Grundy values of Fibonacci nim
Combinatorics
2015-05-21 v2
Abstract
In this article, we investigate the Grundy values of the popular game of Fibonacci nim. The winning strategy, which amounts to understanding positions of Grundy value 0, was known since Whinihan in 1963. In this paper, we extend Whinihan's analysis by computing all the positions of Grundy value at most 3. Furthermore, we show that, when we delete the Fibonacci numbers (which have Grundy value 0), the Grundy values of the starting positions are increasing, and we give upper and lower bounds on the growth rate.
Cite
@article{arxiv.1410.0332,
title = {Grundy values of Fibonacci nim},
author = {Urban Larsson and Simon Rubinstein-Salzedo},
journal= {arXiv preprint arXiv:1410.0332},
year = {2015}
}
Comments
To appear in International Journal of Game Theory