Measuring the Non-Transitivity in Chess

Abstract

quantifications-Nash Clustering and counting the number of Rock-Paper-Scissor cycles-on over one billion match data from Lichess and FICS. Our findings positively indicate that the strategy space occupied by real-world Chess strategies demonstrates a spinning top geometry, and more importantly, there exists a strong connection between the degree of non-transitivity and the progression of a Chess player's rating. In particular, high degrees of non-transitivity tend to prevent human players from making progress on their Elo rating, whereas progressions are easier to make at the level of ratings where the degree of non-transitivity is lower. Additionally, we also investigate the implication of the degree of non-transitivity for population-based training methods. By considering fixed-memory Fictitious Play as a proxy, we reach the conclusion that maintaining large-size and diverse populations of strategies is imperative to training effective AI agents in solving Chess types of games.

AI in Human-computer Gaming: Techniques, Challenges and Opportunities

“…Most games in real world are in-transitive, i.e., transitive and in-transitive parts are co-existing [25]. The in-transitive characteristic makes precise evaluation of agent a difficult problem.…”

“…In-transitive game. If performance of different players are transitive, a game is called a transitive game [25]. Mathematically, if v t can beat v t−1 and v t+1 can beat v t , v t+1 outperforms v t−1 .…”