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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 1
INSIDERS SECRETS TO PLAYINGTEXAS HOLDEM POKERONLINE
2004
AllRightsReserved.
TheodoreCage2004Canada
AllrightsreservedunderInternationalCopyrightConventions.
PublishedinCanadabyCardSharkBooks.Unlessotherwisenoted,
allmaterialscontainedinthisdocumentarecopyrightedandmaynot
beusedexceptasprovidedunderthesetermsandconditions.This
documentisforpersonaluseonlyandisnottoberedistributed,soldorcopiedwithouttheauthorsexplicitpermission.
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 2
AN INTRODUCTIONTO ONLINE POKERTHINKING ANDINSIDERS SECRETS
IdiscoveredthesecretrecipetoKFCChicken15yearsagoandI
havebeenhookedonInsidersSecretseversince.
aveyou everbeen to apartyor abarwhereyouvemetsomeoneforthefirsttimewhotoldyouaninsiderssecret
to theirbusinessorwork?Maybe Imjustagood listener
but this happens tome all the time.We all know these insider
kinds of details about our own littleworld. For example, ifwe
workedatCadbury,theCadburySecretwouldbeoneofthefirst
thingswewouldlearnaboutonthejob(evenifitwasntofficially
part of the training program). There are other kinds of insider
knowledge howsomething isreallymadeattheplantwework
at ho e tai odu t a e a keted he e a idea eally a e
H
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 3
price.
Dontyouwishyoucouldtalktoaninsiderattheplantwherethe
caryouareconsideringbuying ismade?Orsomeonewhoreally
knowsthescooponthemortgageindustrywhenitstimetogetre
financed?How about talking to the guywho programmed the
VLTmachineyouplayeverydayat lunch?Would thathelpyou
winmore?
EverybodywehavetalkedtoaboutTexasHoldemhassaidthatwhattheyreallywantismorethanjustabookthattellsthemthe
rules to thegame.Theywantsomethingnew.Somethingfresh
that will give them an edge over the other players. Something
exciting.
Sowetalkedtotheinsiders.Howdoesthesystemwork?Howare
the cards shuffled (whats the randomizing algorithm)? Hasanyonedoneanystudiesonwhatcardsreallypaythebest?What
tables play thebest?Are there systems thatwork onlinebetter
thanothers?Whatdotheinsidersknowaboutcardstoplay?Can
wereallymakemoneyatthisgame?
Fromthisfeedbackwedevelopthisbookconcept.Thenwehunted
down
the
facts.
In
the
end,
this
has
been
a
lot
of
fun
and
quite
profitable.WelovethegameofTexasHoldembutnowwehave
the tools towinmore games.As usual, if you have the insider
stuff,youarebetterarmedtosucceed.Prettymuchoneofthose
simplerulestoliveyourlifebyifyouaskme.
Ibelievethatwinninginlife,love,businessandsportsandyes,
poker,isallaboutthreedynamicsIliketocalltheCSIs.
Contingency (chance or luck)
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 4
Intelligence(orstreetsmarts)
Wehavedivided thisbook into these threekeyareas foravery
goodreason.Whenyouplayonlinepokerforrealmoneyfor the
firsttimeyouwillfinditdifficultjusttosurvive.Yourstack(your
personal chips)willdisappear like anumbrella in a typhoon. If
youhavewhat it takes tostick itout through this initiation (and
theexpendablecashtolast),youwillnextdiscoverthatwhatyou
arelackingisrealtechnicalknowledge.Youwillsoonrealizethat
you need to play this game more with field intelligence thaninstinct.Thatis,ifyouwanttowinconsistently.
Finally,asyouprogressintolargerpotgames,therealtestwillbe
yourabilitytobementallytough,disciplinedandaggressive.Our
last section on selfawareness discusses the philosophy of great
pokerplayers.
Therearedozensofbooksavailabletodayonpoker.Ivereadmost
ofthem.Theytendtofocusononeormoreofthefollowingareas:
Analysisofoddsandstrategy
Historyandactualplayexamples
Techniquesontellsorhowtoreadtheotherplayers
Mental
preparation
for
the
game
itself
Noteventhebestbookscoveralloftheseareasorattempttobring
thesedifferentpracticestogetherinsomemeaningfulway.Thisis
ourgoalwithInsidersSecretsToPlayingTexasHoldemOnline;
to linkstrategyand intelligenceandmentalpreparation inaway
thatwill ramp you up tobe successful at thebest game in the
worldintheshortestpossibletime.
Whats new about this book? First unlike most of the books on the
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 5
the traditional bricks andmortar game of Poker.Our focus is
specifictothenewonlineversionsofTexasHoldemPoker,played
by over 20,000,000 peopleworldwide over theNet every single
day.Anyonewhohasplayedonlinepokerknows this isquitea
differentanimalindeed.
Secondly,wepresenttheCageFoodChainTheory,anewsystem
of playbased on the results of three major research programs
carriedoutbycomputersimulationsonTexasHoldemPoker. If
you follow the system religiously, youwill find yourwinningsincreasing gradually at first, and then substantially. All the
researchshowsthataggressiveplayisthekeytowinningmonster
pots; aggression at the right time andbased on a solidbody of
knowledge.Wewillshowyoutheprocessandoutlinethestepsto
beingatruecardshark.Butyoumustfollowtherules.Whenwe
runlabsontheCageFoodChainTheorywefindthatplayersget
caughtup in thegameandbend the rulesof the system, lettingtheir emotions rule their play. Or they goby gut feeling on a
decisivehandinsteadofconsideringpotoddsandcardodds.The
online casinos love that kind of play itmakes them millions
everymonth.Itwonthoweverputanyextramoneyinyourbank
account.Youvegottostopplayingbygutfeel.
Of
the
three
dynamics,
we
start
with
the
intel
section
and
contingencydata first; this iswhere the rubberhits the road for
mostplayersandwewanted togetyoustartedwithanexciting
newsystemofplayingthatwillgiveyouafirsthandadvantage.
WhatsIntel?typical militaryspeakforfieldintelligence or
relevantknowledge.Whatyouneed toknow,now. In thecovert
worldofspiesandagents,havingtherightnuggetofinformation
availablewhen required can saveyour lifeor someoneelses. In
Poker it means making the win when others wouldnt and adding
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 6
experience which you can only gain from playing the game
thousandsoftimes.
Fieldintelhelpsyouparachuteintoasituationandbecompetent
andsavvyinabighurry.
TheTheoCageFoodChainTheoryofPokercondensesdozensof
schoolsof thoughtonPoker intoaneasy todigestprogram that
youcanbeginusingimmediately.Thegoalofthistechniqueisto
get you out of the fish category and in to the shark categorybeforeyougeteatenalive.Pardonthefoodpunsbutthespeedand
aggressiveness of real money online poker can spin your head
around.Youwillneedtobearmedandready.
Inmanyareasof thisbookwedealwiththe latest inresearchon
contingency,anotherwordforodds.Whynotjustcallitluck?
Becausecontingencyisafarbroaderandmoreelegantterm.Luckis not a thing you canbuy or create and you certainly cannot
attractitorcaptureit(orchaseitaway).Whatweashumansseeas
luckisreallyjustchancecircumstanceplayingoutbeforeus.
Thebestway tovisualizecontingency is to imaginea fork in the
road.Which then leads to another fork.And still another. Each
requires
a
decision
and
each
decision
can
lead
to
very
different
conclusions.Thatswhat contingency isallabout.Sometimeswe
choosethepathwithoutknowingwhere itwilltakeusandother
timeswedontgettochooseatall.
InPoker,wecanusemathtobetterunderstandtheoddsofcertain
combinations occurring in your game.Really understanding the
odds inPoker is one of the keys to success;not onlybecause it
helps you to better understand the possibilities but because it
teaches us the expected monetary value of our hand as well
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 7
Queen is1:7 ifwedontknowhow to translate that information
intoapracticalbettingdecision?
Recent computer simulations of Texas Holdem have taught us
quiteabitaboutrealgameoddsandstrategy.What theyvealso
shownusisthatittakesseverallifetimestoaverageouttheodds
betweenmatchedplayers. Soyouneedapowerfuladvantage to
win against others with similar skills and preparation. That
advantageisbetterselfawareness.
Assumethatyouandanotherplayerareperfectlymatchedincardskills.Youplay eachother everyweek.Butoneofyouhashad
lifetimewins of several times the otherbased on pullingbetter
cards.Howlongdoyouhavetokeepplayingbeforethewinnings
evenout?About250,000yearsaccordingtocomputerresearch.
Sohowdoesabetterplayergainadvantage if theydonthavea
few thousand lifetimes at their disposal? Bybeing significantlybetter than the otherplayers.Youneedhuge advantage tobe a
consistentwinner.Youneed toknow theotherplayers andyou
need togain this advantage asquickly aspossible.Youneed to
understandbettingoddsbetter.Youneed toknowyourself.And
youneedtobeveryaggressivewhenthetimeisright.
Thats
the
essence
of
a
shark.
Skilled.
Aggressive.
Knows
the
environment.Knowstheprey.Undaunted.
Havefunandbestofluckatthetables.
