The New Card Shark
Ian Jackson for The New York Times
intelligence programs that can beat human opponents at poker are the
focus of Darse Billings, a doctoral researcher at the University of
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understood the math perfectly," Mr. Rao said. "It knows the value of
any holding at any point in time, allowing it to make proper calls."
For example, many poker players consider 10's and jacks to be
relatively low cards with little winning potential, but game theory
suggests that they can still win hands in some situations with few
players. The bot used knowledge like this to good effect. "It will win
its share of pots," Mr. Rao said. "If you think you can over-aggress
it, you will lose."
thousand hands, Mr. Rao shifted away from aggressive play. Instead of
raising early and forcing the bots to react to his bets, he hung back
more often to learn from their actions. This gave him more control, and
he won more frequently.
Mr. Rao said that experience taught him a
lesson. "Whenever you enter a new situation, don't assume you can
execute a strategy that will win,'' he said. "Be quiet and listen
instead of presuming or assuming."
Peter Muller, a friend of Mr.
Rao's who has played against the same bot, said the approximations in
the game-theory model left a weakness and limited the bot's chances to
do more than break even. Game-theory models usually assume that every
player uses the best possible strategy, something that rarely if ever
happens with humans.
"An optimal game theoretic strategy might
ensure that you don't lose, but it won't be effective at exploiting an
opponent's weaknesses," Mr. Muller said. "The best players learn how to
exploit predictability, but don't do it often enough so that the
opponents catch on."
Mr. Billings is working on giving the next
generation of bot the ability to track the behavior of an opponent and
adapt to his moves. He believes that the foundation of game theory
gives the bot the ability to manage losses, a crucial skill for winning
in the long run.
All of this knowledge can have a downside,
because analysis can kill a game as easily as it can a joke. Games like
tic-tac-toe are well understood and therefore rarely satisfying. While
poker is far from being understood at the same level, the deeper
knowledge of a broader range of players is squeezing the margins for
Mr. Wilson spoke almost wistfully about the days in the
early 1990's when card rooms first opened in California and began
offering Texas Hold'em. "The games were crazy and loose," he said. "The
games were wild. There were very few people who understood the game.
Then the real turkeys ran out of money and stopped playing. They got
smarter and started understanding the more subtle areas of the game."
the skill is more even and well distributed, the effects of chance grow
stronger, leading to more turbulence in the game. No one knows this
better than Robert Varkonyi, the unknown who surprised everyone by
winning the World Series of Poker in 2002. This year he was eliminated
the first day.