Abstract
Krawec (2015) developed a method of analyzing n-player games where a subset of players plays randomly. In this paper, we use this method to analyze a class of combinatorial games “One-Pile Nim with n players”, denoted by OPNim(n), which allows arbitrarily many players to play randomly.We analyze the general structure of random players. The game values of OPNim(n) are determined for the general structure, assuming that a particular alliance matrix A0 defined by Krawec is adopted.We next try to answer the question: Fix a structure of random players, does there exist an alliance matrix A′ different from A0 such that the game values under A′ are the same with that under A0? We find a class of alliance matrices As which give this question a positive answer for any structure of random players.
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