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Not only are there a myriad of possibilities but there's another element that computers typically stumble upon -- uncertainty.
And in the case of Poker, there are two uncertainies the software must deal with -- what cards does the opponent hold and how will s/he play them?
To overcome the uncertainties of opponents, the programmers that developed Polaris couldn't use the look-ahead approach of Big Blue, instead they relied on , appropriately enough, game-theory.
there is a set of strategies such that every player's return is maximized and no player would benefit from switching to a different strategy.
Texas Hold 'em is a little more complicated than "Rock, Paper, Scissors," but Nash's math still applies. With game theory, computers know to vary their play so an opponent has a hard time figuring out whether they are bluffing or employing some other strategy.
But game theory has inherent limits. In Nash equilibrium terms, success doesn't mean winning - it means not losing.
"You basically compute a formula that can at least break even in the long run, no matter what your opponent does," Billings said.
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