Some extensions of Delete Nim

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.