TheoCage
June2004
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 8
TABLE OF CONTENTS
INTRODUCTION .............................................................................. 2
WHYISONLINEPOKERSODIFFERENT?................................... 9
GETTINGSTARTED......................................................................... 14
THECAGEFOODCHAINTHEORY!............................................ 15
ODDS,PERMUTATIONSANDROI............................................. 37
THERULES OFTEXASHOLDEM ............................................... 77
WINNINGBEFORE THEFIRSTCARDSDEALT..................... 83
THEIMPORTANCE OFTABLEPOSITION ............................ 103
PLAYERPROFILING ...................................................................... 108
PLAYINGLIMITTOURNAMENTS ............................................ 155
HOWTOPICKANONLINECASINO........................................ 168
POCKETCARDWINNINGODDS.............................................. 180
HOWTOTHINKLIKEASHARK................................................ 182
TEXASHOLDEMDICTIONARY................................................ 190
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 9
WHY IS ONLINE TEXASHOLDEM POKER
SO DIFFERENT?
TexasHoldemPokerhasbecomethefastestgrow
ing game on the Internet. Play it a few times andyouwillunderstandwhy.Itsaddictive.Fast.Enter
taining. Colorful. And there you are, playing live
withpeoplefromallovertheglobe,agreatvirtual
casinoexperience andrealmoneyisbeingwonbypeoplejust
likeyouandme.Whatsnottolike?
Well,
you
say,
I
would
like
to
win
more
often
.
.
.
Lik h l h l l id k i l (VLT)
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 10
They would love to win; they just arent prepared to do the
homework necessary to get really good at the game and win
consistently.Whohastimeforthat?
TheProsdo,thatswho!
And thePros likeOnlinepoker.UnlikeVLTs, theoddsarenot
stackedsomuch in favourof thehouseandplayerscanactually
makeconsistentprofits iftheyunderstandthegamewellenough.
Ihaveanunclewho is famous inourfamily.Hehasanunusual
career.Hehasmadeagreatlivingplayingprofessionalpokerfor
over 40 years. (Hewas known in the trade as a rounder for
detailsseethedictionaryattheendofthisbook.)Andhehasmade
morethanjustadecentlivinghehasseveralhomesandayacht
he moors in Florida. Hes an interesting character and he has
taughtme a lot.Much of thisbook isbased on his advice andteaching.
My uncle says there are two major differencesbetween casual
playersandprofessionals.
One Professionalsalwaysknowexactlywhomtheyareplaying
with.
Dontbe deceived. When you play poker you are not playing
againstthecardsyouareplayingagainsttheotherplayers.Great
pokerplayersnever forget this. Thegoalofourbook is to teach
youhow tobetterunderstand theguyorgal sittingacross from
you at the virtual poker table. A better understanding of the
dynamicsbetween humans at the table alone will dramatically
improveyourchancesofwinning.
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 11
Thisbookwillteachyouhowtocalculateoddsusingactualgame
examples and give you shortcuts thatwill help you to increase
yourchancesofwinningeverytimeyouplay.
Oddsdonttellyouhowtoplay,theytellyouhowtobet.
Firstyouneedtounderstandwhyreadingabouttheconventional
brickandmortargameofTexasHoldem(thekindyouplayina
realcasino)certainlywonthurtbutitwilldefinitelynotprepare
youfortheuniqueexperienceofplayingthegameonline.
WHY IS ONLINE POKER SO DIFFERENT?
Online poker adds several interesting wrinkles to the game of
TexasHoldem. Somuchischangedinfact,thatthereareawhole
newsetofgamestrategies.Theoddsofwinningtheonlineversion
ofthisgamearenowstackedevenmoreinthefavourofthebettereducatedplayers.This isoneof thesecrets to realsuccessat the
virtualtable.
1.YOUCANWATCH.
Ifyouwalkintoabricksandmortarcasinotomorrowanddecide
you
would
like
to
just
watch
a
game
of
Texas
Hold
em
to
better
understandhow itsplayed, securitywillsoonhustleyououtof
thebuilding.Pokerisnotaspectatorsportatcasinos.Ifyouwant
tolearnthegame youneedtoplay.Andplayingwhenyourea
rookie (or as the pros call it a fish) canbe a very expensive
learningexperience.
On theotherhand,online,youcanwatcharealgameas longas
youwant,fornocostandfornorisk.Watchingatablecanteach
you a lot about the players and their betting style and the game in
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 12
general.Watchingplayersforfreeisoneofthegreatadvantages
ofonlinepoker.
TakingnotesisanothergreatstrategyinOnlinePoker.
Thereisnothingwrongorunethicalaboutkeepingnotesonother
players. Some Online Poker rooms even provide a feature that
allows you to take notes online while you play. This feature
facilitates thebuildingofadatabasearound theplayingstylesof
consistentplayers.Our advice is to recordwhat kinds of hands
theyplay,howquicklytheyreact,andtorecorddetailonbetting
andraisingbehaviour.
In the heat of the game, you may not always have time to go
throughallof thedetails.Butoneday,aregularplayerwilljoin
your tablewith ahealthy stackof chipsandyouwillappreciate
knowing everything you can ahead of time about their playingstyle.
2.YOUKNOWEXACTLYWHATSINTHEPOT?
Ata regularcardgame,youneed todosomeroughguessingat
pot totals. (Theotherplayersrarelyencourageyou togodigging
throughthe
pot
to
come
up
with
atally).
Online,
the
total
is
calculated for you to the penny. Thismakes calculations about
howmuch tobetveryaccurate.Why is this important?Youwill
learnlaterthatoneofthekeystowinningisasystemusedbypros
fordecadescalledPotBetting.Themoreaccurateyourknowledge
ofthepot,thebetterableyouaretoknowexactlyhowmuchyou
shouldbebettingonagivenhand.OnlinePoker isaPotBetting
dreamcometrue.Sharpenupyourmathskillsabit,andyouare
ontheroadtomakingmoney.
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 13
3.YOUHAVEMORETABLEANDBETTINGCHOICES!
Haveyoueverwalkedintoarealcasinolookingforaseatatacard
game?Youmaybe lucky to finda fewdozen.Whichone is the
best foryourplaying style?Youwontknowuntilyou sitdown
andplayanumberofhands.Andifyoudontlikeyourcompany
atthattable?Youmovetoanothertableandtryagain.
Therearethousandsofonlinecasinoswithdozensorhundredsof
tables at each one froyou to choose from.You canpick from a
widerange of betting options and from an infinite variety of
different player combinations combinations you will have
observedbeforeputtingdownyourhardearedmoney.Andyou
can do this in a matter of minutes right from your computer
screen.
Never have there been so many options for the poker playerwilling to learn.Remember,youarenotjustplayingagainst the
odds,youareplayingagainstotherplayersandinamathematical
sense, the tableasawhole.This is therealkey towinning.Look
for a tablewith thegreatestnumberofweakerplayers andyou
willhaveanautomaticadvantage.
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 14
FOR THOSE OF YOUWHO JUST WANT TOGET STARTED NOW!
f you are anything likeme,youjustwant toget to thegood
stuff. So letsjump right into the game and theFood Chain
system.
Sure,therearerulestolearnandtechniquestounderstand and
all kinds of interesting tips on betting and odds. This book is
fullofstrategyandbackground.
But Ijustwant tojump into the game itself as a startingpoint.
Howcanyoubeawinner?OK!Letsstartwithanexampleofhowthissystemworks.Thenyou can learnabout thedetailsmoreat
I
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 15
TheCageFoodChainTheoryofOnlineTexasHoldemPoker!
Fish,astheyarecalledinTexasHoldem,areprey.
Fisharethelosers andthebeginners andthesloppy
playerswhoget eaten everydayby thebigger fish. In
nature they are called prey. Thank goodness for the
fish.Theysustaintheentirepokerfoodchain.Withoutfish,there
wouldbenomonsterpotsorbigpaychecksandthegamewould
notbenearlyasinterestingnorasprofitable.
Dont getmewrong. Everyone is a fish in thebeginning and
thereisnowayaroundthisessentialtruth.Everyonegetsburned
and eaten repeatedly when they start to play poker. Everyonelosesoneventhebestnutshands.
This book is about how to get out of the fish category as
quicklyaspossibleandstarttakingmoneyhome.
Anoteabouttheresearchthatbacksthisbook.
The book you are reading, unlike most of the poker books
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 16
guyswhohavespentdecades learning theropes; themajorityof
themplayingtheoldfashionedbricksandmortarversionofthe
game.
IamaComputerProgrammerwithanintenseloveforPoker(and
othergames)wherethereisastrongcomponentofskillinvolved.
InsiderSecrets2004isallaboutthescienceofPoker.
CardShark,ourresearchteam,hasgonethroughmillionsof lines
of code,data resultsandanalysisonbillionsofplayedhandsof
Poker.Agoodpercentageof this researchwas sourced from the
same online casinos you and I play at everyday. The rest came
fromreputablesourcessuchasCarnegieMelonUniversitywhere
grad students havebeen running computerized Texas Holdem
simulations for years. Our theories are based on solid
mathematics, proven odds calculations and the results of some
veryinterestingcomputerstudies.
At least three major research studies over the past three years
have generated over 5 billion virtual hands of Texas Holdem
poker.
Youwouldhavetoplaypokereverydayforseveralmillionyears
toexperience
that
many
hands.
(I
know
youre
trying
to
live
a
healthierlifestylebutImnotbettingonanyoneschancestomake
itthatfar!)
Mostof thestrategy in thisbook isbasedon thisnewexciting
research PLUS some good oldfashioned table sense based on
over20yearsofreadinggreatcardplayers.
Youmaybesurprisedbywhatthisnewresearchshows.IknowI
was
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 17
The better the information you have about what is really
happeningwiththecardsandthetable,thefasteryouwillgetout
of the fishcategoryand intothewinningzone.Weopenup the
bigblackonlinepokerboxandshowyoutheinsides.Whatcould
bemorefun?
Heres the question we hear every day. How much money can
you make? Again,based on recent surveys, a good player can
make $40,000 to $50,000 per year playingmedium $3$10 stake
games.
