S im ula t io n s

T im e fo r c a r ry in g o u t a m o v e 2 s

T im e fo r c o m p u t in g m o v e -g e n e r a tin g h e u r is tic 2 0 s

T im e fo r c o m p u t in g e v a lu a t io n 1 0 s

U p p e r l im it o f fu z z in e ss 5 0

In c r e a se o f fu z z in e s s p e r m o v e 1

In c re a se o f f u z z in e ss p e r s e c o n d 2

D e c re a s e in fu z z in e ss d u e to te m p la te 5

306 GOBET

E x p e rts a n d G ra n d m as ters h a d res p e ctiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 8 a n d

5 3 T h e reg res sio n e q u a tio n d e riv e d f ro m C h a rn e ss rsquos (1 9 8 1 ) d ata y ie ld a n

a v e rag e d e p th o f se a rc h o f a b o u t 2 3 p lies a t th e 1 3 0 0 E L O 1 le v e l o f 4 1 a t th e

E x p e rt le v e l (2 0 0 0 E L O ) a n d o f 5 7 a t th e G ra n d m a s te r le v el U n fo rtu n a tely n o

stu d y te ste d p la y e rs ra n g in g fro m n o v ic es to G ran d m a ste rs an d S E A R C H rsquos

p re d ic tio n o f a p o w e r la w o f p rac tic e c an n o t b e te ste d (y e t) I w ill re p o rt la te r

sim u la tio n s a d d re ssin g d a ta co lle c ted b y S a arilu o m a (1 9 9 0 ) w h e re In tern atio n a l

M a ste rs a n d G ra n d m a s te rs te n d e d to s e arc h le s s th a n M as te rs

T h e ra te o f s ea rc h a lso fo llo w s a p o w e r fu n ctio n o f th e n u m b e r o f c h u n k s (se e

F ig 3 b ) D e G ro o t (1 9 4 6 ) C h arn es s (1 9 8 1 ) a n d G o b e t ( in p res s) a ll f o u n d th a t

stro n g p la y er s te n d e d to s e arc h fa ste r F o r ex a m p le G o b e t ( in p re s s) fo u n d th a t

h is M a ste rs E x p e rts C la ss A a n d C la s s B p lay e rs re sp e c tiv ely se arch e d 4 8 4 1

3 2 an d 3 4 n o d e s p e r m in u te S E A R C H rsquos v a lu es a re h ig h e r b u t s til l p la u s ib le

F o r ex am p le W a g n e r a n d S c u rra h rsquos (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r

m in u te N o te a lso th a t a ll th e ex p erim e n ts m e n tio n e d e a rlier h a v e u se d v e rb a l

p ro to c o ls w h ic h m ay h av e s lo w e d d o w n th e ra te o f se a rc h (c f E ric ss o n amp

S im o n 1 9 8 0 ) F in a lly th e ra te o f se arch m a y h av e b e e n u n d e res tim a ted in th e

lite ra tu re b ec a u se th e r a te o f g e n e ratin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d

b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l t im e H o w e v e r to ta l t im e in c lu d es

tim e n o t sp e n t in s e arc h ( fo r e x a m p le w h a t D e G ro o t c a lls th e ldquo firs t p h a se rdquo)

T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a riab le th e le v e l o f fu zz in e ss a t

w h ic h a se a rc h is e n d e d is m o re d if fic u lt to ju d g e b ec a u se lit tle is k n o w n a b o u t

th e ro le o f fu z z in es s in c h es s th in k in g A g ain S E A R C H p ro p o se s th a t th is

v a riab le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s ee F ig 3 c ) W ith la rg e r

n e ts e p iso d es te n d to b e e n d e d w ith lo w er le v els o f fu z z in e s s T h is su g g es ts th at

in g e n e ra l s tro n g p la y ers s h o u ld b e m o re c o n fid e n t in th e ir c alc u la tio n s as th e y

a re n o t a t th e e d g e o f th eir p o s sib ilitie s N o te th a t th e ra te o f ch an g e is ra th e r h ig h

