IEEEIn this paper we present an interpretable artificial intelligence, and its associated machine learning algorithm, that is capable of automatically learning the rules of a game whenever the rules the relationship between a player's current state and their corresponding set of legal moves can be represented as a set of low degree Zhegalkin polynomials, a special class of Boolean functions. This is true for many popular games including Spanish Domin and the card game President. Our method takes advantage of the low polynomial degree to compute an exact representation of the rules in polynomial time instead of the required exponential time for generic Boolean functions. The rules can also be represented using significantly less storage than in the generic case which, for many games, leads to a representation that is easy to interpret.