Berlin 2008 – scientific programme

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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme

AKSOE 9: Social, information-, and production networks I

AKSOE 9.1: Talk

Tuesday, February 26, 2008, 14:00–14:30, EW 203

Zipf law in the popularity distribution of chess openings — Bernd Blasius¹ and •Tönjes Ralf² — ¹ICBM, University of Oldenburg — ²Institute of Physics, University of Potsdam

Human fascination with the game of chess is long-standing and pervasive. However, despite a large body of theoretical investigations, a quantitative understanding of playing behavior remains elusive. Here we demonstrate, based on an analysis of extensive chess databases, that there are simple statistical laws underlying the choice of opening moves in games of chess grandmasters and amateur players. We find that the frequencies of chess openings are distributed according to a power-law with an exponent that increases linearly with the game depth. Thus, in their initial phase the majority of chess games are concentrated among a small number of fashionable openings, whereas with increasing game depth rarely used move sequences are dominating. We present a simple stochastic process that is able to capture the observed playing statistics, providing a universal mechanism for the generation of Zipf's law. Our findings are of relevance in general composite decision processes and long tail economics.