A real expert, aSHARK,canmake$100,000or more peryear
andhundredsdo.
Letsstartwiththeresultsofarecentcomputeranalysis.
Imagine what we could learn about this game if we created avirtual10playerTexasHoldem table,programmed theplayers
indifferentwaysandthenjustletthemplayforafewthousand
years.
Withsomeof the testrunswewoulduseveryaggressiveplayer
behavioursjust to see how that type of combination of players
effectswinning
and
losing.
In
other
examples
we
would
use
avery
tightandconservativegroupofplayerstoseehowthataffectsthe
gameoveraperiodof time.Billionsofhandswere thenplayed
andanalyzedagainandagainoverseveralmonths. More than
manylifetimesofplay.
Here is thesimplest formof theresultsof thisresearchbasedon
yourchancesofwinningwiththefirsttwoholecards.
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 18
Player Type If you are a beginner, you are fish. If
you aremore interested inplaying thanwinning,you
arefish.Ifyoudontdoyourhomeworkandcompletely
understandhowtheoddsaffectyourchancesthenyesVirginia,
youareafish.
Butevengoodplayerscanbecomefishduringplay.Tournament
play is a good example where the game can change radically
dependingonthenumberofplayersleftinthegame.Ifyoustartto panic or get shortstacked, youmayunintentionally revert to
fishtactics.Asabeginneryouwilltendto act likeafishyou
maystayinthepotlongerthanyourhandwouldjustify.Youmay
raisewhenyour cardsarenot that strong.Fishare typifiedbya
playingcharacteristiccalledloose.Loosenessimpliesadisregard
for card odds and a general lack of knowledge about the other
players.Combine
this
looseness
with
aggressive
behaviour
and
youhaveoneofthemostinterestingcreaturesataPokertablea
maniac.
Tosurviveandmakemoney,fishneedtoplayaverytightgame.
Asknowledgeand table smarts improve, they can increase their
aggressiveness,boldwithfreshwinnings.
Thebestguide tobeginnercardplay is touse theFishRuleas
t t d i th Pl T Ch t B d th l t t t
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 19
research, fish should onlystay in thehand if they haveoneof
thetop24pocketcardsdealt.
Why?Because if theyhaveoneof thesehands, regardlessof the
type of talent at the table, theywillhave an excellent chanceof
winning. Theywill alsobegin to understand the discipline of a
tighterplaying style,which isbasedonknowing theoddsand
readingthetable.
Bettingtacticsshouldnotbeanissuehereandneithershouldthe
readingof tellsorevenplayerposition(whichwewilldiscussin
detaillater).
Here are the top 24 pocket hands in any Texas Holdem game
(outofapossible169).
Letsstartoffwiththetopofthehitparade.(Thesreferstocards
inthesamesuit.)
ThebigTop4AA,KK,QQ,JJareridiculouslyprofitableatany
table.Alwaysraiseandreraisewiththesecards.Theydontcome
alongoften,sotakeadvantage.Notraisingonthesecardsisasign
offoolishness.Beingaggressivehereisanobrainer.
The
top
16
ranked
starting
2
card
Hold
em
hands
(or
cards)arefundamentaltowinningplay.Theymakeuponly7%
f ll h d d lt it lik l th t ill t i h b
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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 20
limitingyourplaytojustthesecardcombinations.Butyouneed
toknowwhattheyrepresentwhentheydocomealong.
IfyoucomparethischarttoolderbooksonPokeryoumaynotice
an obvious variation. The latest research has shown that the
overall power of AKs is slightly greater than that of KQs
especiallyingameswherefewplayersareleftaftertheriver.
Infact,withsixplayersaftertheriver,AKplaces10th,whileina
game with 6 players, it places 5th. This revelation was first
discovered in theR&Dbeingdoneusing the latestcomputerized
pokersimulationsinthelate90s.
JJisanotherexampleofholecardsthatvarygreatlydependingon
the typeofgame theyareplayed in.Theyhavebeenhighlighted
onthechartforthefollowingreason
Atalargetableof6ormoreplayers,JJisranked4thinpower.Ina
situationwheretherearefewerplayers,thepowerofthispairgoes
downto9th.
GamerankwithonlyTWOplayersaftertheriver(Top10)
GamerankwithSIXplayersaftertheriver(Top10)
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ThekeydecisionanyHoldemplayermakesiswhetherornotto
playthestarting2cardhandtheyaredealtwith.Andiftheydo
play,howdotheyplaysmartthroughthehand.
IyouareaFISH,neverbetonanythingbutthetop
ranked24pocketcards.
InsiderSecret
WewouldalsosuggestthatyouALWAYSraiseontheTop10.
Raise on the Top 16 unlessyou think the raise isnot likely to
driveoutotherplayersinaveryloosegame.
Underverytighttableconditions,onlytheTop5shouldberaised
beforetheflop.
However,ouradvicewouldbeifyoufindyourselfataverytight
table, you should probably get up and go find better playing
conditionselsewhere.
AK isagoodexampleofholecards thatonlydoreallywell ina
shorthanded game so you need to raise and drive out other
players right away. If you cant, youwill have lostmost of the
powerand
advantage
of
these
cards.
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TT on the other hand drops dramatically in powerwith fewer
playerssoraisingtopushoutweakerhandsisapoorstrategy.
BarracudaThenextlevelupfromtheFishcategoryisBarracuda.Youre not thebiggest andmeanest fish in
the sea,butyouhaveexperienceandyouve survived.
Andyouremakingmoneywhenyouplay.
TheBarracudaPlayercansafelyplay theTop40pocketcardsas
listednext.
Youarenow in the landofthemediumsuitedconnectors KQs,
QJs,JTs,T9s whichdoverywellinsmallstakegamesaswellas
thebiggishoffsuitaces AQ,AJ.
BarracudaTip:
Pickyour10playertablecarefully.Lookforplayerswhoseem tobehavingfun,andwhereat leasthalf
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isamajordeterminantofhowwellyourhandswillholdupin
thelongrun.
When other players know what youre holding, you suffer
tremendousdisadvantage.Justplayinggoodcards isnotenough
asaBarracuda.RaisingAAandKKisclearlynotenough.
Youneedacarefullyplannedbuthardtoreadraisingstrategyas
well.At theBarracudastageyoubegin toexperimentwithmore
aggressive play.As youwill read later, timing your aggressive
strategy is the key. Being aggressive with a large number of
playersatthetable,unlesstheyareallveryconservative,willnot
workmostofthetime.Andnomatterhowaggressiveyouare,if
youaresurroundedbysharks,youwillbechum.
AsaFishyouwere focusedon the top1016pocket cardsdealt.
Youneedtoexpandthisnowintwoways.
One,youneed tobemoreaggressivebefore the floponawider
rangeofcards.
Two,youneed tomixupyourbetting strategy.Asyouwill see
later, the best player type is tightaggressive. This
characterizationis
based
more
on
how
the
other
players
see
you
andlessonyourownstrategy.Inpoker,perceptioniseverything.
Youneedtobeseenbyyouropponentassomeonewhosstyleis
slightlyhard to readandoccasionallyunpredictable.Thenwhen
youdoraiseaggressively,youropponentswilltakeyouseriously
andsurrenderthepot.
Be aware that in online Poker, because players come and go
constantly,itsmoredifficulttobuildareputationatthetable.Its
like performing on the stage you need to exaggerate your mo es a
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tobeaggressiveonline,youraggressionneeds tobe clear that
meanspushingupthebetsmorethanyouwouldatarealtable.
Slowplaycanhave itsadvantageshere too. It tends tocatch the
attention of otherweaker players anxious to donate to the pot.
Evenifyouknowexactlyhowmuchyouplantoraise,slowdown.
Letthecounterclickoff.Thisisagreatattentiongettingdevice.If
afterstalling,youfold,youcommunicateindecision.Ontheother
hand,ifyouraiseheavy,youvemadethemovequiteclearand
youvegottheotherplayersthinking.
Mentaltoughnessisoneofthekeystosuccessasyoumoveupthe
pokerfoodchain.Beingmentallytoughmeansignoringtheother
playersconcernsabouthowfastyouplay.
Mr.SlowPlay
One of the toughest tournaments Iveplayed in had oneplayer
who constantly ranup to the last few secondsof their available
timeoneveryturn.Atfirstitlookedliketheyweredistracted,or
playinganothergameonlineatthesametime.Virtuallyeverytime
itcametotheirturn,theywouldstalluntilthecountdown.Soon,
other playersbegan chatting about the slow play.Namecalling
began.One
player
suggested
taking
aggressive
action
against
this
player as a group, simply because of the shared aggravation.
Which is exactly what happened. At one point, one playerbet
aggressivelyagainstMr.SlowPlayandwentallinandlost.
Whowon the tournament?Mr.SlowPlay.Whatagreatstrategy.
Herattledalmostalloftheotherplayerswithhisslowdetermined
pace.Hewent right down to the last few seconds on the clock
dozensoftimes.Themoretheotherplayerscomplained,themore
he hesitated
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Becausehewasslowoneveryplay,itwasverytoughtoreadhis
actual playing style. He was consistent. He also got a lot of
attention.Whenhewon,noonemissedit.Hemanagedtocontrol
thetableinaway.Tablecontrolisclearlyagoaloftheconsistent
winner.
The Shark Playerwillhave80hands in theirplay list (seechart
following)knowing that theyaregoodhands if the flop isgood
flop, that your opponentswill generally discount the likelihood
youllbeholdingthem,andthattheywillhavethewilltofoldon
asmanyroundsasittakeswhentheflopdoesntgointheirfavor.
