Can some simple games lead to chaos?

Abstract

Some combinatorial games, like GRUNDY'S GAME, are simple to describe, but follow chaotic patterns and can prove very difficult to analyze entirely. In this thesis we will look at some games, including a combinatorial version of Mancala; the game of BLASH & SLASH, played by drawing diagonals on a rectangular grid; and BLASH, SLASH & DASH, played by removing edges in triangular arrays. While some of these games might seem very simple at a first, they often exhibit patterns that are very hard to predict. In Chapters 1 and 2 we give an introduction to the subject of combinatorial games by looking at the theories crafted by Conway and by Sprague and Grundy before him. In Chapter 3 we analyze the game of BLASH & SLASH in some of its versions, and find an equivalence between this game and NODE KAYLES. In Chapter 4 we look at the game of BLASH, SLASH & DASH and find a sparse space in one of its cases. In Chapter 5 we analyze some versions of BASIC MANCALA. Lastly, we give suggestions for future research in these games.