H. W. Kuhn. A simplified two-person poker. Contributions to the Theory of Games, 1:97--103, 1950.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the game of poker, specifically Texas Hold em, the most popular form of casino poker and the poker variant used to determine the world champion at the annual World Series of Poker. Due to the computational limitations involved, only simplified poker variations have been solved in the past (e.g. [Kuhn, 1950; Sakaguchi and Sakai, 1992 ] While these are of theoretical interest, the same methods are not feasible for real games, which are too large by many orders of magnitude ( Koller and Pfeffer, 1997 ] Shi and Littman, 2001] investigated abstraction techniques to reduce the large search space ....

H. W. Kuhn. A simplified two-person poker. Contributions to the Theory of Games, 1:97--103, 1950.

....deceptive plays) All of these are challenging dimensions to a difficult problem. 1 Certain aspects of poker have been extensively studied by mathematicians and economists. There are two main approaches to poker research. One approach is to use simplified variants that are easier to analyze [10] [11] [12] For example, one could use only two players or constrain the betting rules. However, one must be careful that the simplification does not remove the challenging components of the problem. The other approach is to pick a real variant, but to combine mathematical analysis, simulation and ad ....

....to put in a second. However, even if players fold you still have their money from the opening bet. ffl Bluffing: is an essential strategy in poker. It has been mathematically proven that you need to over play or under play (bluff or slowplay) in some way for optimal play in simplified poker [11]. Bluffing allows you to make a profit from weak hands, but it also creates a false impression which will increase the profitability of future hands (a lot of money can be won when betting a very strong hand and your opponent suspects you may be bluffing) In practice, you need to be able to ....

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H. W. Kuhn. Simplified two-person poker. In H. W. Kuhn and A. W. Tucker, editors, Contributions to the Theory of Games I, pages 97--103. Princeton University Press, 1950.

....Once randomized strategies are allowed, the existence of optimal strategies in imperfect information games can be proved. In particular, this means that there exists an optimal randomized strategy for poker, in much the same way as there exists an optimal deterministic strategy for chess. Kuhn [1950] has shown for a simplified poker game that the optimal strategy does, indeed, use randomization. The optimality of a strategy has two consequences: the player cannot do better than this strategy if playing against a good opponent, and furthermore the player does not do worse even if his strategy ....

....such nodes. To encode this constraint, the game tree is augmented with information sets. An information set contains a set of nodes that are indistinguishable to a player at the time she has to make a decision. Figure 1 presents part of the game tree for a simplified variant of poker described by Kuhn [1950] . The game has two players and a deck containing the three cards 1, 2, and 3. Each player antes one dollar and is dealt one card. The figure shows the part of the game tree corresponding to the deals (2; 1) 2; 3) and (1; 3) The game has three rounds. In the first round, the first player can ....

H.W. Kuhn. A simplified two-person poker. In Contributions to the Theory of Games I, pages 97--103. Princeton University Press, 1950.

....are allowed, the existence of optimal strategies in imperfect information games can be proved [ Nash, 1951 ] In particular, this means that there exists an optimal randomized strategy for poker, in much the same way as there exists an optimal deterministic strategy for chess. Indeed, Kuhn [ 1950 ] has shown for a simplified poker game that the optimal strategy does, indeed, use randomization. The optimal strategy has several advantages: the player cannot do better than this strategy if playing against a good opponent, and furthermore the player does not do worse even if his strategy is ....

....Probability of betting Card received First round Second round Figure 3: Gambler strategies for 8 card poker. The optimal strategies for the gambler in this game, as obtained for the Gala system, are shown in Figure 3. They demonstrate an interesting phenomenon (first observed in a simpler game by Kuhn [ 1950 ] Behaviors such as bluffing, that seem to arise from the psychological makeup of human players, are actually game theoretically optimal. These strategies were generated completely automatically by the Gala system, starting from the description of the rules of Poker, described in Figure 2. ....

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H. W. Kuhn. A simplified two-person poker. In H. W. Kuhn and A. W. Tucker, editors, Contributions to the Theory of Games I, pages 97--103. Princeton University Press, 1950.

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H. W. Kuhn. A simplified two-person poker. Contributions to the Theory of Games, 1:97--103, 1950.

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H.W. Kuhn, A simplified two-person poker, Contributions to the Theory of Games 1 (1950) 97--103.

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H. W. Kuhn. A simplified two-person poker. Contributions to the Theory of Games, 1:97--103, 1950.

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