fo r th is p o w er law w h ic h s u g g e sts th at it sh o u ld b e p o ss ib le to d e te c t i t

e x p erim e n tally

G e n e ra tio n o f M o ve s H o w is m o v e g en e ra tio n af fec te d b y sk ill le v e l A s

sh o w n in F ig 4 a S E A R C H m a k es c le a r p re d ic tio n s W ith sm a ll n u m b e rs o f

c h u n k s th e tim e -c o n s u m in g p ro ce s s o f g en e ra tin g m o v es b y h e u ristic s is

e m p lo y e d T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y ch u n k s

w h ic h is in tu rn d o m in a te d b y te m p la te g e n eratio n

1 T h e E L O ra t in g i s a n in te r v a l sc a le th a t ra n k s c o m p e t it io n c h e ss p la y e rs I ts s ta n d a rd de v ia t io n

(2 0 0 p o in ts) is o f te n in te r p re te d a s a m e a su r e o f sk i ll c la s s in c h e ss G r a n d m a s te r s a re n o rm a lly ra te d

a b o v e 2 5 0 0 In te rn a t io n a l M a s te r s a b o v e 2 4 0 0 M a s te r s a b o v e 2 2 0 0 a n d E x p e rt s a b o v e 2 0 0 0

B e lo w c la sse s (A B e tc ) d iv id e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in ts

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

306 GOBET

E x p e rts a n d G ra n d m as ters h a d res p e ctiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 8 a n d

5 3 T h e reg res sio n e q u a tio n d e riv e d f ro m C h a rn e ss rsquos (1 9 8 1 ) d ata y ie ld a n

a v e rag e d e p th o f se a rc h o f a b o u t 2 3 p lies a t th e 1 3 0 0 E L O 1 le v e l o f 4 1 a t th e

E x p e rt le v e l (2 0 0 0 E L O ) a n d o f 5 7 a t th e G ra n d m a s te r le v el U n fo rtu n a tely n o

stu d y te ste d p la y e rs ra n g in g fro m n o v ic es to G ran d m a ste rs an d S E A R C H rsquos

p re d ic tio n o f a p o w e r la w o f p rac tic e c an n o t b e te ste d (y e t) I w ill re p o rt la te r

sim u la tio n s a d d re ssin g d a ta co lle c ted b y S a arilu o m a (1 9 9 0 ) w h e re In tern atio n a l

M a ste rs a n d G ra n d m a s te rs te n d e d to s e arc h le s s th a n M as te rs

T h e ra te o f s ea rc h a lso fo llo w s a p o w e r fu n ctio n o f th e n u m b e r o f c h u n k s (se e

F ig 3 b ) D e G ro o t (1 9 4 6 ) C h arn es s (1 9 8 1 ) a n d G o b e t ( in p res s) a ll f o u n d th a t

stro n g p la y er s te n d e d to s e arc h fa ste r F o r ex a m p le G o b e t ( in p re s s) fo u n d th a t

h is M a ste rs E x p e rts C la ss A a n d C la s s B p lay e rs re sp e c tiv ely se arch e d 4 8 4 1

3 2 an d 3 4 n o d e s p e r m in u te S E A R C H rsquos v a lu es a re h ig h e r b u t s til l p la u s ib le

F o r ex am p le W a g n e r a n d S c u rra h rsquos (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r

m in u te N o te a lso th a t a ll th e ex p erim e n ts m e n tio n e d e a rlier h a v e u se d v e rb a l

p ro to c o ls w h ic h m ay h av e s lo w e d d o w n th e ra te o f se a rc h (c f E ric ss o n amp

S im o n 1 9 8 0 ) F in a lly th e ra te o f se arch m a y h av e b e e n u n d e res tim a ted in th e

lite ra tu re b ec a u se th e r a te o f g e n e ratin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d

b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l t im e H o w e v e r to ta l t im e in c lu d es

tim e n o t sp e n t in s e arc h ( fo r e x a m p le w h a t D e G ro o t c a lls th e ldquo firs t p h a se rdquo)

