An evolutionary game-theoretic analysis of poker strategies

Abstract In this paper we investigate the evolutionary dynamics of strategic behavior in the game of poker by means of data gathered from a large number of real world poker games. We perform this study from an evolutionary game theoretic perspective using two Replicator Dynamics models. First we consider the basic selection model on this data, secondly we use a model which includes both selection and mutation. We investigate the dynamic properties by studying how rational players switch between different strategies under different circumstances, what the basins of attraction of the equilibria look like, and what the stability properties of the attractors are. We illustrate the dynamics using a simplex analysis. Our experimental results confirm existing domain knowledge of the game, namely that certain strategies are clearly inferior while others can be successful given certain game conditions.

[1]  T. D. Schneider,et al.  Evolution of biological information. , 2000, Nucleic acids research.

[2]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[3]  P. Taylor,et al.  Evolutionarily Stable Strategies and Game Dynamics , 1978 .

[4]  G. Tesauro,et al.  Analyzing Complex Strategic Interactions in Multi-Agent Systems , 2002 .

[5]  Tom Lenaerts,et al.  A selection-mutation model for q-learning in multi-agent systems , 2003, AAMAS '03.

[6]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and an Introduction to Chaos , 2003 .

[7]  David Sklansky,et al.  The Theory of Poker , 1999 .

[8]  Jörgen W. Weibull,et al.  Evolutionary Game Theory , 1996 .

[9]  E. Zeeman.  Dynamics of the evolution of animal conflicts , 1981 .

[10]  D. Stauffer.  Life, Love and Death: Models of Biological Reproduction and Aging , 1999 .

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

[12]  Nicholas R. Jennings,et al.  Analysing Buyers' and Sellers' Strategic Interactions in Marketplaces: An Evolutionary Game Theoretic Approach , 2007, AMEC/TADA.

[13]  Karl Tuyls,et al.  An Evolutionary Dynamical Analysis of Multi-Agent Learning in Iterated Games , 2005, Autonomous Agents and Multi-Agent Systems.

[14]  Herbert Gintis,et al.  Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction - Second Edition , 2009 .

[15]  Richard S. Sutton,et al.  Reinforcement Learning: An Introduction , 1998, IEEE Trans. Neural Networks.

[16]  Kurt Driessens,et al.  Bayes-Relational Learning of Opponent Models from Incomplete Information in No-Limit Poker , 2008, AAAI.

[17]  J M Smith,et al.  Evolution and the theory of games , 1976 .

[18]  Michael H. Bowling,et al.  Bayes' Bluff: Opponent Modelling in Poker , 2005, UAI 2005.