Mis\`ere Greedy Nim and Mis\`ere Bounded Greedy Nim
Nanako Omiya, Ryo Yoshinaka, Ayumi Shinohara
TL;DR
This paper provides a complete characterization of P-positions in the misère versions of k-Bounded Greedy Nim and Greedy Nim, advancing understanding of these combinatorial games.
Contribution
It offers necessary and sufficient conditions for P-positions in misère Greedy Nim variants, filling a gap in the analysis of these games.
Findings
Complete solution for P-positions in misère Greedy Nim games
Necessary and sufficient conditions for P-positions identified
Enhanced understanding of misère game strategies
Abstract
In this paper, we analyze the mis\`ere versions of two impartial combinatorial games: k-Bounded Greedy Nim and Greedy Nim. We present a complete solution to both games by showing necessary and sufficient conditions for a position to be P-positions.
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Taxonomy
TopicsArtificial Intelligence in Games · Polynomial and algebraic computation · Advanced Graph Theory Research