T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a riab le th e le v e l o f fu zz in e ss a t

w h ic h a se a rc h is e n d e d is m o re d if fic u lt to ju d g e b ec a u se lit tle is k n o w n a b o u t

th e ro le o f fu z z in es s in c h es s th in k in g A g ain S E A R C H p ro p o se s th a t th is

v a riab le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s ee F ig 3 c ) W ith la rg e r

n e ts e p iso d es te n d to b e e n d e d w ith lo w er le v els o f fu z z in e s s T h is su g g es ts th at

in g e n e ra l s tro n g p la y ers s h o u ld b e m o re c o n fid e n t in th e ir c alc u la tio n s as th e y

a re n o t a t th e e d g e o f th eir p o s sib ilitie s N o te th a t th e ra te o f ch an g e is ra th e r h ig h

fo r th is p o w er law w h ic h s u g g e sts th at it sh o u ld b e p o ss ib le to d e te c t i t

e x p erim e n tally

G e n e ra tio n o f M o ve s H o w is m o v e g en e ra tio n af fec te d b y sk ill le v e l A s

sh o w n in F ig 4 a S E A R C H m a k es c le a r p re d ic tio n s W ith sm a ll n u m b e rs o f

c h u n k s th e tim e -c o n s u m in g p ro ce s s o f g en e ra tin g m o v es b y h e u ristic s is

e m p lo y e d T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y ch u n k s

w h ic h is in tu rn d o m in a te d b y te m p la te g e n eratio n

1 T h e E L O ra t in g i s a n in te r v a l sc a le th a t ra n k s c o m p e t it io n c h e ss p la y e rs I ts s ta n d a rd de v ia t io n

(2 0 0 p o in ts) is o f te n in te r p re te d a s a m e a su r e o f sk i ll c la s s in c h e ss G r a n d m a s te r s a re n o rm a lly ra te d

a b o v e 2 5 0 0 In te rn a t io n a l M a s te r s a b o v e 2 4 0 0 M a s te r s a b o v e 2 2 0 0 a n d E x p e rt s a b o v e 2 0 0 0

B e lo w c la sse s (A B e tc ) d iv id e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in ts

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

PATTERN -R ECOGN IT ION AND SEA RCH 307

307

F IG 3 U p p e r p a n e l m e a n d e p th o f s e a rc h (in p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t M id d le p a n e l r a te o f se a r c h (in m o v e s p e r m in u te ) a s a f u n c tio n o f th e n u m b e r o f

c h u n k s in th e d isc rim in a t io n n e t L o w e r p a n e l le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h ic h

e p iso d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

308 GOBET

F IG 4 U p p e r P a n e l a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra te d b y h e u r is tic s c h u n k s o r

te m p la te s a s a fu n c t io n o f th e n u m b e r o f c h u n k s in th e d isc r im in a t io n n e t L o w e r P a n e l a r e a g ra p h o f

th e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e th e le v e l o f fu z z in e ss w a s to o h ig h b e c a u se th e p o s i tio n

w a s e v a lu a te d o r b e c a u se n o m o v e w a s p r o p o se d a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e

d isc rim in a tio n n e t

308

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

PATTERN -R ECOGN IT ION AND SEA RCH 309

S to p p in g a n E p iso d e A g a in S E A R C H m a k e s c lea r p re d ictio n s a b o u t th e

w a y e p iso d e s ar e s to p p e d ( se e F ig 4 b ) A t f irs t a b o u t 6 5 o f ep is o d e s a re

sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a li t tle le ss th an 2 5 are s to p p e d

b e c au s e th e in fo rm atio n in th e m in d rsquos e y e an d in w o rk in g m e m o ry is to o fu zz y

