Almost always raise your opponent’s first bet, which can provoke an immediate fold. In later rounds, if your opponent raises, re-raise if you are holding at least a pair of threes. Err on the side of playing a hand, not folding.
These and thousands of other decisions in the popular two-person version of the poker game “limit Texas hold ’em” produce a strategy so close to optimal that it cannot be beaten in the long run, according to a study published on Thursday in the journal Science.
A computer program running this strategy is the first to “solve” any form of poker: It plays as close to perfectly as is mathematically possible, coming out no worse than even — over many hands — no matter what an opponent holds or does, said University of Alberta computer scientist Michael Bowling, who led the research.
Far from being a frivolous exercise, the poker-playing program, named Cepheus, could be applied to cybersecurity, medicine and even business negotiations, Carnegie Mellon University computer scientist Sam Ganzfried said, the co-author of the program that won last year’s computer poker competition.
“The result is a significant achievement in computer poker and in artificial intelligence,” he said.
Computers and games have a long, intertwined history. Programs that beat the best human players at checkers, chess and Jeopardy have served as testbeds for advances in artificial intelligence as well as more mundane matters: Strategies used by chess-playing computers, for instance, led to optimization strategies for sewer routing, Bowling said.
Poker presents an especially difficult challenge because, unlike chess or checkers, a computer does not know its opponent’s situation — his cards. The number of theoretically possible situations where players must estimate odds and choose whether to bet, call, raise or fold is so huge — 319 trillion — that it taxes any machine’s computational and memory capacity.
Cepheus plays two-person limit Texas hold ’em. The “limit” is a cap on the size of bets and number of raises.
Among Cepheus’s winning strategies: Almost always raise after the first two cards, but fold with likely losers such as a 3 and 7 or a 2 and Jack. The public can see the ideal moves and play against Cepheus at http://poker.srv.ualberta.ca.
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