Some extensions of Delete Nim
Tomoaki Abuku, Ko Sakai, Masato Shinoda, Koki Suetsugu

TL;DR
This paper explores various extensions of the combinatorial game Delete Nim, analyzing the win-loss conditions for multiple variants with different heap deletion and splitting rules.
Contribution
It introduces and studies generalized variants of Delete Nim with multiple heaps and different deletion rules, expanding the understanding of their strategic properties.
Findings
Characterization of win-loss conditions for each variant
Extension of Delete Nim to three or more heaps
Analysis of strategic differences among variants
Abstract
Nim is a well-known combinatorial game with several variants, e.g., Delete Nim and Variant Delete Nim. In Variant Delete Nim, the player deletes one of the two heaps of stones and splits the other heap on his/her turn. In this paper, we discuss generalized Variant Delete Nim, which generalizes the number of stone heaps to three or more, All-but-one-delete Nim, Half-delete Nim, No-more-than-half-delete Nim, and Single-delete Nim. We study the win-loss conditions for each of these games.
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Taxonomy
TopicsArtificial Intelligence in Games · Digital Games and Media · Gambling Behavior and Treatments
