
TL;DR
This paper analyzes two variants of the slow k-Nim game, computing their Sprague-Grundy functions for small parameters and characterizing P-positions in specific cases, advancing understanding of these combinatorial games.
Contribution
It provides explicit Sprague-Grundy functions for small cases and characterizes P-positions for certain parameter ranges in slow k-Nim variants.
Findings
Sprague-Grundy functions computed for n=k=2 and n=k+1=3.
P-positions characterized for n ≤ k+2 and n=k+3 ≤ 6.
Enhanced understanding of game structure for small parameters.
Abstract
Given piles of tokens and a positive integer , we study the following two impartial combinatorial games Nim and Nim. In the first (resp. second) game, a player, by one move, chooses at least and at most (resp. exactly) non-empty piles and removes one token from each of these piles. For the normal and mis\`ere version of each game we compute the Sprague-Grundy function for the cases and . For game Nim we also characterize its P-positions for the cases and .
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Taxonomy
TopicsArtificial Intelligence in Games · Advanced Combinatorial Mathematics · Polynomial and algebraic computation
