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.
- Received 28 February 2008
DOI:https://doi.org/10.1103/PhysRevLett.103.218701
©2009 American Physical Society
Viewpoint
Power laws in chess
Published 16 November 2009
The popularity of various chess openings follows a power law distribution, but the exponent depends on the depth of the opening sequence.
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