Measuring the Non-Transitivity in Chess

In this paper, we quantify the non-transitivity in chess using human game data. Specifically, perform quantification two ways—Nash clustering and counting number of rock–paper–scissor cycles—on over one billion matches from Lichess FICS databases. Our findings indicate that strategy space real-world strategies has a spinning top geometry there exists strong connection between degree progression player’s rating. Particularly, high degrees tend to prevent players making progress their Elo ratings. We also investigate implications for population-based training methods. By considering fixed-memory fictitious play as proxy, conclude maintaining large diverse populations is imperative effective AI agents solving chess.