Multi-player End-Nim games

Abstract

W.O. Krawec (2012) [17] introduced a method of analyzing multi-player impartial games, and derived a recursive function capable of determining which of the n players has a winning strategy. The present paper is devoted to “Multi-player End-Nim games”, abbreviated by ENim(N,n), assuming that the standard alliance matrix is adopted. The game values of ENim(N,n) are completely determined for three cases n>N+1, n=N+1 and n=N. For the case n<N, by letting d=N−n≥1, the game values of ENim(n+d,n) are completely determined if n≥d+4. The case 3≤n≤d+3 is more complicated, we present the game values for d=1.