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A Study of Memory Effects in a Chess Database.

Ana L Schaigorodsky1,2, Juan I Perotti3, Orlando V Billoni1,2

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Summary
This summary is machine-generated.

This study explains how chess game popularity follows Zipf's law and shows long-range memory effects simultaneously. A preferential growth model demonstrates this is due to game-line aging, not player activity bursts.

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Area of Science:

  • Complex systems analysis
  • Statistical physics
  • Network science

Background:

  • Chess game popularity distributions often follow Zipf's law.
  • Time series analysis of chess game sequences reveals long-range memory effects.
  • Simultaneous emergence of these phenomena in systems has been studied separately.

Purpose of the Study:

  • To explain the simultaneous emergence of Zipf's law and long-range memory effects in chess game-lines.
  • To investigate the role of preferential growth dynamics and aging in these phenomena.
  • To determine if burstiness in player activity is necessary for long-range correlations.

Main Methods:

  • Utilized a variant of the Yule-Simon preferential growth model (Cattuto's Model).
  • Analyzed a database of 1.4 million human chess games (1998-2007).
  • Examined popularity distributions, time series properties, and player activity patterns.

Main Results:

  • Cattuto's Model successfully reproduces both Zipf's law and long-range correlations.
  • The model explains these phenomena through preferential growth dynamics and a memory kernel, leading to an aging process.
  • Burstiness in subsets of players' activity was observed, but not required for long-range correlations.

Conclusions:

  • The simultaneous emergence of Zipf's law and long-range correlations in chess game-lines is explained by an aging process driven by preferential growth.
  • Burstiness in player activity is not the cause of long-range correlations in this chess database.
  • Findings support the hypothesis that aging, not burstiness, underlies long-range correlations in such complex systems.