Relationship between mis\`ere NIM and two-player GOISHI HIROI

Autor:	Abuku, Tomoaki, Fukui, Masanori, Katayama, Shin-ichi, Suetsugu, Koki
Rok vydání:	2024
Předmět:	Computer Science - Computer Science and Game Theory Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	In combinatorial game theory, there are two famous winning conventions, normal play and mis\`ere play. Under normal play convention, the winner is the player who moves last and under mis\`ere play convention, the loser is the player who moves last. The difference makes these conventions completely different, and usually, games under mis\`ere play convention is much difficult to analyze than games under normal play convention. In this study, we show an interesting relationship between rulesets under different winning conventions; we can determine the winner of two-player GOISHI HIROI under normal play convention by using NIM under mis\`ere play convention. We also analyze two-player GOISHI HIROI under mis\`ere play convention. Comment: 13 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.03996 Zobrazit plný text záznamu View this record from Arxiv