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're 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 poker known as 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 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 computer scientist Michael Bowling of the University of Alberta, who led the research.
Far from being a frivolous exercise, the poker-playing program, Cepheus, could be applied to cybersecurity, medicine or even business negotiations, said Carnegie Mellon University computer scientist Sam Ganzfried, co-author of the program that won the 2014 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 the TV game show "Jeopardy!" have served as platforms for testing 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 steep challenge because, unlike in chess or checkers, a computer does not know its opponent's situation — his cards. And the number of theoretically possible situations in which 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. ("Limit'' means the size of bets and number of raises are capped.) The dealer gives each player two cards face down, and then lays out five shared cards, one at a time and face up. Players bet after each deal and use the shared cards to assemble the best possible five-card hand.
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.