A heads-up no-limit Texas Hold'em poker player: discretized betting models and automatically generated equilibrium-finding programs

We present Tartanian, a game theory-based player for heads-up no-limit Texas Hold'em poker. Tartanian is built from three components. First, to deal with the virtually infinite strategy space of no-limit poker, we develop a discretized betting model designed to capture the most important strategic choices in the game. Second, we employ potential-aware automated abstraction algorithms for identifying strategically similar situations in order to decrease the size of the game tree. Third, we develop a new technique for automatically generating the source code of an equilibrium-finding algorithm from an XML-based description of a game. This automatically generated program is more efficient than what would be possible with a general-purpose equilibrium-finding program. Finally, we present results from the AAAI-07 Computer Poker Competition, in which Tartanian placed second out of ten entries.

[1]  Tuomas Sandholm,et al.  A Competitive Texas Hold'em Poker Player via Automated Abstraction and Real-Time Equilibrium Computation , 2006, AAAI.

[2]  Tuomas Sandholm,et al.  Lossless abstraction of imperfect information games , 2007, JACM.

[3]  Yurii Nesterov,et al.  Excessive Gap Technique in Nonsmooth Convex Minimization , 2005, SIAM J. Optim..

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

[5]  Michael H. Bowling,et al.  Regret Minimization in Games with Incomplete Information , 2007, NIPS.

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

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

[8]  Michael H. Bowling,et al.  A New Algorithm for Generating Equilibria in Massive Zero-Sum Games , 2007, AAAI.

[9]  Kevin B. Korb,et al.  Bayesian Poker , 1999, UAI.

[10]  Michael H. Bowling,et al.  Computing Robust Counter-Strategies , 2007, NIPS.

[11]  Rickard Andersson.  Pseudo-Optimal Strategies in No-Limit Poker , 2006, J. Int. Comput. Games Assoc..

[12]  Tuomas Sandholm,et al.  Computing an approximate jam/fold equilibrium for 3-player no-limit Texas Hold'em tournaments , 2008, AAMAS.

[13]  Troels Bjerre Lund,et al.  Potential-Aware Automated Abstraction of Sequential Games, and Holistic Equilibrium Analysis of Texas Hold'em Poker , 2007, AAAI.

[14]  Jonathan Schaeffer,et al.  Approximating Game-Theoretic Optimal Strategies for Full-scale Poker , 2003, IJCAI.

[15]  Tuomas Sandholm,et al.  Better automated abstraction techniques for imperfect information games, with application to Texas Hold'em poker , 2007, AAMAS '07.

[16]  Javier Peña,et al.  Gradient-Based Algorithms for Finding Nash Equilibria in Extensive Form Games , 2007, WINE.

[17]  B. Stengel,et al.  Efficient Computation of Behavior Strategies , 1996 .

[18]  Jonathan Schaeffer,et al.  Game-Tree Search with Adaptation in Stochastic Imperfect-Information Games , 2004, Computers and Games.

[19]  Peter Bro Miltersen,et al.  A near-optimal strategy for a heads-up no-limit Texas Hold'em poker tournament , 2007, AAMAS '07.

[20]  Javier Peña,et al.  A GRADIENT-BASED APPROACH FOR COMPUTING NASH EQUILIBRIA OF LARGE SEQUENTIAL GAMES , 2007 .

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