Approximating Game-Theoretic Optimal Strategies for Full-scale Poker

The computation of the first complete approximations of game-theoretic optimal strategies for full-scale poker is addressed. Several abstraction techniques are combined to represent the game of 2-player Texas Hold'em, having size O(1018), using closely related models each having size O(1O7). Despite the reduction in size by a factor of 100 billion, the resulting models retain the key properties and structure of the real game. Linear programming solutions to the abstracted game are used to create substantially improved poker-playing programs, able to defeat strong human players and be competitive against world-class opponents.

[1]  E. Rowland Theory of Games and Economic Behavior , 1946, Nature.

[2]  Philip Wolfe,et al.  Contributions to the theory of games , 1953 .

[3]  J. Nash Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[5]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[6]  D. Koller,et al.  The complexity of two-person zero-sum games in extensive form , 1992 .

[7]  Bart Selman,et al.  Local search strategies for satisfiability testing , 1993, Cliques, Coloring, and Satisfiability.

[8]  坂口 実,et al.  Solutions of Some Three Person Stud and Draw Poker , 1993 .

[9]  Bernhard von Stengel,et al.  Fast algorithms for finding randomized strategies in game trees , 1994, STOC '94.

[10]  Avi Pfeffer,et al.  Representations and Solutions for Game-Theoretic Problems , 1997, Artif. Intell..

[11]  Henry A. Kautz,et al.  BLACKBOX: A New Approach to the Application of Theorem Proving to Problem Solving , 1998 .

[12]  Darse Billings,et al.  The First International RoShamBo Programming Competition , 2000, J. Int. Comput. Games Assoc..

[13]  Michael L. Littman,et al.  Abstraction Methods for Game Theoretic Poker , 2000, Computers and Games.

[14]  Holger H. Hoos,et al.  Scaling and Probabilistic Smoothing: Efficient Dynamic Local Search for SAT , 2002, CP.

[15]  Jonathan Schaeffer,et al.  The challenge of poker , 2002, Artif. Intell..

[16]  Holger H. Hoos,et al.  Scaling and Probabilistic Smoothing: Dynamic Local Search for Unweighted MAX-SAT , 2003, Canadian Conference on AI.

[17]  Holger H. Hoos,et al.  UBCSAT: An Implementation and Experimentation Environment for SLS Algorithms for SAT & MAX-SAT , 2004, SAT.

[18]  Thomas Stützle,et al.  Stochastic Local Search: Foundations & Applications , 2004 .

[19]  Lakhdar Sais,et al.  Boosting complete techniques thanks to local search methods , 1998, Annals of Mathematics and Artificial Intelligence.

[20]  Edward A. Hirsch,et al.  UnitWalk: A new SAT solver that uses local search guided by unit clause elimination , 2005, Annals of Mathematics and Artificial Intelligence.

[21]  J. M. Bilbao,et al.  Contributions to the Theory of Games , 2005 .