![]() After each round of cards, a player can check, bet, match his opponent's bet, raise that bet, or fold. ![]() Each player then tries to make the best five-card hand-say, three of a kind-from his own cards and those on the table. Then two more cards are played face-up on the table. Three cards-the flop-are then laid face-up in the middle of the table. To begin, each player places a bet and is dealt two cards. In it, only two players compete and the size of bets is limited. In fact, poker is so complicated that Bowling and colleagues decided to study only a relatively specialized version called heads-up limit Texas Hold 'em. And unlike tic-tac-toe and checkers, poker involves luck, betting, and bluffing, factors that make it impossible to find a strategy that guarantees a win or a draw on every hand. In poker, players cannot see each other's cards. In both tic-tac-toe and checkers, both players have full knowledge of the state of the game at every turn. And either of those games is much simpler than poker for a number of reasons. In contrast, it took computer scientists years and plenty of computing power to solve checkers. For example, in tic-tac-toe even a child can learn to force a draw every time. Some games are easier to solve than others. So "for all purposes that anyone would ever care about, we've solved the game," Bowling says. But on average the program is so good that a human would have no chance of ever edging ahead of it, even if the two played 60 million hands. The program has yielded insights that could help players improve their game, and the general approach may have real-world usefulness in security and health care applications.īecause of the hidden information and the luck of the draw, the program won't necessarily win every hand, explains computer scientist Michael Bowling of the University of Alberta in Edmonton, Canada, who led the study. Researchers had previously developed unbeatable algorithms for other games such as checkers, but the new work marks the first time scientists have found such an algorithm for-or "solved"-a complex game in which some information about the state of the game (i.e., the cards in his opponent's hand) remains hidden from the player. A new program cannot be beaten at a variety of poker called heads-up limit Texas Hold 'em-at least in a human lifetime-a team of computer scientists reports.
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