Asagambler,withthesecards,therealmagicisgettingtheright
flopcards.
Based on using the Shark play list you would on average,
participate
in
about
1/3rd
of
all
pots
at
your
table.
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Again, if your goal is towin, please stay away from very tight
tablesbecausenomatterhowwellyouplay,onlythehousewins
wheneveryoneisgood.
AuthorsSklanskyandMalmuth(S&M)haveauthoredoneofthe
most popular pokerbook to date calledHoldemforAdvanced
Players.Ourprefloprecommendationsdifferinmanyways.
S&Mhas always advised raisingwithyour strongesthands and
limping (calling)withyourweakest. But thisamajormistake in
tightergames, sinceyour strongesthands areworthmuchmore
than theblinds,while yourweakesthands areworthmuch less
thantheblinds.Foldingisthewisestchoice.
Also, S&M advises not raisingwith hands like KT after several
looselimpers.Thenewestresearchhoweverindicatesyoushould
usuallyraisesinceyourhandislikelytobebestandwillwinmorethan your fair share of pots (though usually notmuchmoney).
S&Ms argument is that fish will call correctly with gutshots
(drawingonecardtoastraight)andpairsontheflopifyouraise
preflop,andyouwillsuckmoreplayersintothepot.Raisingwill
notgreatlyreduceyourchanceofyourwinningthepot,soifyou
willwinmore thanyour fairshareofpots,youshouldgenerally
raise.
StatsfromanumberofonlinecasinoshaverevealedanotherS&M
myth thatyoushould raisewithbabypairs like 33even ifyou
know theblindswillcall.Theoddsare thatyouwill flopa thrip
more then1 in9 timesbutyouwillwin thepot less than1 in9
times. Since youwillwin thepot less than your fair share, you
shouldnotraise.
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PLAYING THE PROGRAM STEP-BY-STEP
Letsstartwithanexamplehand.Iftherearetermshereyoudontunderstand, you can check the Dictionary in the back or the
IntroductionToTheGamechapter.
Ready?
The threebasicsyouneed tounderstandbeforeyoubetonecent
on
any
Texas
Holdem
game.
1) Ch k t th th l ! A h d l ? Ch k
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notesonthestrengthofeachplayer.Ihavesuppliedasystemyou
canusetodeterminetheirabilitytoplay.
2)Decideontherightspotatthetable.Veryimportant.Probably
oneof themost importantdecisionsyouwillmake in thegame.
YouwillfindalotoftipsinthechapteronTablePosition.
3) Make sure you have enough chips.Stack sizedoesmatter in
thisgame.Youwill find tipsonhow todecideonhowmuch to
playwiththislaterinthebook.
OK!Youreseated.Youhavereadthetableandtheotherplayers.
Youhaveenoughchipstowin.Nowwhat?
Fromthispointon,justfollowoursystem.
InthisexampleyouaredealtaKingandanine.
Yourfirstquestionwillbehowgoodismyhand?
Well,welltellyou.ReferfirstofalltotheOpeningOddsChartat
theendofthisbook.
Look up K9 from the chart (which youwill keepby your side
whenyouplay.)
The odds of winning with these two cards is 14%
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Now lookat thepot.What is the totalnow?This iseasybecause
thecomputerkeepstrackofthisforyoutothepenny.
Letssaythepottotalis$80.
14%of$80 is$11.20.(This isourPotOddscalculation.This tells
youhowmuchyoushouldbetbasedonwhatyouhave.)
Soyoumatch thebetof $10 andyouare in. (Tendollars is less
thanyour$11.20limit.Youunderpaidtostayinthegame.
Nowtheotherskeepbetting.Itgetsbacktoyouagainandthepot
isnow$120.
Whats14%of$120?Around$17.
Youve alreadybet $10. That leaves $7. (Your firstbet on thatroundplus$7)
Youneedanother$10tostayin.
Accordingtomyrulesthen,youshouldfold.
Nowthe$3differenceisnotmuch.Youmightdecidetogotothe$20 ifnecessary. But dont go any further.Theoddsareagainst
you and you are overpaying for the cardsyouhaveyet to see.
Nowyouareplayingscientificallyandbasedonwellunderstood
odds.This is how theprosplay.Theywatch the otherplayers.
Theywatchtheothercards.Andtheyknowthemath.
The
secret
to
winning
Texas
Holdem?
Beat
the
odds
by
knowingtheodds.
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You need tobeat the other playersby knowing the oddsbetter
than they do.Now lets learnmore about the secrets of online
poker.
Letsgetbacktoourtwopocketcards.
HerestheFLOP.
Now youre pretty excited. You just ended up with a pair of
Kings.IsapairofKingsgoodenoughtowin?Areyoureadyto
betthefarm?DoyouhavetheNuts?
50%ofTexasHoldempotsarewonwithapairof9s
orbetter.
InsiderTip
So that sounds good. Except there is a partial straight on the
table.
Atthispoint,aftertheFLOP,thereareTHREEthingstoconsider.
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Whatdotheotherplayershave(Tells)?
Whataremyoddsofgettingawinninghand?
Whatwillitcostmetoseethenextcard?
Backtothefirstpoint.
Whatdotheotherplayershave?Shortofthosexrayglassesthey
usedtoadvertiseinthecomicswhenyouwereakid,howwillyou
know?This is theartof the tellsevaluating theotherplayers
cards.
First,lookattheoddsfortheotherplayers.
Inourgame,thereisa2cardstraightonthetable.Anotherplayer
needstohavea56or69or9T inanysuitandtheyareclosetoastraight.(Lateronwewillshowyouexactlyhowtofigureoutthe
exactodds.)
It isvery likely that someone at the table is 1or2 cards froma
straight.Andtheystillhavetwomorecardstofillthatstraight.
Clearly, you need threeofakind to stay in the game. Another
King.
As far as you know there are 2 other Kings in the deck (you never
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Theoddsaresimpletocalculate.
Thereare17 cardsdealt (basedon3downand7playerswith2
cardseach).
Youneed2outof17cards=11.7%odds.
Thebettingstartsandyoucanseethepot is$180when itgetsto
you.
Howmuchcanyoubet?
11.7%of$180=$20.
If you know that you need another King to win, the most you
shouldbettoseethenextcard(basedonwhatyouknow)is$20.
Youhaveoneotherveryvaluablebitofinformationatthispoint.
Youcanseehowothersarebetting.Thisshouldgiveyouagood
sense,combinedwithyourreadingofthetablebeforeyoustarted,
ofwhatkindofhandstheyhave.
LetsseethenextcardtheTURNcardasixofhearts.
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WHAT WOULD YOU DO AT THIS POINT IF YOU KNEW
THAT ONE OF THE OTHER PLAYERS ALREADY HAD A
STRAIGHT?
Youwouldfold.Right?Well neverbetonthecome.
Acardinalruleinpoker iftheyvegotyoubeatand
youknowit,foldnow.
InsiderTip
Yes,youmaygetacardtoimproveyourhandbutsocanthey,so
unlessyoucanseethenextcardforfree,dontwasteyourmoney.
Thequestionis,howdoyouknowwhattheotherplayerhas?Are
you making the determinationbased on how they arebetting?
Maybe
theyre
bluffing.
Youknowyoucantbeatastraightwithathrip(threeofakind).
Ontheotherhand,besidethePAIRofKINGS,youhavefourcards
inastraight6,7,8,9.
WhyyoushouldnotplayanythingbelowAToffsuit?Whyits
besttohaveA5sandbeloworATsandaboveoversomethingin
the middle like A8s?
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AnyAceunsuitedhandbelowATcanbebigtroubleinanykind
ofgame.
Somepeoplemighteven considerATandAJdifficulthands too
butforthegamesyouaregoingtobeplayingintheyareadequate
startinghands.
ThereasonA8,A7,A5allsuckisbecauseyoureallycanthitmuch
towin. TakeA8forexample.
Yourkickerisntthatgreat,the8,andyouhavenochanceof
hittinganystraightsorflushes. Theonlywayyoucanwinreally
istohopethattheyhaveaweakerAcethenyoudoandyoucatch
one.
Playingpokerislikeinvestinginthestockmarket.
Youwanttoputyourmoneyintogreatstockthathasachanceto
deliveragoodreturn.A8 isntthatkindofstock.
NowtoanswerthequestionofATsandaboveandA5sandbelow
versusA9sA8sA7sA6s.
The first onesworkbecause you can alsomake a straightwiththem I would take A5s over A8s because the A and the 5 can
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WhenyouplayweakAcesthoughlikeA5s,youhavetobeextra
cautiousifyoucatchanAceontheflop.
Youwontbesure ifyourkicker isgoodornotsoyoullhave to
give the next step some thought. Playing these only in later
positionscanhelpyoumakebetterdecisionsbecausepeoplewill
checkmostlikelyiftheydonthavetheAorthathandbeat.
WhydohandslikeAA,KK,QQ,AK,AQworkbestatsmaller
tables?
Imagineascenariowhereeveryoneisinthehand,andyoulook
downandseetwogorgeousredAces?
Yourpulsestartstorace.Thenyoulookuptoseethateveryone
hasalreadycalled.Atthispointyouhavetoknowthatyour
chancesofwinningareslim.
Powerhandslikethisrarelywinwhentherearethatmanypeople
callingpreflop. Why?
Howdoyouimprovethishand?
Inbigallinpotstwopairrarelywinsagainstflushesandstraights.
Sowhatdoyoudo?
Theres only one tactic left You could check raise on the flop
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someoftheotherplayerstoleave.Limitingthefieldwould
increaseyourchancestowin.
