Single-delete Nim

TL;DR

This paper generalizes the game of Delete Nim to multiple piles, specifically analyzing the case of four piles to determine winning strategies and conditions.

Contribution

It introduces a generalized version of Delete Nim with n piles and derives winning strategies for the case of four piles.

Findings

Derived conditions for winning strategies when n=4

Extended the game to multiple piles beyond the classic version

Provided a mathematical framework for analyzing Delete Nim variations

Abstract

The classic game of Nim has been well-known for many years, inspiring numerous variations. One such variant is Delete Nim, where players take turns eliminating one pile of stones and splitting the remaining pile into two smaller piles. In this paper we generalize the game to include the case of n piles. On each turn, a player eliminates one pile and splits one of the remaining piles into two smaller piles. We specifically analyze the case where n=4, deriving the conditions for a winning strategy.