An investigation of combinatorial game theory and an analysis of Nim with Pass

Abstract

This paper acts as an overview of the basics of combinatorial game theory followed by an in-depth analysis of the combinatorial game Nim with Pass. In doing so, it also provides a descussion of perfect play in traditional Nim as well as a description of P and N-positions. In terms of the analysis of Nim with Pass, it uses a graphical approach with charts P-positions and N-positions of small piles in order to reveal P-positions of larger ones. Although Nim with Pass is not solved, an algorithm to find the position of an game state is offered.