A s th e n u m b e r o f c h u n k s in cre a se s th e p ro p o rtio n o f ep iso d e s en d e d b y

e v a lu a tio n (th ro u g h c h u n k o r tem p la te re c o g n itio n a s w e ll a s th ro u g h h eu r is tic s )

in c rea s es to a b o u t 7 5 w ith la rg e n e ts

V aria b ility o f D ep th o f Sea rch

In S a a rilu o m a rsquos (1 9 9 0 ) ex p e rim e n t In te rn atio n a l M a ste rs a n d G ra n d m a s te rs

te n d ed to s ea rc h les s th a n re la tiv e ly w ea k M a s te rs (aro u n d 2 2 0 0 E L O ) W h e n

p lo tted a g a in st s k ill b o th th e to ta l n u m b e r o f n o d es se a rch ed a n d th e m e a n d e p th

o f se a rc h sh o w e d a n in v e rte d U -c u rv e w ith M a ste rs s ea rc h in g th e larg e s t n u m b e r

o f n o d e s (5 2 ) a n d a t th e larg es t av e ra g e d e p th (5 1 m o v e s) B y c o m p a riso n

S a a rilu o m a rsquos to p -le v e l p la y ers s ea rc h e d th ro u g h a s p a ce o f 2 3 n o d e s w ith a n

a v e rag e d ep th o f 3 6 m o v e s

N o te th a t as is u n fo rtu n a te ly th e ru le in c h e ss re se arch S a arilu o m a u se d few

p la y er s a n d fe w tes t p o sitio n s T h u s o n e c a n ex p ec t larg e flu c tu atio n s ju s t b y

c h a n ce T h is is a c tu ally h o w S E A R C H b e h av e s w h en th e n u m b er o f tr ia ls is lo w

F ig u re 5 il lu stra tes th e r es u lts o f s im u la tio n s w ith th e n u m b er o f ep is o d e s fo r

e ac h n e t s iz e lim ite d to 5 0 w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u ce d b y

fiv e p la y er s s e arc h in g a n av e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -

m in u te lim it to h is p la y e rs) T h e o th e r p a ra m ete rs a re th e sa m e a s in th e c an o n ic a l

m o d e l

A lth o u g h th e cu rv es c an b e w e ll f it ted b y a p o w er fu n c tio n o n e ca n o b se rv e

im p o rta n t v aria tio n s fro m o n e c u rv e to a n o th e r A ll c u rv e s sh o w an in c re as e w ith

d ip s an d p e ak s a n d a ll p re d ict th a t s o m e ca te g o ry o f s tro n g e r p la y e rs w ill se a rc h

le ss d e e p ly th a n s o m e c ate g o ry o f w e ak er p la y er s T h e b e s t e x a m p le w ith re sp e c t

to S a a rilu o m a rsquos d a ta is th e b o tto m c u rv e H is (w e ak ) M as ter s m a y b e co m p a re d

to th e 4 0 0 0 0 -ch u n k n e t w h ic h s h o w s d e e p e r s ea rc h th a n th e larg er n e ts

in c lu d in g th e n ets c o rre sp o n d in g to G ra n d m as te rs

T h u s S a a rilu o m a rsquos d a ta a re c o n s is ten t w ith S E A R C H an d its p re d ictio n th a t

d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill T h a t M a s te rs se a rch d ee p e r th a n to p -

le v el p lay e rs m a y b e a cc o u n te d fo r b y ra n d o m f lu c tu a tio n s a s sh o w n in th e

sim u la tio n s

S EARCH SUMM ARY AN D CON CLU S IO N S

A c o m p u ter m o d e l o f s e arch in c h es s h a s b e e n p re se n ted b a se d o n th e te m p la te

th e o ry T h e m o d e l e m p lo y s h eu ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s

a n d te m p la te s) to g e n e ra te in d ep e n d e n t e p iso d e s W h ile it is a ss u m e d th a t th e

p a ra m e te rs re la te d to h eu ris tic s a re c o n sta n t a c ro ss s k ill lev e ls i t is p ro p o se d th a t

th e p aram e ters re la te d to p atte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

