# Tools for Deriving Card Games from Mathematical Games

### Daniel Ashlock and Justin Schonfeld

Submitted to Game and Puzzle Design

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.