1998/09/16 by Uri Blass, Blass, Uri, Aviezri S. Fraenkel +3
Computer Science · Mathematics · #Artificial Intelligence in Games #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.math/9809079
To appear in J. Combinatorial Theory (A)
arxiv created 1998/09/16 · openalex publication_date 1998/09/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A move in the game of nim consists of taking any positive number of tokens from a single pile. Suppose we add the class of moves of taking a nonnegative number of tokens jointly from all the piles. We give a complete answer to the question which moves in the class can be adjoined without changing the winning strategy of nim. The results apply to other combinatorial games with unbounded Sprague-Grundy function values. We formulate two weakened conditions of the notion of nim-sum 0 for proving the results.