arXiv subjects

Mark Spindler

Publications and source records attributed to Mark Spindler.

2 recordsLinked to original sources

arXiv2019

An Extension of the Normal Play Convention to $N$-player Combinatorial Games

We examine short combinatorial games for three or more players under a new play convention in which a player who cannot move on their turn is the unique loser. We show that many theorems of impartial and partizan two-player games under normal play have natural analogues in this setting. For impartial games with three players, we investigate the possible outcomes of a sum in detail, and determine the outcomes and structure of three-player Nim.

math.CO↗

arXiv2015

Equality Classes of Nim Positions under Mis\`ere Play

We determine the mis\`{e}re 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.

math.CO↗