2020/10/20 by E. A. Hirsch, Hirsch, Emet
Computer Science · Social Sciences · #Artificial Intelligence in Games #Combinatorics (math.CO) #Digital Games and Media #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2010.10643
openalex publication_date 2020/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The study of the combinatorial game Nim and its variants is rich and varied, but little is known of the game Nim with a Pass. It is Nim, but once per game a player is permitted to skip their turn but this can only be done if a nonempty pile remains. In this paper we define a new binary operation on games which we use to prove novel properties of Nim with a Pass, as well as games which are generalizations of it. Most importantly, we make small progress on finding the P-positions and optimal strategies of the game.