Tools for Deriving Card Games from Mathematical Games

Daniel Ashlock and Justin Schonfeld
Submitted to Game and Puzzle Design

Abstract PDF eprint

In a mathematical game, such as iterated prisoner's dilemma or rock-paper-scissors, an agent playing the game is permitted to choose any of the available moves each turn. When that free choice of moves is replaced by cards with moves printed on them from a fixed deck, the mathematical game becomes a card game. As a result of this transformation, the game often takes on a very differ- ent character. This gives a simple technique for generating card-game mechanics from existing and novel mathematical games. Once a game is card-based, it becomes possible to generalize transparently in a number of ways. A technique for achieving initial balance among the moves (now types of cards) by viewing the payoff matrix as a directed graph is given together with example generalizations of two mathematical games. The payoff matrix of the mathematical game translates into the scoring system for the card game. A technique for using a simple evolutionary algorithm to assess the balance and scoring system is also explored.