Solving Probabilistic Combinatorial Games

Abstract

Probabilistic combinatorial games (PCG) are a model for Go-like games recently introduced by Ken Chen. They differ from normal combinatorial games since terminal position 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 PCG. 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.

Virtual Global Search: Application to 9×9 Go

“…In Scrabble, Maven controls selective simulations [14]. Monte-Carlo has also been applied to Phantom Go, randomly putting opponent stones before each random game [6], and to probabilistic combinatorial games [15].…”

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“…Social games and combinatorial games are built on quite different ideas and many scientists only know one of the types of game theory. There have only been few attempts to combine the two types of game theory [9,22]. In this exposition we will assume that the reader has basic knowledge about social games such as two-person zero-sum games.…”