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P-positions in modular extensions to Nim


  • Tanya Khovanova


  • Karan Sarkar


Abstract In this paper, we consider a modular extension to the game of Nim, which we call m-Modular Nim, and explore its optimal strategy. In m-Modular Nim, a player can either make a standard Nim move or remove a multiple of m tokens in total. We develop a winning strategy for all m with 2 heaps and for odd m with any number of heaps.

Suggested Citation

  • Tanya Khovanova & Karan Sarkar, 2017. "P-positions in modular extensions to Nim," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 547-561, May.
  • Handle: RePEc:spr:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0545-7
    DOI: 10.1007/s00182-016-0545-7

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