Memory and long-range correlations in chess games

TL;DR

This study uncovers long-range memory in chess opening moves, showing that player skill level influences the persistence of move sequences, with stronger correlations observed in higher-level players.

Contribution

It demonstrates the presence of long-range correlations in chess games and links these patterns to player expertise, using multiple analysis methods and mapping rules.

Findings

Long-range memory exists in chess opening moves.

Higher-level players exhibit stronger long-term correlations.

Correlations vary with player skill and are robust across analysis methods.

Abstract

In this paper we report the existence of long-range memory in the opening moves of a chronologically ordered set of chess games using an extensive chess database. We used two mapping rules to build discrete time series and analyzed them using two methods for detecting long-range correlations; rescaled range analysis and detrented fluctuation analysis. We found that long-range memory is related to the level of the players. When the database is filtered according to player levels we found differences in the persistence of the different subsets. For high level players, correlations are stronger at long time scales; whereas in intermediate and low level players they reach the maximum value at shorter time scales. This can be interpreted as a signature of the different strategies used by players with different levels of expertise. These results are robust against the assignation rules and the method employed in the analysis of the time series.