title: Zipf's law in the popularity distribution of chess openings.
abstract: We perform a quantitative analysis of extensive chess databases and show that the frequencies of opening moves are distributed according to a power law with an exponent that increases linearly with the game depth, whereas the pooled distribution of all opening weights follows Zipf's law with universal exponent. We propose a simple stochastic process that is able to capture the observed playing statistics and show that the Zipf law arises from the self-similar nature of the game tree of chess. Thus, in the case of hierarchical fragmentation the scaling is truly universal and independent of a particular generating mechanism. Our findings are of relevance in general processes with composite decisions.
authors.affiliation: ICBM, University Oldenburg, 26111 Oldenburg, Germany.
authors.forename: Bernd
authors.initials: B
authors.lastname: Blasius
authors.forename: Ralf
authors.initials: R
authors.lastname: Tönjes