Zipf's Law in the popularity distribution of chess openings
- 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.
| Author details: | Bernd BlasiusORCiDGND, Ralf ToenjesORCiD |
|---|---|
| URL: | http://prl.aps.org/ |
| DOI: | https://doi.org/10.1103/Physrevlett.103.218701 |
| ISSN: | 0031-9007 |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2009 |
| Publication year: | 2009 |
| Release date: | 2017/03/25 |
| Source: | Physical review letters. - ISSN 0031-9007. - 103 (2009), 21, Art. 218701 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| Peer review: | Referiert |
| Institution name at the time of the publication: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik |
