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=Who is the Master?<span id="WhoistheMaster"></span>=

As a chess lover <ref>[http://www.chess-lovers.org/ Chess lovers] by [[Jean-Marc Alliot]]</ref>, Jean-Marc Alliot proposed a novel approach based on a [https://en.wikipedia.org/wiki/Markov_chain Markovian interpretation] of the game that would rank the greatest chess masters more fairly than the [https://en.wikipedia.org/wiki/Elo_rating_system Elo system] <ref>[https://news.cnrs.fr/articles/how-should-chess-players-be-rated How Should Chess Players Be Rated?] by [https://news.cnrs.fr/authors/martin-koppe Martin Koppe], [https://news.cnrs.fr/ CNRS News], April 25, 2017</ref>. In his study, elaborated and published in the April 2017 [[ICGA Journal#39_1|ICGA Journal]] under the title '''Who is the Master?''' <ref>[[Jean-Marc Alliot]] ('''2017'''). ''Who is the Master''? [[ICGA Journal#39_1|ICGA Journal, Vol. 39, No. 1]], [http://www.alliot.fr/CHESS/draft-icga-39-1.pdf draft as pdf]</ref>, 26,000 games (over 2 million positions) played at regular time control by all [https://en.wikipedia.org/wiki/World_Chess_Championship world champions] since [https://en.wikipedia.org/wiki/Wilhelm_Steinitz Wilhelm Steinitz] have been analyzed using [[Stockfish|Stockfish 190915]] <ref>a small bug was fixed in [[Stockfish|Stockfish 6]] concerning [[Syzygy Bases|Syzygy 6-men bases]]</ref>, running on a [https://en.wikipedia.org/wiki/Computer_cluster cluster] of 640 [[AMD]] [https://en.wikipedia.org/wiki/List_of_AMD_Opteron_microprocessors 6262 HE] [[x86-64|Opteron]] processors in 62000 CPU hours with [[Principal Variation#MultiPV|multiPV]] 2 and 4GB [[Transposition Table|hash]] for each instance, in order to create [https://en.wikipedia.org/wiki/Stochastic_matrix Markov matrices] for each year a player was active based on the conformance of his moves. For each position, the model estimates the probability of making a mistake, and the magnitude of the mistake by comparing the two best moves calculated at an average of 2 minutes by move (26 [[Ply|plies]] on average) with the move actually played, starting from move number 10 <ref>[https://en.wikipedia.org/wiki/Comparison_of_top_chess_players_throughout_history#Markovian_Model Comparison of top chess players throughout history from Wikipedia - 2.2 Markovian Model]</ref>. By using classical [https://en.wikipedia.org/wiki/Linear_algebra 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 Elo prediction for players who actually played each other.

=Selected Publications=