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Partypoker Online Today - November 21, 2008
The game of pokerroom (or at least most of the variants) is considered to be computationally intractable. However, methods are being developed to at least approximate pokerroom from the game theory perspective in the heads-up (two player) game, and increasingly good systems are being created for the multi-player or ring game. Perfect strategy has multiple meanings in this context. From a game-theoretic optimal point of view, a perfect pokerroom one that cannot expect to lose to any other player's strategy; however, strategy can vary in the presence of sub-optimal players who have weaknesses that can be exploited. In this case, a perfect strategy would be one that correctly or closely models those weaknesses and takes advantage of them to make a profit. Some of these systems are based on Bayes theorem, Nash equilibrium, Monte Carlo simulation, and Neural networks. A large amount of the research is being done at the University of Alberta by the GAMES group led by Jonathan Schaeffr.
In game theory, pokerroom the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, where no player has anything to gain by changing only one's own strategy. If there is a set of strategies for a game with the property that no player can benefit by changing pokerroom his strategy while the other players keep their strategies unchanged, then that set of strategies and the corresponding payoffs constitute a Nash equilibrium.
A game may have many Nash pokerroom equilibria, or none. The Brouwer fixed point theorem provides the sufficient, though not necessary, conditions for existence of a Nash equilibrium. Brouwer proved that for a continuous function f: mapping S?S, where S is a non-empty and convex compact set onto itself, there exists x* such pokerroom that x*=f(x*)(x* is a fixed point). In a game context, if the set of strategies by player i, is a compact and continuous set, the payoff functions for all players are quasi-concave and continuous, then the pokerroom game has a Nash Equilibrium (NE).
