Volume 116, Number 1, October 2016
|Number of page(s)||6|
|Published online||22 November 2016|
1 Theory of Soft Condensed Matter, Université du Luxembourg - L-1511 Luxembourg, Luxembourg
2 Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR) D-51170 Köln, Germany Department of Physics, Heinrich-Heine-Universität Düsseldorf - D-40225 Düsseldorf, Germany
Received: 14 September 2016
Accepted: 2 November 2016
We analyze the structure of the state space of chess by means of transition path sampling Monte Carlo simulations. Based on the typical number of moves required to transpose a given configuration of chess pieces into another, we conclude that the state space consists of several pockets between which transitions are rare. Skilled players explore an even smaller subset of positions that populate some of these pockets only very sparsely. These results suggest that the usual measures to estimate both the size of the state space and the size of the tree of legal moves are not unique indicators of the complexity of the game, but that considerations regarding the connectedness of states are equally important.
PACS: 05.10.Ln – Monte Carlo methods / 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.) / 89.20.-a – Interdisciplinary applications of physics
© EPLA, 2016
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