WhyarehandslikeKTs,QJsJTs,89s,79s,and46sbetterwhen
youhaveafulltableofplayersin?
Youcanalmostnevergetintotroublewiththesekindsofpocket
cards.Ifyouhitsomething,itslikelytobequitestrong.Ifyou
dontgetthecardsyouwant,itseasyatthispointtofold.
TrythatwithapairofAces!Withthosekindsofcardsyouare
marriedtothepotusuallytothebitterend.AhandlikeJTsand
89sareidealforplayingagainstbigallinpots.Ouradviceisto
alwaysraisetobuildthepot.
Thereasonthesefavourbigpotsisbecausetheyarealways
drawingtoflushesandstraights.
Makeyourhand...andyouwillbehardtobeat.
SUMMARY FOR THE BEGINNER
Readthetable.
Play
very
tight,
especially
in
the
beginning.
Startwithenoughchips.
Betbasedonwhatthepotoddsare(neveroverbetthepot)
Watchtheoddsforupcomingcards.
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EVERYTHING YOU ALWAYS WANTEDTO KNOW (AND MAYBE DIDNT)ABOUT ODDS, PERMUTATIONS
AND RETURN ON INVESTMENT
WHATARECARDODDS?
Ifyouhaventalreadynoticed,probabilityisahugefactorinTexas
Hold em.Forexample,thereare2,598,960possiblehandsina52
carddeckbutonly4RoyalFlushes.Iftheaverageseriouspoker
player is dealt 100 000 hands in their lifetime they will never hold
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(onthefirstfivecards)morethan4percentofallthepossible
hands.Andlikelyalotless.
Figuringoutstraightcardcombinationsforthepurposeofthistext
are called Card Odds (youwillbe introduced to other kindsof
odds later).CardOdds can reveal some quite interesting infor
mation.
For
example,
how
many
pat
straight
flushes
will
you
see
in
your
lifetime?Todeterminethatnumber,theexpectednumberofhands
that could be dealt during your lifetime is estimated by the
followingcalculation:
10completepokerhands/hr.x5hrs./game x 50games/yr.
x40yrs./pokerlife=l00,000handsofpokerperlifetime.
This is a pretty aggressive estimate, as most people will never
come close to thisnumberof completehands inTexasHoldem.
Based on this level ofplay, the number ofpat (on the first five
cards) poker hands that you should get during your lifetime is
calculatedfromthecardoddsandtabulatedasfollows:
CardsDealt NumberofPatHands
Nopair 50,000
Onepair 40,00
Twopair 5,000
Threeofakind 2,000
Straight 400
Flush 200
Fullhouse 170
Fourofakind 25Straight flush 1.4
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Sostatistically,youshouldseeapatstraightflushonyourfirst
fivecards
once
or
twice
during
your
lifetime.
Most
average
poker
playerswillneverseeevenone.
Cardplayersoftentalkabouthavingaluckystreakorarun.
Mathematically,streaksdontexist.Butsupposeyoudidhavean
amazingrunofcardsoneevening.Whatwouldtheoddsbeof
havingfiveconsecutivestraightflushesinarow?
Royal Flush 4 .0000015391
Other StraightFlush
36 .0000138517
Four of a kind 624 .0002400960
Full House 3,744 .0014405762
Flush 5,108 .0019654015
Straight 10,200 .0039246468
Three of akind
54,912 .0211284514
Two Pairs 123,552 .0475390156
One Pair 1,098,240 .4225690276
Nothing 1,302,540 .5011773940
Total 2,598,960 1.0000000000
In
every
1.7x1024
deals
.
.
.
or
once
in
every
700,000,000,000,000,000,000years. Youdhavetoreadthosecards
in thedark though,becauseoursunwillbelonggoneby that
time.
Playersusecardoddstomakeplayingdecisions.Adecisionmade
without taking into account card oddsmakes poker a guessing
game.Thechancesoffinishingaflushorastraight,theprobability
ofgettinganovercard(facecard),thepercentageoftimesyoure
going to flop a card to match your pocket pair are all extremely
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Knowledgeofthesestatisticsiskeytowinning.
Herearesomeotherbasicprobabilitiesthatyoushouldknow
about:
Youneedonemorehearttomakeyourflushontheturn
orriver 35%
Probabilityofhittinganopenendedstraightdraw(i.e.4
straight
cards,
need
one
on
either
end
to
hit
on
turn
or
river) 31.5%
Probabilityofbeingdealtsuitedcards:23.5%
Probabilityofhittingathreeorfourofakindattheflop
whenyouholdapocketpair:11.8%
Probabilityyouwillmakeapairattheflop,holdingtwo
unpairedcardsinthehole:32.4%
Probabilityof
being
dealt
AA:
.45%
Probabilityofnooneholdingaspecificcard,bynumberof
players,assumingyoudonothavethatcard,bynumber
oftotalplayers.
2 84.5%
3 70.9%
459%
5 48.6%
6 39.7%
7 32.1%
8 25.6%
9 20.1%
10 15.6%
Probabilitysomeoneelsedoesnothaveanace,assuming
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2 88.2%
3 77.5%
4 67.6%
5 58.6%
6 50.4%
7 43%
8 36.4%
9 30.5%
10 25.3%
HOWARETHEODDSCALCULATED?
Letslookattheexampleofhaving4outs(fourcardsyouneedto
makeyourhand).Sayyoureholding6c7dandtheflopcomes9s
10hKc.Inthiscaseyouneedan8tomakethestraight.Sincethere
arefour8sinthedeck,youhave4outs.
YOURPOCKET
THEFLOP
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ODDSWITHONECARDTOCOME
Calculatingtheoddswithonecardtocomeisrelatively
straightforward.
Whenyoure looking tomake the inside straight,youhave four
outs.Thereareatotalof46unknowncards(52minusthe2cards
inyourhandminusthe3cardsfortheflopandthe1turncard).42
of
the
cards
don
t
make
your
hand
and
four
do.
42:4
or
10.5:1
=
about 9%. I prefer to use the percentage as it helps when
calculatingPotOdds(tocomelater).
ODDSWITHTWOTOCOME
To calculate the appropriate odds with two cards to come, you
must
first
determine
the
total
number
of
two
card
combinations
possibleaftertheflop.
Theeasiestway tocalculate this isbymultiplying thenumberof
cardsavailablefor the turn(47)bythenumberofcardsavailable
for the river (46)anddividing thatnumberby2 (becauseacard
cantmatchitself).47*46/2=1081.
Acertainnumberof these1081 twocardcombinationswillhave
eightsinthem.Todetermineoddsproperly,youneedtocalculate
twomorefigures.
EIGHTS ON BOTH THE TURN AND THE RIVER
Oneof the four eights can appearon the turn.And ifonedoes,
therewillbe three left for the river. If youmultiply 4by 3 and
di id b 2 (b d t t h it lf) th t th
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EIGHTSONTHETURNORRIVER
Ifaneightcomesontheturn,thereare46unseencardsremaining.
Butyoureno longer interested in the three remainingeights, so
youcansubtractthose.Thisleaves43unseencardsthatwillmake
auniquepairwithoneoftheeights.Multiply4(thenumberof8s
inthedeck)by43(thenumberofunseencards)toarriveat172.
FINISH
THE
CALCULATION
172 plus 6 comes to 178 the total number of twocard
combination thathaveat leastoneeight in themandasmanyas
twoeights.
Outof1081possibletwocardcombinationsontheturnandriver,
178
of
those
combinations
help
us
make
our
hand.
Subtract
178
from1081tofindthenumberofcombinationsthatdontmakethe
straight(1081178=903).
The odds againstmaking a straightby the river are: 903:178, or
20%.
What
About
The
Cards
The
Other
Players
Are
Holding?
Everwonderwhyweneverfactortheopponents cardsorthe
burncardswhenfiguringouthowmanycardsareleft?
The reason is thatwe only consider unseen cards. If you saw
whattheburncardswere,oranopponentshowedyouhishand,
youwouldknowthat thosecardsarenotgoingtobedrawnand
coulduse that.We typicallydonotknowwhat theyhave,sowe
dont even think about it when talking about odds
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Forinstance,takeastandarddeckof52cards,remove2Acesand
burn25ofthem.Ifyoudrewthenextcard,whatarethechancesof
itbeing anAce? Itwouldbe 2/50 (2Aces left out of 50unseen
cards). ItwouldNOTbe 2/25justbecause youburned half the
deck.Okay,dothesamethingagain,butthistimeyougettolook
attheburncards.Letssaythatofallthecardsyouburned,none
wereanace.Nowyouroddsare2/25becausetherearestill2Aces
andnowonly25 unseencards.
Youwill find that you can easily remember a few of themost
commonsituationsforoutssuchasthefourflushorstraightdraw
buttherehastobeaneasierwaythanmemorizingthefiguresfor
everynumberofouts.Thegoodnewsisthatthereisawaytogeta
goodestimationoftheoddswithouttheheavymathandyoucan
alsousehandyoddscharts.
WHATHANDSWILLWINTHEPOT?
The following are the most valuable starting hands in Texas
Holdem. This chart assumes a medium to loose $510 Texas
Holdemgame.Theresultsarebasedonacomputersimulationof
5,000,000 played hands. The percentage shown indicates how
manytimesintypicalgamethatthesehandswinthepot.
2Pair 31%
Pair 27%
Threeofakind 12%
Straight 9%
Flush 9%
Fullhouse 9%
Bust(nothing) 2%Fourofakind 1%
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Thisisinterestingdatabutheresthekickerlookatthepower
oftwopairsandsinglepairhands.Itsnotonlyhigherthanthe
WHATAREMYCHANCESOFWINNING?
