Beating Your Friends at Board Games: An Introduction to Combinatorial Game Theory
In this first of a series of talks, we will introduce and play some simple combinatorial games and discuss the basics of their analysis. A combinatorial game is one in which play alternates over turns, and all information about the state of the game is public. For example, Tic-Tac-Toe and chess are combinatorial games while poker is not, as cards in a player’s hand cannot be seen by others. We will develop a working vocabulary and toolbox of theorems to determine when we can say a game is solved, what an ideal move is in a certain game state, whether there are advantages built in to the game’s design, etc, and in doing so develop potent mathematical methods to determine gaming strategies. Our goal throughout this series will be to heighten our appreciation of games of strategy rather than take the fun out of them. Come prepared to pit your wits against UVM’s mathematical community!