Move-by-Move Dynamics of the Advantage in Chess Matches Reveals Population-Level Learning of the Game

Departamento de Física and National Institute of Science and Technology for Complex Systems, Universidade Estadual de Maringá, Maringá, Brazil
PLoS ONE (Impact Factor: 3.23). 01/2013; 8(1):e54165. DOI: 10.1371/journal.pone.0054165
Source: PubMed


The complexity of chess matches has attracted broad interest since its invention. This complexity and the availability of large number of recorded matches make chess an ideal model systems for the study of population-level learning of a complex system. We systematically investigate the move-by-move dynamics of the white player's advantage from over seventy thousand high level chess matches spanning over 150 years. We find that the average advantage of the white player is positive and that it has been increasing over time. Currently, the average advantage of the white player is [Formula: see text]0.17 pawns but it is exponentially approaching a value of 0.23 pawns with a characteristic time scale of 67 years. We also study the diffusion of the move dependence of the white player's advantage and find that it is non-Gaussian, has long-ranged anti-correlations and that after an initial period with no diffusion it becomes super-diffusive. We find that the duration of the non-diffusive period, corresponding to the opening stage of a match, is increasing in length and exponentially approaching a value of 15.6 moves with a characteristic time scale of 130 years. We interpret these two trends as a resulting from learning of the features of the game. Additionally, we find that the exponent [Formula: see text] characterizing the super-diffusive regime is increasing toward a value of 1.9, close to the ballistic regime. We suggest that this trend is due to the increased broadening of the range of abilities of chess players participating in major tournaments.

Download full-text


Available from: Haroldo Valentin Ribeiro
  • Source
    • "The game of chess [22] has been extensively studied in science [7] [30] [26] [27], especially for decision making [7] [30] [12], and it can be used to study innovation phenomena. Chess is a competitive game with a game tree complexity estimated as 10 120 different move sequences [29]. "
    [Show abstract] [Hide abstract]
    ABSTRACT: We study innovation in chess by analyzing how different move sequences are played at the population level. It is found that the probability of exploring a new or innovative move decreases as a power law with the frequency in which the preceding move sequence is played. Chess players also exploit already known move sequences according to their frequencies, following a preferential growth mechanism. Furthermore, innovation in chess exhibits Heaps' law suggesting similarities with the process of vocabulary growth. We propose a robust generative mechanism based on nested Yule-Simon preferential growth processes that reproduces the empirical observations. These results, supporting the self-similar nature of innovations in chess, are important in the context of decision making in a competitive scenario.
    Full-text · Article · Sep 2013 · EPL (Europhysics Letters)
  • Source
    • "Since the skill level of chess players can be correctly identified [13] chess has contributed to the scientific understanding of expertise [5]. In addition, nowadays, there is a big world-wide community of chess players which makes the game a benchmark for studying, for instance, decision making processes [4] and population level learning [3]. "
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper we report the existence of long-range memory in the opening moves of a chronologically ordered set of chess games using an extensive chess database. We used two mapping rules to build discrete time series and analyzed them using two methods for detecting long-range correlations; rescaled range analysis and detrented fluctuation analysis. We found that long-range memory is related to the level of the players. When the database is filtered according to player levels we found differences in the persistence of the different subsets. For high level players, correlations are stronger at long time scales; whereas in intermediate and low level players they reach the maximum value at shorter time scales. This can be interpreted as a signature of the different strategies used by players with different levels of expertise. These results are robust against the assignation rules and the method employed in the analysis of the time series.
    Full-text · Article · Jul 2013 · Physica A: Statistical Mechanics and its Applications
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Is football (soccer) a universal sport? Beyond the question of geographical distribution, where the answer is most certainly yes, when looked at from a mathematical viewpoint the scoring process during a match can be thought of, in a first approximation, as being modeled by a Poisson distribution. Recently, it was shown that the scoring of real tournaments can be reproduced by means of an agent-based model (da Silva et al. (2013) [24]) based on two simple hypotheses: (i) the ability of a team to win a match is given by the rate of a Poisson distribution that governs its scoring during a match; and (ii) such ability evolves over time according to results of previous matches. In this article we are interested in the question of whether the time series represented by the scores of teams have universal properties. For this purpose we define a distance between two teams as the square root of the sum of squares of the score differences between teams over all rounds in a double-round-robin-system and study how this distance evolves over time. Our results suggest a universal distance distribution of tournaments of different major leagues which is better characterized by an exponentially modified Gaussian (EMG). This result is corroborated by our agent-based model.
    Full-text · Article · Mar 2014 · Physica A: Statistical Mechanics and its Applications
Show more