2025/02/16 by Hiromi Oginuma, Oginuma, Hiromi, Masato Shinoda +1
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #91A46 #Artificial Intelligence in Games #Combinatorics (math.CO) #FOS: Mathematics #Game Theory and Applications #Game Theory and Voting Systems
paper · pdf · doi:10.48550/arxiv.2502.10971
openalex publication_date 2025/02/16 · openalex created_date 2025/02/19 · openalex updated_date 2026/07/28
Nim is a well-known combinatorial game in which two players alternately remove stones from distinct piles. A player who removes the last stone wins under the normal play rule, while a player loses under the misère play rule. In this paper, we propose a new variant of Nim with scoring that generalizes both the normal and misère play versions of Nim as special cases. We study the theoretical aspects of this extended game and analyze its fundamental properties, such as optimal strategies and payoff functions.