Whataremychancesofwinningahandwithagivensetofpocket
cards?Whataretheoddsoffillingastraight?
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Howmuchyoucanexpecttoprofitfromthesestartinghands?
Thestartinghandaveragewinforeachtimeplayedbasedon
mediumtolooseTexasHoldemPokergameswitha $5/$10limit.
AA $34.19
KK $24.13
QQ $17.36
JJ $12.08AKsuited $11.63
AKoffsuit $8.65
AQsuited $8.32
1010 $7.72
AJsuited $5.69
AQoffsuit $5.47
POCKETCARDODDS
Hole Cards Odds
Any Pair 16 : 1
Suited Cards 3 : 1
A-K 82 : 1
Suited Connecting Cards 24 : 1
A-A or K-K 110 : 1
A-anything 5.3 : 1
Any two cards J's or Higher 10:1
After the Flop
Pair J's or Higher 55 : 1
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Pair improving to 3 of a Kind 8 : 1
Flop being 3 of a Kind 391 : 1
The River (5th Street)
A-K hitting an A or K by the River 1:6 : 1
Q-Q vs A-K (A or K hitting) 1.5 : 1
Hitting 5th card to complete a Flush 1.6 : 1
Completing an Open Ended Straight 2.9 : 1
Three of a Kind improving to Full House 2.7 : 1
Pocket Pair improving to 3 of a Kind after the
Flop12 : 1
Hitting a Backdoor Flush 33 : 1
More Interesting Texas Hold'em Odds
5 Players, there's an A on the flop. Chances aplayer has an A in their hole.
1.7 : 1
4 Players, there's an A on the flop. Chances a
player has an A in their hole.2.1 : 1
3 Players, there's an A on the flop. Chances a
player has an A in their hole.2.9 : 1
2 Players, there's an A on the flop. Chances a
player has an A in their hole. 4.3 : 1
WHATAREPOTODDS?
Potoddsaretheoddsyougetwhenanalyzingthecurrentsizeof
the pot vs. your next call or bet. Pot Odds help you make
importantcall,raiseorfolddecisions.
Example 1: There is $200 in the pot and a final $10 bet coming at
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one of four suits, the shortcut math is 1:4 chances or 25%.
Winning consistently is aboutbeating Pot Odds and not over
betting.IfyourCardOddsare25%(youhavefourheartsandneed
another towin) andyouonlyneed tobet5%of thepresentpot
($10 asapercentageof the$200) to see the last card,youare in
great shape. Based on Pot Odds for thishandyou couldgo as
highas25%ofthepotbasedonyouroddstopullaheartonthe
river.
Example 2: You are in a $5/$10 Holdem game with JackTen
pocketcards
and
one
opponent
left
on
the
turn.
Youhaveanoutside straightdrawwithaboardof259Q,and
only therivercard lefttomakeyourstraight.Any8oranyKing
willfinishthisstraightforyou,soyouhave8outs(four8sand4
Ksleftinthedeck)and46unseencardsleft.8/46givesyoua6:1
chance or a 17% chanceof getting thewin.Your opponentbets
$10.
6/1=17%PotOdds
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Ifyoutakea$10betyoucouldwin$100.Yourbetisthen10%of
thefinalpot.The10%betissmallerthanthe17%odds,soyouare
ingoodshapefromaninvestmentpointofview.
Wheneveryourcallorbet(in thiscase10%ofthepot) issmaller
thanyouroddsofgettingthewinninghand(17%)youarebuying
thenext card at adiscount.The key is looking at theoddsof a
winninghand,notbuildingapartofawinninghand.
Toomanybeginnersjustplaygoodcardsandjusttossbadones
oriftheyhavetheprospectofstraightoraflush theywilljust
drawanddrawwithlittleconsiderationtoanythingelse.
Unlessyouhave the NUTS (nuts= theverybestpossiblehand)
every time there is a certain degree of riskwhen you put your
moneyinthepot.
Intheheatofthebattleyoumaynotalwayshavetimetogetout
yourcalculatoranddothenumbercrunching.YoucanlookatPot
Oddsinamuchsimplerway justaskyourselfifthereisenough
moneyinthepottojustifytherisk?
If there is abig pot unless youjust know you arebeat, or it
simplycosts
too
much
too
call
(which
means
your
pot
odds
may
notbesogreatafteritsallsaidanddone) trytogetsomeaction.
Evenifyouknewyouwerealongshot wouldyoubet$25or$50
ona chance towin$500or$1000ormore?Whileyoumaybea
long shot itsnot abadbet if there is a reasonable chanceyou
couldwin.
On the flip side, and this is important, youmay have a decent
hand anditmayevenbethewinner,(useyouropponentortells
kno ledge) but if its going to cost you $250 to call and you stand
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toonlywinafewhundredthenyourpotoddsarenotsogreatand
isprobablynotworththerisk.
Potoddsratiosareausefultooltoseehowoftenyouneedtowin
thehandtobreakeven.
Ifthereis$100inthepotandittakes$10tocall,youmustwinthis
hand1outof11 times inorder tobreakeven.The thinkinggoes
alongthelinesof:Ifyouplay11times,itllcostyou$110,butwhen
youwin,youget$110($100+your$10call).
Theusefulnessofcardoddsandpotoddsbecomesveryapparent
whenyoustartcomparing the two.Asweknownow, ina flush
draw,yourcardodds formakingyour flushare1.9 to1or35%.
Letssayyoureinahandwithanutflushdrawandits$5toyou
on theflop tocall.Doyoucall?Youranswershouldbe:Whatare
mypotodds?
Ifthereis$15inthepotplusa$5betfromanopponent,thenyou
aregetting20:5or4:1potodds25%.Thismeansthatinorderto
breakeven,youmustwin1outofevery5 times.However,with
yourflushdraw,youroddsofwinningare1outofevery3times!
You shouldquickly realize thatnotonlyareyoubreakingeven,
butyouremakinganiceprofitonthistoo.Letscalculatetheprofit
margin
on
this
by
theoretically
playing
this
hand
100
times
from
theflop,whenisthencheckedtotheriver.
TotalCosttoPlay=100hands*$5tocall= $500
PotValue=$15+$5bet+$5call=$25
OddstoWin=1.9:1or35%(Fromtheflop)
TotalHandsWon=100*OddstoWin(35%)=35wins
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= $500+(35*$30)
= $500+$1,050
=$550Profit
Asyoucansee,youhaveagreatreason toplay this flushdraw,
becauseyoullbemakingmoneyinthelongrunaccordingtoyour
cardoddsandpotodds.Themostfundamentalpointtotakefromthisis:
IfyourPotOdds>CardOdds,thenyouaremakingaprofit.
So,eventhoughyoumaybefacedwithagutshotstraightdrawat
times,whichisaterribledrawat5to1handodds,itcanbeworth
it to call if you are getting pot odds greater than 5 to 1.Othertimes, ifyouhaveanexcellentdrawsuchas the flushdraw,but
someonehasjustraiseda largeamountsoyourpotoddsare1:1
for instance, then you obviously should not continue trying to
draw to a flush, asyouwill losemoney in the long run. In this
situation, a fold or semibluff is your only solution, unless you
knowtherewillbecallersbehindyouthatimproveyourpotodds
to
better
than
break
even.
Yourability tomemorizeor calculateyour cardoddsand figure
out your pot odds will lead you to make many of the right
decisionsinthefuture.Justbesuretorememberthatfundamental
principle of playing drawing hands when your pot odds are
greaterthanyourcardodds.
Anothergoodrule tofollow a lotofplayerswant tosomehow
factor in money they wagered on previous rounds With the last
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ofthat$200pot.Letssay$50.Doesthatmeanyoushouldplayor
foldbecauseofthatmoneyyoualreadyhaveinthere?$50/$200?
Thatsabigno.
Thats not your money anymore! Its in a pool ofmoney tobe
given to thewinner. You have no stake in that pot. The only
stakeyoumighthaveistotallymentalandhasnobearingonhard
statistics.
Thenextstepistousebetoddsandimpliedodds.Thatstougher,
becauseitinvolvespredictingreactionsofotherplayers.Withbet
odds, you try to factor in howmany people are going to call a
raise.With impliedodds,youre thinkingabout reactions for the
restofthegame.Oneexampleonimpliedodds...
Sayitsanother$5/$10Holdemgameandyouhaveafourflushontheflop.
Yourneighbourbets,andeveryoneelsefolds.Thepotis$50atthis
point.Firstyoufigureoutyourchanceofhittingyourflushonthe
turn,anditcomesouttoabout19%(about1in5).Youhavetocall
this$5betvs.a$50pot,sothatsa10xpayout.1/5ishigherthan
1/10,
so
bet
odds
are
okay,
but
you
must
consider
that
this
guy
s
goingtobetintoyouontheturnandriveralso.Thatsthe$5plus
twomore$10bets.
Sonowyourfacing$25moretilltheendofthehand.Soyouhave
toconsideryourchancesofhittingthatflushontheturnorriver,
whichmakesitabout35%(betterthan1in3now),butyouhaveto
invest $25 for a finishing pot of $100. $100/$25 is 1 in 4. Thats
prettyclose.
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Ifyoudontmake itonthe turn, itllchangeyouroutsandodds!
Youllhavea19.6%chanceofhittingtheflush(littleworsethan1
in5),buta$20investmentforafinishingpotof$100!$100/$20is1
in 5. So the chances could take anasty turn if youdidnthit it!
Whatsmakes itmorecomplicated is that ifyoudidhit iton the
turn,youcouldraisehimback,andgetanextra$20ormaybeeven
$40inthepot.
