Misère Nim with multi-player

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• 作者：Wen An Liu ; ^{liuwenan@126.com} ; Jia Wei Duan
• 关键词：Impartial combinatorial game ; Nim ; Misè ; re play convention ; Alliance ; Multi-player
• 刊名：Discrete Applied Mathematics
• 出版年：2017
• 出版时间：11 March 2017
• 年：2017
• 卷：219
• 期：Complete
• 页码：40-50
• 全文大小：457 K
• 卷排序：219

文摘

Krawec (2012) introduced a method of analyzing multi-player impartial games, and derived a recursive function capable of determining which of the nn players has a winning strategy. The present paper is devoted to the game “Misère NN-pile Nim with nn players”, abbreviated by MiNim(N,nN,n), assuming that the standard alliance matrix is adopted. The game values of MiNim(N,nN,n) are completely determined for three cases: n>N+1n>N+1, n=N+1n=N+1 and n=Nn=N. The case n<Nn<N is more complicated, we present the game values of MiNim(N,nN,n) only for n=3n=3 and N=4N=4.