310 GOBET

F IG 5 M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s in th e d is c rim in a tio n

n e t in fi v e s im u la t io n s w h e re th e n u m b e r o f e p iso d e s is sm a ll ( n = 5 0 )

310

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

PATTERN -R ECOGN IT ION AND SEA RCH 311

n u m b e r o f c h u n k s O th e r p a ra m e te rs re la te d to tim e n e e d ed to c a rry o u t a n

o p e ra tio n a n d to le v e l o f fu zz in e ss in th e s y ste m a re a ls o u s ed T h e m o d e l

a cc o u n ts r ea so n ab ly w e ll fo r s e v e ral e m p iric a l d a ta b o th q u a lita tiv e ly a n d

q u a n tita tiv ely (e g m e a n d ep th o f se arch a n d ra te o f se a rc h ) I t a lso s h e d s lig h t o n

S a a rilu o m a rsquos (1 9 9 0 ) e m p irica l re su lts w h ich p rev io u s ly se e m e d a n o m a lo u s

P e rh a p s m o re im p o rta n tly th e m o d e l p ro v id e s s o m e n ew th e o re tica l in s ig h t

w ith res p e ct to th e ro le o f c h u n k s in p ro b le m so lv in g C h a se an d S im o n rsquos

c h u n k in g th e o ry a lth o u g h sim p le in ap p e a ra n c e h a s u n ex p ec te d c o n se q u e n c es

d u e to th e n o n -lin ea r d y n a m ic s in v o lv ed in th e a c q u isitio n o f ch u n k s F o r

e x a m p le i t h a d b e en o v e rlo o k e d fo r 2 5 y e a rs th at C T (c o rre c tly ) p re d ic ts a sk ill

e ffe ct in th e re c a ll o f ran d o m p o sitio n s (G o b e t amp S im o n 1 9 9 6 b ) T h e c u rre n t

p a p e r sh o w s th at c o n tra ry to a c o m m o n in te rp re ta tio n o f C T a cq u is itio n o f m o re

c h u n k s lea d s to d e e p er se a rc h

T h e m o d e l a lso d ra w s a tte n tio n to s ea rc h fe a tu res n o t h e ed e d in c u rre n t

re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s F o r e x a m p le w h at is th e ro le o f th e

fu z z in es s p a ra m ete r an d w h a t is i ts re la tio n to w o rk in g m e m o ry A re v a ria b les

su ch a s d ep th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w er fu n c tio n o f s k ill

u b iq u ito u s in c o g n itiv e p sy c h o lo g y o r b y a lin e a r fu n c tio n a s p ro p o se d a m o n g

o th e rs b y C h a rn e ss (1 9 8 1 ) an d H o ld in g (1 9 8 5 ) F in a lly th e m o d e l is a f irs t

a tte m p t to r ig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f

m em o ry a n d p erce p tio n (th e te m p la te th e o ry an d its C H R E S T im p le m e n ta tio n )

th u s p ro v id in g a f irs t s te p in to a u n ifie d c o m p u tatio n a l th eo ry o f c h e ss p la y e rs rsquo

c o g n itio n

T h e S E A R C H m o d el a d m itted ly ta ck le s o n ly a s u b se t o f p ro b lem so lv in g mdash it

m ay b e co m p le m e n te d b y N ew ell an d S im o n rsquos (1 9 6 5 ) o r W a g n e r a n d S c u rra h rsquos

(1 9 7 1 ) m o d e lsmdash b u t it m a k es p re c ise a n d c le a r p re d ic tio n s T h is is a d istin c t

a d v a n tag e in co m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g

su c h as S E E K (H o ld in g 1 9 8 5 ) w h ic h a re ty p ic ally v ag u e

T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n eralise to

o th e r d o m a in s o f e x p e rtis e O n e o f th e m ain tea c h in g s o f re c en t re se a rc h is th a t

d iffe re n t ta sk en v iro n m e n ts ta x c o g n itiv e fu n c tio n s d if fer en tly In p a rticu la r

e n v iro n m en ts d iffe r m a ss iv e ly in th e a m o u n t o f s e arc h n e e d e d to c a rry o u t th e