Onceyouvemasteredsimpleoutsandpotodds,betandimplied
odds arejust a longer extensionof theseequations. Ifyou thinkabout these thingswhile you play, theywill eventuallybecome
secondnaturetoyou.
MoreOddsExamples:Apocketpair
YoustartwithapairofJacks in thepocket.Not tooshabby.The
flophowever,doesntcontainanotherJack.
YOURPOCKET
THEFLOP
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Lesson 1: Whats my chance of getting a Jack on the turn?
Youneedtojustfigureoutthenumberofoutsanddivideitbythe
numberof cards in thedeck.Thereare2moreJacks.Theres 47
morecardssinceyouveseenfivealready.Theanswer is2/47,or
.0426,closeto4.3%.
Lesson 2: No luck on the turn, how about the river card?
Still2Jacks left,butone lesscard in thedeckbringingthegrand
total to46.Whats2/46?Thats .0434,which isalsoclose to4.3%.
Yourchancesdidntchangemuch.
Lesson3: ForgetjustgettingjustoneJack!Iwantthemboth!What
aremychances?
Sincewere trying tofigureout thechancesofgettingoneon the
turnAND the river,andnotgettingoneonEITHER the turnor
river, we dont have to reverse our thinking.Just multiply theprobabilityofeacheventhappening.Chancesofgetting thatfirst
Jack on the turnwas .0426, remember? The chance of getting a
secondJackon the riverwouldbe 1/46,because therellonlybe
oneJackleftinthedeck.Thatsabout.0217,or2.2%.
Togettheanswer,multiplythem..0426X.0217isabout.0009!
Thatsaroundonetenthofapercent. Iwouldntbankonthat
one.
Lesson4:Hey,whatweremychancesofgettingapairofJacks
anyway?
To figure that out, think of it as getting dealt one card, then
another.Whatareyourchancesof thesecondcardmatching the
fi t ? Th ill b 3 d l ft lik th h Th
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itllbeJacks?Well,thereare13differentcards.So,.059/13isabout
.0045,alittlelessthanhalfapercent.
Lesson 5:Whatweremy chances of getting aJack on the flop?
Nowyoudohaveto thinkinreverse asinthepreviousexample.
Figureout thechancesofNOTgettingaJackoneachsuccessive
cardflip.Firstcardyouhavea48/50chance(48nonJackcardsleft,
50cardsleftinthedeck),secondcardis47/49,thirdcardis46/48.
Thosecomeoutto.96,.959,and.958.Multiplythemandget.882,
oran88.2%chanceofNOTgettinganyJacksontheflop.Invertit
to figure outwhat your chances really are and you get .118 or
11.8%.ThiswillbeyourchancetogetoneortwoJacks.
Example#2 Thestraightdraw
THEPOCKET
You startwithaJackofSpades and aTenofSpades.Youget a
rainbowflopwithaQueenofSpades,aThreeofDiamonds,anda
NineofClubs.Youvegotastraightdraw.
THEFLOP
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Lesson 1: What aremy chances of hitting it on the next card?
Sameasbefore,butwithdifferentouts.AKingoranEightwill
completeyourhand.There ispresumably fourofeach left in the
deck.Youvegot8outs.Thechanceofgettingoneofthemonthe
turn is 8 over 47,because theres 47 cards left in thedeck.That
comesouttoabout.170,oraround17%.
Lesson 2: Ididntget iton the turn!Whataremy chancesnow?
Therearestill8cardsleftinthedeckthatllhelpyou,but46cards
leftinthedeck.Thats8over46.Itchangesto.174.Itsimprovedto
awhopping17.4%!
Lesson3:Ishouldofthoughtaboutmytotalchancesfirst,Imsuch
anidiot.WhataremychancesofgettingthatcardontheturnOR
theriver?
Onceagainwellhave tocalculate thechancesofaKingorEight
NOTappearing,sowecandoitlikethelastproblem(inthiscase,
{39/47}X{38/46}).Or,sincewevealreadyfiguredoutourchances
in the previous two lessons,we canjust invert theprobabilities
andmultiplythem.Youhada.170chanceontheturn,anda.174
ontheriver.Byinverting,Imeansubtractingthemfromone.Now
weve
got
.830
and
.826!
Multiply
and
get
.686!
That
sour
chance
of
NOT hitting our card at all. So invert it again and get .314, or
31.4%.
Example#3 Toptwopair
THEPOCKET
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THEFLOP
YougetdealtaKingofDiamondsandaNineofHearts.Theflopis
looking pretty good for youwith a King of Spades, aNine of
Clubs,andaFourofClubs.Toptwopair!
Lesson 1: What are my chances of getting a full house on the
turn?
To get a full house, you need anotherKing orNine topopup.
Thereistwoofeachleftinthedeck.Soyouvegot4outs.Afterthe
floptheresalways47cardsunaccountedfor.4/47isaround.085or
an8.5%chanceofyougettingtheFullHouse.
Lesson 2: What are my chances of getting a full house on the
river?
Ifitdidnthappenontheturn,yourchancesusuallydontchangeall toomuch,but lets check.Youve stillgot 4outsandnow46
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unseencards left.4/46 isabout .087oraroundan8.7%chanceof
hittingitontheriver.A.2%difference.
Lesson3:Howaboutthechancesofgettingtheboatontheturn
ORtheriver?
Like theprevious examples, to figureyour chanceof something
happeningonmultipleevents,youneedtocalculatethechanceof
itNOThappening first.On the turn itwonthappen43/47times.
Ontheriveritwonthappen42/46times.43/47is.915,and42/46is
.913. Multiply them and get .835, or 83.5% chance of it not
happening.Invertthatandyougeta16.5%ofgettingatleastafull
housebytheshowdown.
Lesson4:Whatdoyoumeanby atleast aFullHouse?
Sincewe figured the chances toNOTgetdealt a fullhouse, thechancesarebuiltiniftheturnandriveraretwoKings,twoNines,
oraKingandaNine.IfyouaredealttwocardsbothofeitherKing
orNine,itllbefourofakindandnotaKingandNine33%ofthe
time.Thinkof itasbeingdealtonecardthentheother.Whatare
thechancesof the firstcardmatching thesecond?Whether itsa
KingorNine, therewillbeonlyoneunaccountedfor,but twoof
theother.
That
s1/3,
or
33%.
Lesson5:Thenwhataremychancesofgettingfourofakind?
Thisone requires a littlemore thought. Itdoesntmatterwhich
cardwerehopingfor.Weneedtofirstgetafullhouseontheturn.
According to lesson#1, thechanceof thathappening is .085.The
chanceofgettingthesamecardwegotontheturnis1/46.Theres
onlyoneout,andtheusual46unseencards.1/46isaround.022,or
2 2% Multiply the t o probabilities ( 022 X 085) and get 002 or
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onefifthofapercent. ItwillbeKingshalfof the timeandNines
theotherhalf
Is thismaking any sense? If you reallywant tobe amaster of
calculatingodds,youneedtoseethesecalculationsinaction,over
and over. Like anything else, practice makes perfect. In online
games especially with very few if any tells (shown cards),
statistical knowledge becomes the main factor when choosing
whethertobet,call,orfold.
Ifyoudohaveahandthatyouknowcantloseyouhavethenut.
Betlikecrazy.
While there isa lotmore toTexasHoldempoker than this this
should open your eyes tomore things about thegame ofpoker
thanjustthecardsandtheirstatistics.
Yes YouDOneedtoknowyourgeneralchancesofpullingwhat
typesofhands but ifyou learn to studyyouropponents, they
will tellyou theirhandsandyoullbeable tobeat themwithout
evenknowingyours.
RETURNONINVESTMENT(ROI)
When the stakes required to play a game of Texas Holdem
increase, there is not a proportional increase in the average
winnings ormoney flowbecausemostplayers, especially at the
startofplay,playtighterathigherstakes.
Hereshowthatworks.
Higherstakescauseplayerstobemorecautious.Potsdonotgrow
ti t l th t k d bli d i Y t
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Max Bet Pot Size
$ 2 Max 28 - 37$ 4 Max 25 - 35$ 6 Max 20 - 22$ 10 Max 10 - 28$ 20 Max 6 - 7$ 50 Max 12$ 60 Max 7.6$ 100 Max 6.11$ 200 Max 5.5
Most major online casinos release data on hands played (for a
price)ona regularbasis.A recentstudy (June2004) fromoneof
thelargestonlinecasinos,basedonseveralmillionactualhandsof
Pokerplayed,revealedthatthereturnoninvestmentvariesquitea
bitbasedonthemaximumbet.
Inthe
$2
games,
the
value
of
the
winning
pot
varied
from
28
to
37
timestheBigBlind(BB)themostyouwouldhavetoinvesttosee
theflop(shortofraises).Theaveragepotswereinthe$60range.
With the right cards, you could expect a return of 3000% on a
winninghand.
Asyoucanseeinthechartabove,thisratiofallsastheBlindsgo
up. In the $200 game, with pots averaging $6001200, the ratio
averages5.5:1.Sure,greateroverallwinnings butmuchgreater
riskbasedontheinvestmentyouhavetomaketoseetheflop.
Also notice the volatility or variance of this ratio.On the high
stakes tables, play is very tight and often passive, so the ratio
remainsverynarrowpotsarepredictably56timestheBigBlind.
At thesmallerstakestables,there isconsiderablymorevolatility,
indicativeofa lotof looserplayersandmoreaggressiveplayingstyles.
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The$1/$2tablesaretheloosestwithpotsrangingfrom2837times
theBigBlind.
AreLowStakeTablesFaster?
