The Game of Cycles with Sources Allowed

TL;DR

This paper introduces 'Cycles with Sources,' a variant of the Game of Cycles allowing source nodes, significantly altering game outcomes even on simple graphs, analyzed through Sprague-Grundy Theory.

Contribution

It presents a new game variant with sources, analyzing its strategic implications and outcomes using Sprague-Grundy Theory, expanding understanding of combinatorial game modifications.

Findings

Sources drastically change game outcomes on simple graphs

Optimal play analysis reveals new strategic complexities

Sprague-Grundy Theory effectively analyzes the variant

Abstract

In this paper, we introduce a variant of Francis Su's "Game of Cycles," that we call "Cycles with Sources." The only change to the rules is permitting nodes to be sources, while sinks are still prohibited. Despite this minor change in the rules, we show that even on simple games, like line graphs, there is a great change in the outcome of optimal play, which we fully analyze using Sprague-Grundy Theory.