P-positions in modular extensions to Nim

P-positions in modular extensions to Nim

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Article ID: iaor20171823
Volume: 46
Issue: 2
Start Page Number: 547
End Page Number: 561
Publication Date: May 2017
Journal: International Journal of Game Theory
Authors: ,
Keywords: optimization, simulation
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.

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