Notnecessarily.TexasHoldem is thekingof fastplay. Several
$1000pluspotswereplayed in less thanaminuteandrangedas
longas6minutesthesamerangeforthesmallstaketables.Over
all,theaveragelengthofanonlinePokergametodayisjustover
oneminuteor5060handsperhour.
Inhigherstakesgames,onethingisquiteclear.Thereareahigher
percentageoftighterandaggressiveplayersatthesetablesthanat
thesmallstakegames.Thatmeanstherearemoresharksatthebig
tablesandamuchbetterchance thatyouwillbeoneof the fish.
The smart thing to do here is to say away from these kinds of
tables.
Given the fact that the returnon investment is lowerat thehigh
stake games, that the average level of play is much more
aggressiveand thatamuch largerstake isrequired,there isvery
littleopportunitytobeaconsistentwinnerontableswith$50and
upblinds.
Alloftherecentresearchpointsto$5/$10Limittables
asidealcombinationofriskandreward.
InsiderTip
FACT!Whentheaverageloosegamblerloses,heorshekeepson
playinginanattempttorecovertheloss.Thisisirrationaland
unplannedplayandcanbeveryexpensive.
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Ontheotherhand,whenmostinnategamblerswin,theyforgetall
about their lossesandconclude incorrectly that theyhave finally
learnedhow towin orthat their luckhasfinallychanged.They
express what is an irrational optimism at this point a totally
unfoundedandundeservedoptimismthatkeepstheminthegame
untiltheyrevertbacktoalosingstreak.
Sharksexploitthisirrationalplayingstyleingamblerstogenerate
acontinuousincome.
OUTSODDSCHART
OutsHolding
HandDrawing To 2 to come 1 to come
21 98 % 83%
20 98 % 77%
15openstraightflush draw
straight, flush,straight flush
85% 48%
14 96% 44%
13 92% 39%
12gutshotstraightflush draw
straight, flush,straight flush
82% 35%
11 71% 31%
10 54% 28%
9 four flush flush 54% 24%
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draw
7 39% 18%
6 32% 15%
5 26% 12$
4gutshotstraight
straight 20% 9%
3 14% 7%
2 pocket pair 3 of a kind 9% 4%
1 3 of a kind 4 of a kind 4% 2%
POCKETCARDODDS
HoleCardsDealt Dealt Percent Expected Percent
SuitedStarters 680,351 23.56% 679,596 23.53%
ConnectedStarters 454,220 15.73% 453,064 15.69%
SuitedConnected
Starters114,304 3.96% 113,266 3.92%
PairedStarters
AADealt 13,010 0.45%
KKDealt 13,182 0.46%
QQDealt 13,122 0.45%
JJDealt 13,069 0.45%
TTDealt 12,886 0.45%
99Dealt 13,092 0.45%
88Dealt 13,046 0.45%
77 D lt 13 111 0 45%
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66Dealt 13,130 0.45%
55Dealt 13,173 0.46%
44Dealt 13,015 0.45%
33Dealt 13,075 0.45%
22Dealt 13,076 0.45%
AllPairedStarters 169,987 5.89% 169,899 5.88%
AKSuitedStarters 8,717 0.30% 8,713 0.30%
AKOffsuitStarters 26,051 0.90% 26,138 0.90%
AllAKStarters 34,768 1.20% 34,851 1.21%
THERULEOFFOURTWO
Theruleoffourtwoisaneasierwaytofiguretheoddsforany
situationwhereyouknowyourouts.Itisnotcompletelyaccurate
but itwillgiveyouaquick ballpark figureofyourchances for
makingahand.
Hereishowitworks.
With twocards tocomeaftertheflopyoumultiplyyournumber
ofoutsbyfour.Withonecardtocomeaftertheturn,youmultiply
yournumberofoutsbytwo.
Thiswillgiveyouaquickfiguretoworkwith.
If you have a fourcard flush after the flop youhavenine outs.
Withtwocardstocome,youmultiplytheninebyfourandyouget
36percentchanceofmakingtheflush.
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The chart shows the true odds at 35 percent.With one card to
come you multiply nineby two and get 18 percent. The chart
showsthatthetruefigureis19.6.Itisnotcompletelyaccuratebut
itisprettyclose,anditisaneasycalculationtodoinyourhead
Howtocalculatehandodds(thelongerway):
Onceyou knowhow to correctly count thenumber ofoutsyou
haveonahand,youcanusethattocalculatewhatpercentofthe
time you will hit your hand by the river. Probability can be
calculated easily for a single event, like the flippingof the river
cardfromtheturn.Thiswouldsimplybe:TotalOuts/Remaining
Cards.Fortwocardshowever,likefromthefloptotheriver,itsa
bitmorecomplicated.Thisiscalculatedbyfiguringtheprobability
ofyourcardsnothittingtwiceinarow.Thiscanbecalculatedas
shownbelow:
FloptoRiver%=1 [((47 Outs)/47)*((46 Outs)/46)]
TurntoRiver%=(47 Outs)/46
Thenumber47representstheremainingcardsleftinthedeckafter
theflop(52totalcards,minus2inourhandand3ontheflop=47
remaining cards).Even though theremightnot technicallybe47
cardsremaining,
we
do
calculations
assuming
we
are
the
only
players in the game. To illustrate,here is a two overcarddraw,
whichhas3outs foreachovercard,givinga totalof6outs fora
toppairdraw:
TwoOvercardDraw=1 [(47 6)/47*(46 6)/46]
=1 [(41/47)*(40/46)]
=1 [0.87*0.87]
=1 0.76
= 0 24
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However, most of the time we want to see this in hand odds,
whichwillbeexplainedafteryoureadaboutpotodds.Tochange
apercenttoodds,theformulais:
Odds=(1/Percentage) 1
Thus,tochangethe24%drawintoanoddwecanuse,wedothe
following:
Odds=(1/24%TwoOvercardDraw) 1=(1/0.24) 1
=4.17 1
=3.17orapprox3.2
ANALYZINGPROBABILITIESINDEPTH
Youmaywanttoskipthissectionandgobacktoitlater.Someofthisisprettydeep.Butimportant!
Gettingahandleon theprobabilityofbeingdealtvariouspoker
handsisoneofthemostimportantandvaluableskillsaplayercan
have. We present a number of different ways to do these
calculations,fromaroughguesstimatesystemcalledthe24Rule
totheactualcombinationmath.
Thefirstoddscalculationthatmustbemadeistodeterminethe
totalnumberofpossiblepokerhandsinadeck.
Asweveshown,apokerhandconsistsof5cardsdrawn froma
deck of 52 cards. Therefore, the number of combinations is
COMBIN(52,5)=2,598,960.
If you use Microsoft Excel, you can duplicate these calculations
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combinationsforagivennumberof items. TofindtheCOMBIN
factorinExcelgotoINSERT...FUNCTION ...MATH&TRIG.
Foreachoftheabove NumberofCombinations wedivideby
thisnumbertogettheprobabilityofbeingdealtanyparticular
hand.
For the calculations,wewill first split out the No Pair hands
which includeRoyal Straight Flushes, Straight Flushes, Flushes,
Straights,and Nothings.Then,wewill lookatallcombinationsthathaveatleast1pair.
The cards in a hand without any pairs will have 5 different
denominations selected randomly from the 13 available (2, 3,
4...Ace).Also,eachof the5denominationswillselect1suitfrom
the four available suits.Thus the totalnumberofnopairhands
willequal:
COMBIN(13, 5) * (COMBIN(4, 1))^5 = 1287 * 1024 = 1,317,888.
AStraightFlushismadeupof5consecutivecardsinthesamesuit
andmayhaveahighcardof5,6,7,8,9,10,Jack,Queen,King,or
Aceforatotalof10differentranks.Eachofthesemaybeinanyof
4
suits.
Thus
there
are
40
possible
Straight
Flushes.
An
Ace
high
Straight Flush is aRoyal Flush. Since there are only 4 different
suits there are only 4possibleRoyal StraightFlushes.Whenwe
subtractthe4RoyalStraightFlushesfromthetotalof40Straight
Flusheswe are leftwith 36 other Straight Flushes that areKing
highorless.
AFlush consists of any 5of the 13 cards from aparticular suit.
There are 4 possible suits. The number of possible Flushes is:
COMBIN(13 5) * 4 = 5 148 However this includes the 40 possible
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Straight Flushes.Whenwe subtract these out,we are leftwith:
5,148 40=5,108possibleordinaryflushes.
Astraightconsistsof5cardswithconsecutivedenominationsand
mayhaveahighcardof5,6,7,8,9,10,Jack,Queen,King,orAce
foratotalof10differentranks.Eachofthese5cardsmaybeinany
of the4 suits.Thus thereare10 *4^5= 10,240differentpossible
straights. However, this total includes the 40 possible Straight
Flushes.Thuswesubtract40,whichleavesuswith10,200possible
ordinarystraights.
Finally,wecometothe nothing handswhicharebasicallyallthe
left over garbage. This is simply the total number of No Pair
handsminusall thegoodstuff.Thisgivesus:1,317,888 4 36
5,108 10,200=1,302,540 nothing hands.
Howabouttheoddsofgetting1pairorbetter?
A handwithjust 1 pair has 4 different denominations selected
randomly from the 13 available denominations. 3 of these
denominationswill select 1 card randomly from the 4 available
suits.The4thdenominationwillselect2cardsfromtheavailable4
suits. Finally, the pair can be any one of the four available
denominations. Thus the calculation is: COMBIN(13, 4) *
(COMBIN(4,
1))^3
*
COMBIN(
4,
2)
*
4
=1,098,240
possible
hands
thathavejustonepair.
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