Combined Games

What happens when you play Chess and Tic-Tac-Toe at the same time? What about Mancala, Othello and Checkers? Playing multiple games together as a Combined Game introduces an entirely new, infinite set of games to analyze and play. We use traditional Game Theory tools to examine combined pairs of small, well-solved games, yielding information on the optimal strategies for playing each combined game. The results of our analysis reveal patterns for two Normal Games or any amount of Meiseré Games being played as one Combined Game and suggest that such patterns exist when combining other classes of games. 1 An Introduction to Combined Games What exactly is a Combined Game? The definition is derived and generalized from one’s intuition: a game where you combine at least two other games. For example, playing two games of Tic-Tac-Toe at once is a combined game; playing Nim and Checkers is another combined game. Such combinations create completely new games to explore. In this section, we formalize and define the concept of a Combined Game and introduce properties combinations of games exhibit. 1.