A general game player is an agent capable of taking as input a description of a game’s rules in a formal language and proceeding to play without any subsequent human input. To do well, an agent should learn from experience with past games and transfer the learned knowledge to new problems. We introduce a graph-based method for identifying previously encountered games and prove its robustness formally. We then describe how the same basic approach can be used to identify similar but non-identical games. We apply this technique to automate domain mapping for value function transfer and speed up reinforcement learning on variants of previously played games. Our approach is fully implemented with empirical results in the general game playing system.