摘要翻译：
我们对大量的国际象棋数据库进行了定量分析，结果表明，开球次数按幂律分布，其指数随对局深度线性增加，而所有开球权重的集合分布服从齐普夫定律，其指数随对局深度线性增加。我们提出了一个简单的随机过程，它能够捕获观察到的博弈统计量，并证明了Zipf定律是由象棋博弈树的自相似性质产生的。因此，在分层碎片的情况下，缩放是真正通用的，独立于特定的生成机制。我们的发现与综合决策的一般过程有关。
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英文标题：
《Zipf law in the popularity distribution of chess openings》
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作者：
B. Blasius, R. Toenjes
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最新提交年份：
2009
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分类信息：

一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/704.2711