Who is the Master?

There has been debates for years on how to rate chess players living and playing at different periods (see Keene and Divinsky (1989)). Some attempts were made to rank them not on the results of games played, but on the moves played in these games, evaluating these moves with computer programs. However, the previous attempts were subject to different criticisms, regarding the strengths of the programs used, the number of games evaluated, and other methodological problems. In the current study, 26,000 games (over 2 millions of positions) played at regular time control by all world champions since Wilhelm Steinitz have been analyzed using an extremely strong program running on a cluster of 640 processors. Using this much larger database, the indicators presented in previous studies (along with some new, similar, ones) have been correlated with the outcome of the games. The results of these correlations show that the interpretation of the strength of players based on the similarity of their moves with the ones played by the computer is not as straightforward as it might seem. Then, to overcome these difficulties, a new Markovian interpretation of the game of chess is proposed, which enables to create, using the same database, Markovian matrices for each year a player was active. By using classical linear algebra methods on these matrices, the outcome of games between any players can be predicted, and this prediction is shown to be at least as good as the classical ELO prediction for players who actually played against each others.