01,2.*3455 - Harvey Mudd Collegebenjamin/papers/BackgammonFocus.pdf · Backgammon is one of the...
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PDDRUJSXEVIRFXVKWPO v 2FWREHU1RYHPEHU v 0$$ )2&86 | 9 Backgammon: Game On at MathFest 2011 By Art Benjamin M ath major John VanBuren never expected to come back from MathFest a few hundred dollars richer. But that’s exactly what happened when he was one of the win- ners at the MAA’s rst backgammon tournament. e event took place the evening of August 4; it attracted more than 50 students and professors who competed for the chance to win more than $1,000 in cash prizes. e event was sponsored by the U.S. Backgammon Federation (USBGF) and was free and open to all MathFest participants. Backgammon is one of the world’s oldest games of strat- egy, combining luck of the dice with strategic thinking. It’s a two-player game where the goal is to move your checkers around a board and take them o before your opponent does. e rules of the game are easy to follow, and it can be enjoyed by children and adults. But with a few simple mathematical tools, like combinatorics and probability, you can quickly become a very strong player. Many of the attendees had never played backgammon before, so group lessons were given by experts Phil Simborg, Chuck Bower, and Frank Frigo. “I was amazed at how quickly everyone learned the game and was impressed with the questions they were asking,” said Frigo, a former world champion. Aer the group lessons, players were treated to a quiz, created by myself and Jennifer Quinn (University of Wash- ington, Tacoma), that combined elementary knowledge of backgammon and mathematics. Some of the questions appear in the box. e quiz answers are online at maa.org/ pubs/FOCUSOct-Nov11_BGquiz and will appear in the De- cember 2010/January 2011 issue of MAA FOCUS. Seventy-ve people took the quiz, with Mathematics Magazine editor Walter Stromquist earning 12 of the 13 pos- sible points. Scoring 10 points apiece were professors David Nacin (William Paterson University) and Jonathan Kane (University of Wisconsin, Whitewater) and graduate student Liz Fitzgibbons (Boston University). Since backgammon combines skill and luck, each of the seminalists then rolled two dice, and the total was added to their score, with Nacin winning the $200 prize. en came the big event—a single-elimination tourna- ment, directed by Phil Simborg, with 51 players competing for big prize money. Paul Coe from Dominican University won the $500 rst prize. Coe has written many papers on the mathematics of games of strategy and organized a con- tributed paper session on recreational mathematics. His vic- tory brings to mind a Damon Runyon quote: “e victory is not always to the swi, nor the battle to the strong, but that’s the way to bet.” John VanBuren nished second, winning $250. VanBuren just graduated from Augustana College and will be starting graduate studies in mathematics at the University of Iowa this fall. Scott Lewis of Murray State University and junior Todd Schrader of Texas A&M University were the seminal- ists, earning $125 apiece. Karen Davis, chairman of the USBGF Board of Directors, called the event a big success. “We are trying to raise aware- ness of the game of backgammon among college students and faculty. It was especially exciting to see so many bright young people get turned on to backgammon.” Davis hopes that MathFest will lead to a greater turnout at the upcoming USBGF National Collegiate Backgammon Tournament, to be held in November, where students will Acing Backgammon Math a) How many rolls of two dice are needed, on average, until a 1 or 2 appears? b) How many ways can 15 identical backgam- mon checkers be allocated among six distinct landing spots? c) What is the size of an average roll in backgam- mon? The size of a roll is its total, except when doubles are rolled, in which case the size is twice the total. For example, a roll of 64 has size 10, but a roll of 55 has size 20. The final game at MathFest’s Backgammon Night. John VanBuren (left) took home $250, and Paul Coe won $500. | 9 10-11.indd 9 10/12/2011 3:30:28 PM
Transcript of 01,2.*3455 - Harvey Mudd Collegebenjamin/papers/BackgammonFocus.pdf · Backgammon is one of the...