ta sk su c c es sfu lly H en ce i t is u n lik e ly th a t f in d in g s fro m ch es s re se arch w ill

a p p ly w ith o u t q u a lif ica tio n to o th e r d o m a in s H o w e v e r th e in tera c tio n s b e tw e e n

lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n o n th e o n e h a n d a n d b e tw e e n

k n o w le d g e a n d se a rc h o n th e o th er h a n d a re a lso a p p aren t in se v e ra l d o m a in s

su ch a s m e d ic al d ia g n o s is p h y sic s a n d tex t c o m p re h e n sio n T h e te m p la te

th e o ry w h ich a c co u n ts fo r th e s e in te rac tio n s th u s o ffe rs th e p e rsp e c tiv e to

in teg rate th e se v a rio u s d o m ain s o f e x p e rtise in to a s in g le fra m ew o rk

T h e c h u n k in g th e o ry h a s so m e tim e s b ee n m is in te rp re te d a s a c la im th a t

re c o g n itio n o f fa m iliar p atte rn s a n d re trie v al o f m o v e s a s so c ia te d w ith th e m is

a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e g H o ld in g 1 9 8 5 ) T h e c o rre c t

c la im a n d th e o n e a ctu a lly m a d e b y C h as e a n d S im o n is th a t sk ill in p la y in g

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

312 GOBET

c h e ss d ep en d s b o th o n (a ) re co g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n

p la y in g g a m e s a n d (b ) ex p lo rin g p o s sib le m o v e s a n d ev a lu a tin g th e ir

c o n se q u e n c es H en c e e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m em o ry o f

in fo rm a tio n ab o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a ttern s o f p ie c e s a n d

o n th e a v a ilab ility o f s tra te g ie s fo r h ig h ly s e le c tiv e s ea rc h in th e m o v e tr ee

E x p e rt m e m o ry in tu rn in clu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry

(te m p la te s) th a t a u g m en t sh o rt- te rm m e m o ry w ith s lo ts (v a riab le p lac e s) th a t c a n

b e filled r ap id ly w ith in fo rm a tio n a b o u t th e cu rr en t p o s itio n

R EFER EN CES

B a y lo r G W amp S im o n H A (1 9 6 6 ) A c h e s s m a tin g c o m b in a t io n s p ro g ra m P ro c e e d in g s o f th e

1 9 6 6 S p r in g J o in t C o m p u te r C o n fe re n c e B o s to n 2 8 4 3 1 ndash 4 4 7

C h a rn e s s N (1 9 7 6 ) M e m o ry f o r c h e s s p o s i t io n s R e s is ta n c e to in te rf e re n c e J o u rn a l o f

E x p e r im e n ta l P sy c h o lo g y H u m a n L e a rn in g a n d M e m o ry 2 6 4 1 ndash 6 5 3

C h a rn e s s N (1 9 8 1 ) S e a rc h in c h e ss A g e a n d sk i ll d i ff e re n c e s J o u rn a l o f E x p e r im e n ta l

P sy c h o lo g y H u m a n P e r c e p tio n a n d P e r fo r m a n c e 2 4 6 7 ndash 4 7 6

C h a rn e s s N (1 9 9 1 ) E x p e r tise in c h e s s T h e b a la n c e b e tw e e n k n o w le d g e a n d s e a rc h In K A

E ri c sso n amp J S m ith ( E d s ) S tud ie s o f e x p e r t is e P ro sp e c ts a n d lim i ts C a m b r id g e C a m b rid g e

U n iv e rs ity P re ss

C h a se W G amp E ri c sso n K A (1 9 8 2 ) S k il l a n d w o rk in g m e m o ry In G H B o w e r (E d ) T h e

p sy c h o lo g y o f le a rn in g a n d m o t iv a tio n (V o l 1 6 ) N e w Y o r k A c a d e m ic P re ss

