One-pile misère Nim for three or more players

@article{Kelly2006OnepileMN,
  title={One-pile mis{\`e}re Nim for three or more players},
  author={Annela R. Kelly},
  journal={Int. J. Math. Mathematical Sciences},
  year={2006},
  volume={2006},
  pages={40796:1-40796:8}
}
The analysis of the classical game of Nim relies on binary representation of numbers as shown in the books of Berlekamp and Gardener. There is considerable interest in generalizations and modifications of the game. We will consider one-pile misère Nim for more than two players. In the case of three or more players, the impartial game theory results rarely apply. In this note, we analyze the game in a variety of cases where alliances are formed among the players. 

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Winning Ways for Your Mathematical Plays

  • E. R. Berlekamp, J. H. Conway, R. K. Guy
  • Vol. 1, A K Peters, Massachusetts
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2 Excerpts

Mathematical Puzzles and Diversions

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