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Backgammon: Game On at MathFest 2011By Art Benjamin
Math major John VanBuren never expected to come back from MathFest a few hundred dollars richer. But
that’s exactly what happened when he was one of the win-ners at the MAA’s ! rst backgammon tournament. " e event took place the evening of August 4; it attracted more than 50 students and professors who competed for the chance to win more than $1,000 in cash prizes. " e event was sponsored by the U.S. Backgammon Federation (USBGF) and was free and open to all MathFest participants.
Backgammon is one of the world’s oldest games of strat-
egy, combining luck of the dice with strategic thinking. It’s a two-player game where the goal is to move your checkers around a board and take them o# before your opponent does. " e rules of the game are easy to follow, and it can be enjoyed by children and adults. But with a few simple mathematical tools, like combinatorics and probability, you can quickly become a very strong player. Many of the attendees had never played backgammon before, so group lessons were given by experts Phil Simborg, Chuck Bower, and Frank Frigo.
“I was amazed at how quickly everyone learned the game and was impressed with the questions they were asking,” said Frigo, a former world champion.
A$ er the group lessons, players were treated to a quiz, created by myself and Jennifer Quinn (University of Wash-ington, Tacoma), that combined elementary knowledge of backgammon and mathematics. Some of the questions appear in the box. " e quiz answers are online at maa.org/pubs/FOCUSOct-Nov11_BGquiz and will appear in the De-cember 2010/January 2011 issue of MAA FOCUS.
Seventy-! ve people took the quiz, with Mathematics Magazine editor Walter Stromquist earning 12 of the 13 pos-
sible points. Scoring 10 points apiece were professors David Nacin (William Paterson University) and Jonathan Kane (University of Wisconsin, Whitewater) and graduate student Liz Fitzgibbons (Boston University). Since backgammon combines skill and luck, each of the semi! nalists then rolled two dice, and the total was added to their score, with Nacin winning the $200 prize.
" en came the big event—a single-elimination tourna-ment, directed by Phil Simborg, with 51 players competing for big prize money. Paul Coe from Dominican University won the $500 ! rst prize. Coe has written many papers on the mathematics of games of strategy and organized a con-tributed paper session on recreational mathematics. His vic-tory brings to mind a Damon Runyon quote: “" e victory is not always to the swi$ , nor the battle to the strong, but that’s the way to bet.”
John VanBuren ! nished second, winning $250. VanBuren just graduated from Augustana College and will be starting graduate studies in mathematics at the University of Iowa this fall. Scott Lewis of Murray State University and junior Todd Schrader of Texas A&M University were the semi! nal-ists, earning $125 apiece.
Karen Davis, chairman of the USBGF Board of Directors, called the event a big success. “We are trying to raise aware-ness of the game of backgammon among college students and faculty. It was especially exciting to see so many bright young people get turned on to backgammon.”
Davis hopes that MathFest will lead to a greater turnout at the upcoming USBGF National Collegiate Backgammon Tournament, to be held in November, where students will
Acing Backgammon Math
a) How many rolls of two dice are needed, on average, until a 1 or 2 appears?
b) How many ways can 15 identical backgam-mon checkers be allocated among six distinct landing spots?
c) What is the size of an average roll in backgam-mon? The size of a roll is its total, except when doubles are rolled, in which case the size is twice the total. For example, a roll of 64 has size 10, but a roll of 55 has size 20.
The final game at MathFest’s Backgammon Night. John VanBuren (left) took home $250, and Paul Coe won $500.
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compete for scholarship money. At the upcoming Joint Mathematics
Meetings in Boston, I will coteach the MAA minicourse “Mathematics and Backgammon” with professor Bob Koca (Community College of Balti-more County), a world-class player and one of the game’s best theoreticians. If you are interested in setting up a backgammon club at your college or university, then contact me or Phil Simborg ([email protected]) or visit the USBGF website, usbgf.org.
Art Benjamin ([email protected]) teaches at Harvey Mudd College. He is a past winner of the American Backgam-mon Tour.
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