This document discusses different aspects of game complexity, including state-space complexity (the number of possible positions in a game), game tree size (the number of possible end-states reached through different paths), and decision complexity (how difficult it is to determine the best move). It provides examples of these measures for simple games like tic-tac-toe (765 possible positions) and complex games like chess (around 10^43 possible positions). The document also discusses game tree complexity and computational complexity in more depth.