Global Fibonacci Nim

TL;DR

This paper explores a multi-pile variant of Fibonacci Nim, analyzing its properties and providing a solution for the two-pile case, extending the understanding of this Fibonacci-based game.

Contribution

It introduces and solves the two-pile version of Fibonacci Nim with a global move-size restriction, expanding the game theory of Fibonacci-based combinatorial games.

Findings

Solved the 2-pile Fibonacci Nim variant

Identified key properties of the multi-pile game

Extended Fibonacci Nim analysis to a new variant

Abstract

Fibonacci nim is a popular impartial combinatorial game, usually played with a single pile of stones. The game is appealing due to its surprising connections with the Fibonacci numbers and the Zeckendorf representation. In this article, we investigate some properties of a variant played with multiple piles of stones, and solve the 2-pile case. A player chooses one of the piles and plays as in Fibonacci nim, but here the move-size restriction is a global parameter, valid for any pile.