Solving Probabilistic Combinatorial Games

Ling Zhao, Martin Müller

Abstract: Probabilistic combinatorial games (PCGs) are a model for Go-like games recently introduced by Ken Chen. They differ from normal combinatorial games since terminal positions in each subgame are evaluated by a probability distribution. The distribution expresses the uncertainty in the local evaluation. This paper focuses on the analysis and solution methods for a special case, 1-level binary PCGs. Monte-Carlo analysis is used for move ordering in an exact solver that can compute the winning probability of a PCG efficiently. Monte-Carlo interior evaluation is used in a heuristic player. Experimental results show that both types of Monte-Carlo methods work very well in this problem.