C h a se W G amp S im o n H A (1 9 7 3 ) T h e m in d rsquos e y e in c h e ss I n W G C h a s e (E d ) V isu a l

in fo rm a tio n p ro c e s s in g N e w Y or k A c a d e m ic P re ss

C o o k e N J A t la s R S L a n e D M amp B e rg e r R C (1 9 9 3 ) R o le o f h ig h -l e v e l k n o w le d g e in

m e m o ry fo r c h e ss p o s i tio n s A m e ric a n J o u rn a l o f P sy c h o lo g y 1 0 6 3 2 1 - 3 5 1

D e G ro o t A D (1 9 4 6 ) H e t d e n k e n v a n d e n s c h a k e r A m ste rd a m N o o rd H o lla n d sc h e

D e G ro o t A D (1 9 7 8 ) T h o u g h t a n d c h o ic e in c h e s s [r e v is e d tr a n s la tio n o f D e G ro o t 1 9 4 6 2 n d

e d n ] T h e H a g u e M o u to n P u b l ish e r s

D e G ro o t A D amp G o b e t F (1 9 9 6 ) P e rc e p t io n a n d m e m or y in c h e ss H e u r is t ic s o f th e

p ro fe ss io n a l e y e A s se n V a n G o rc u m

E ri c sso n K A amp K in tsc h W (1 9 9 5 ) L o n g - te r m w o r k in g m e m o ry P sy c h o lo g ic a l R e v ie w 1 0 2

2 1 1 ndash 2 4 5

E ri c sso n K A amp S im on H A (1 9 8 0 ) V e rb a l re p o rt s a s d a ta P sy c h o lo g ic a l R e v ie w 8 7 2 1 5 ndash 2 5 1

G o b e t F (1 9 9 3 ) L e s m eacute m o ire s d rsquo u n jo u e u r d rsquo eacute c h e c s [T h e m e m o rie s o f a c h e s s p la y e r] F r ib o u rg

(S w itz e rl a n d ) E d it io n s U n iv e r s i ta i re s

G o b e t F (1 9 9 6 ) M e m o ry in c h e ss p la y e rs C om p a r iso n o f fo u r th e o r ie s (T e c h R e p N o 43 )

U n iv e rs ity o f N o t t in g h a m (U K ) D e p a r tm e n t o f P sy c h o lo g y E S R C C e n tre f o r R e se a r c h in

D e v e lo p m e n t I n s tru c t io n a n d T ra in in g

G o b e t F (in p re ss ) C h e ss th in k in g r e v is ite d S w iss J o u rn a l o f P sy c h o lo g y

G o b e t F amp Ja n se n P (1 9 9 4 ) T o w a r d s a c h e ss p r o g ra m b a se d o n a m o d e l o f h u m a n m e m o ry I n

H J v a n d e n H e rik IS H e rs c hb e rg amp J W U ite rw ijk (E d s ) A d v a n c e s in c o m p u te r c h e ss 7

M a a st ri c h t U n iv e rs ity o f L im b u rg P r e ss

G o b e t F amp S im o n H A (1 9 9 6 a ) T e m p la te s in c h e ss m e m o r y A m e c h a n is m fo r re c a ll in g s e v e ra l

b o a rd s C o g n i tiv e P sy c h o lo g y 3 1 1 ndash 4 0

G o b e t F amp S im o n H A (1 9 9 6 b ) R e c a l l o f ra p id ly p re se n te d ra n d o m c h e s s p os it io n s i s a f u n c tio n

o f s k il l P sy c h o n o m ic B u lle t in amp R e v ie w 3 1 5 9 ndash 1 6 3

PATTERN -R ECOGN IT ION AND SEA RCH 313

G o b e t F amp S im o n H A (1 9 9 6 c ) T h e ro le s o f re c o g n it io n p r o c e sse s a n d lo o k -a h e a d se a r c h in

t im e - c o n s t ra in e d e x p e r t p ro b le m s o lv in g E v id e n c e f ro m g ra n d m a ste r le v e l c h e ss P sy c h o lo g ic a l

