Darse Billings

UAI Conference 2005 Conference Paper

Bayes? Bluff: Opponent Modelling in Poker

• Finnegan Southey
• Michael H. Bowling
• Bryce Larson
• Carmelo Piccione
• Neil Burch
• Darse Billings
• D. Chris Rayner

Poker is a challenging problem for artificial intelligence, with non-deterministic dynamics, partial observability, and the added difficulty of unknown adversaries. Modelling all of the uncertainties in this domain is not an easy task. In this paper we present a Bayesian probabilistic model for a broad class of poker games, separating the uncertainty in the game dynamics from the uncertainty of the opponent's strategy. We then describe approaches to two key subproblems: (i) inferring a posterior over opponent strategies given a prior distribution and observations of their play, and (ii) playing an appropriate response to that distribution. We demonstrate the overall approach on a reduced version of poker using Dirichlet priors and then on the full game of Texas hold'em using a more informed prior. We demonstrate methods for playing effective responses to the opponent, based on the posterior.

AIJ Journal 2002 Journal Article

The challenge of poker

• Darse Billings
• Aaron Davidson
• Jonathan Schaeffer
• Duane Szafron

AAAI Conference 1999 Conference Paper

Using Probabilistic Knowledge and Simulation to Play Poker

• Darse Billings
• Lourdes Peña
• Jonathan Schaeffer
• Duane Szafron
• University of Alberta

Until recently, artificial intelligence researchers who use games as their experimental testbed have concentrated on games of perfect information. Many of these games have been amenable to so-called brute-force search techniques. In contrast, games of imperfect information, such as bridge and poker, contain hidden knowledge making similar search techniques impractical. This paper describes recent progress in developing a high-performance poker-playing program. The advances come in two forms. First, we introduce a new betting strategy that returns a probabilistic betting decision, a probability triple, that gives the likelihood of a fold, call or raise occurring in a given situation. This routine unifies all the expert knowledge used in the program, does a better job of representing the type of decision making needed to play strong poker, and improves the way information is propagated throughout the program. Second, real-time simulations are used to compute the expected values of betting decisions. The program generates an instance of the missing data, subject to any constraints that have been learned, and then simulates the rest of the game to determine a numerical result. By repeating this a sufficient number of times, a statistically meaningful sample can be obtained to be used in the program’s decision-making process. Experimental results show that these enhancements each represent major advances in the strength of computer poker programs.

AAAI Conference 1998 Conference Paper

Opponent Modeling in Poker

• Darse Billings
• Jonathan Schaeffer

Poker is an interesting test-bed for artificial intelligence research. It is a game of imperfect knowledge, where multiple competing agents must deal with risk management, agent modeling, unreliable information and deception, much like decision-making applications in the real world. Agent modeling is one of the most difficult problems in decision-making applications and in poker it is essential to achieving high performance. This paper describes and evaluates Loki, a poker program capable of observing its opponents, constructing opponent models and dynamically adapting its play to best exploit patterns in the opponents’ play.