Analysis of One Pile Misére NIM for Two Alliances

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The traditional game of Nim is an impartial game for two players that plays a central role in combinatorial game theory. The analysis of the two-player game relies on binary representations of numbers, see [1,2]. However, the game for three or more players has not been studied extensively. In this paper, we will consider a one-pile Nim misére version for more than two players. Typically, the strategy for the game of one-pile Nim with three or more players cannot be completely determined without considering alliances. The paper [3] establishes the basic terminology and certain fundamental results for the game with three or more players. The current paper expands it to a general result.

Original Citation

Kelly, A.R. (2011). Analysis of One Pile Misére NIM for Two Alliances. Rocky Mountain Journal of Mathematics, 41(6), pp. 895-1906. https://doi.org/10.1216/RMJ-2011-41-6-1895