S c ie n c e 7 5 2 ndash 5 5

H o ld in g D H (1 9 8 5 ) T h e p sy c h o lo g y o f c h e ss sk i ll H illsd a le N J L a w re n c e E rlb a u m A s so c ia te s

I n c

H o ld in g D H (1 9 9 2 ) T h e o r ie s o f c h e s s sk i ll P sy c h o lo g ic a l R e se a rc h 5 4 1 0 ndash 1 6

H o ld in g D H amp R e y n o ld s R I (1 9 8 2 ) R e c a l l o r e v a lu a t io n o f c h e ss p o s i tio n s a s d e te rm in a n ts o f

c h e s s sk i ll M e m o r y amp C o g n it io n 1 0 2 3 7 ndash 2 4 2

K o e d in g e r K R amp A n d e rs o n J R (1 9 9 0 ) A b s tr a c t p la n n in g a n d p e r c e p tu a l c h u n k s E le m e n ts o f

e x p e r tise in g e o m e try C o gn i t iv e S c ie n c e 1 4 5 1 1 ndash 5 5 0

K r o g iu s N (1 9 7 6 ) P sy c h o lo g y in c h e ss L o n d o n R H M P re ss

N e iss e r U (1 9 7 6 ) C o gn i t io n a n d re a l ity P r in c ip le s a n d im p l ic a t ion s o f c o g n i tiv e p sy c h o lo g y

S a n F r a n c isc o F re e m a n amp C o m p a n y

N e w e l l A ( 1 9 9 0 ) U n if ie d th e o r ie s o f c o g n i tio n C a m b r id g e M A H a r v a rd U n iv e r s i ty P re ss

N e w e l l A S h a w J C amp S im o n H A (1 9 6 3 ) C h e ss- p la y in g p r o g ra m s a n d th e p ro b le m o f

c o m p le x i ty I n E A F e ig e n b a u m amp J F e ld m a n (E d s ) C o m p u te rs a n d th o u g h t N e w Y o rk

M c G ra w -H il l

N e w e l l A amp S im o n H A (1 9 6 5 ) A n e x a m p le o f h u m a n c h e s s p la y in th e lig h t o f c h e ss -p la y in g

p ro g r a m s In N W e in e r amp J P S c h a d e ( E d s ) P ro g r e ss in b io c y b e r n e tic s A m ste rd a m E lse v ie r

N e w e l l A amp S im o n H A ( 1 9 7 2 ) H u m a n p ro b le m so lv in g E n g le w o o d C liff s N J P re n t ic e -H a ll

S a a ri lu om a P (1 9 8 9 ) C h e ss p la y e r s rsquo r e c a l l o f a ud i to ri ly p re se n te d c h e ss p o s i tio n s E u ro p e a n

J o u rn a l o f C o g n i t iv e P s y c h o lo g y 1 3 0 9 ndash 3 2 0

S a a ri lu o m a P ( 1 9 9 0 ) A p p e rc e p tio n a n d r e s t ru c tu rin g in c h e ss p la y e r s rsquo p r o b le m s o lv in g I n K J

G i lh o o ly M T G K e a n e R H L o g ie amp G E r d o s ( E d s ) L in e s o f th in k in g (V o l 2 ) N e w Y o r k

W ile y

S a a ri lu o m a P (1 9 9 2 ) E rr o r in c h e s s T h e a p p e rc e p tio n -r e s tru c tu rin g v ie w P sy c h o lo g ic a l

R e se a rc h 5 4 1 7 ndash 2 6

S e lz O (1 9 2 2 ) Z u r P sy c h o lo g ie d e s p r o d u k tiv e n D e n k e n s u n d d e s Ir r tu m s B o n n F r ie d r ic h

C o h e n

W a g n e r D A amp S c u rr a h M J (1 9 7 1 ) S o m e c h a ra c te r is t ic s o f h u m a n p r o b le m - so lv in g in c h e ss

C o gn i t iv e P sy c h o lo g y 2 4 5 4 ndash 4 7 8