Equality Classes of Nim Positions under Misère Play
arXiv:1506.02261
Abstract
We determine the misère equivalence classes of Nim positions under two equivalence relations: one based on playing disjunctive sums with other impartial games, and one allowing sums with partizan games. In the impartial context, the only identifications we can make are those stemming from the known fact about adding a heap of size 1. In the partizan context, distinct Nim positions are inequivalent.
10 pages, LaTeX; fixed typos, improved formatting consistency, added section on transfinite Nim