An Extension of the Normal Play Convention to -player Combinatorial Games
arXiv:1903.01375
Abstract
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.
45 pages; Presented at Integers Conference 2018, submitted to Proceedings