Computer analysis of World Chess Champions

CG 2006 Computer analysis of World Chess Champions Matej Guid and Ivan Bratko

Introduction Who was the best chess player of all time? • Chess players of different eras never met across the chess board. • No well founded, objective answer. Computers... • Were so far mostly used as a tool for statistical analysis of players’ results. High quality chess programs... • Provide an opportunity of an objective comparisson. Statistical analysis of results do NOT reflect: • true strengths of the players, • quality of play. I Wilhelm Steinitz, 1886 - 1894

Related work Jeff Sonas, 2005: • rating scheme, based on tournament results from 1840 to the present, • ratings are calculated for each month separately, player’s activity is taken into account. • Disadvantages • Playing level has risen dramatically in the recent decades. • The ratings in general reflect the players’ success in competition, but NOT directly their quality of play. II Emanuel Lasker, 1894 -1921

Our approach • computer analysis of individual moves played • determine players’ quality of play regardless of the game score • the differences in players’ style were also taken into account • calm positional playersvs aggresive tactical players • a method to assess the difficulty of positions was designed Analysed games • 14 World Champions (classical version) from 1886 to 2004 • analyses of the matches for the title of “World Chess Champion” • slightly adapted chess program Crafty has been used III Jose Raul Capablanca, 1921 -1927

The modified Crafty • Instead of time limit, we limited search to fixed search depth. • Backed-up evaluations from depth 2 to 12 were obtained for each move. • Quiescence search remained turned on to prevent horizont effects. Advantages • complex positions automatically get more computation time, • the program could be run on computers of different computational powers. Obtained data • best move and its evaluation, • second best move and its evaluation, • move played and its evaluation, • material state of each player. IV Alexander Alekhine, 1927 -1935 and 1937 - 1946

Average error • average difference between moves played and best evaluated moves • basic criterion Formula ∑|Best move evaluation – Move played evaluation| • Number of moves • “Best move” = Crafty’s decision resulting from 12 ply search Constraints • Evaluations started on move 12. • Positions, where both the move suggested and the move played were outside the interval [-2, 2], were discarded. • Positional players are expected to commit less errors due to somewhat less complex positions, than tactical players. V Max Euwe, 1935 - 1937

Average error V Max Euwe, 1935 - 1937

Blunders • Big mistakes can be quite reliably detected with a computer. • We label a move as a blunder when the numerical error exceeds 1.00. VI Mikhail Botvinnik, 1948 - 1957, 1958 - 1960, and 1961 - 1963

Complexity of a position Basic idea • A given position is difficult, when different “best moves”, which considerably alter the evaluation of the root position, are discovered at different search depths. Assumption • This definition of complexity also applies to humans. • This assumption is in agreement with experimental results. Formula ∑|Best move evaluation – 2nd best move evaluation| besti ≠ besti - 1 VII Vasily Smyslov, 1957 - 1958

Complexity of a position Euwe-Alekhine, 16th World Championship 1935 complexity = 0.00 VII Vasily Smyslov, 1957 - 1958

Complexity of a position Euwe-Alekhine, 16th World Championship 1935 complexity = 0.00 + (1.30 – 1.16) complexity = 0.14 VII Vasily Smyslov, 1957 - 1958

Complexity of a position Euwe-Alekhine, 16th World Championship 1935 complexity = 0.14 VII Vasily Smyslov, 1957 - 1958

Complexity of a position Euwe-Alekhine, 16th World Championship 1935 complexity = 0.14 + (4.46 – 1.60) complexity = 0.14 + 2.86 complexity = 3.00 VII Vasily Smyslov, 1957 - 1958

Complexity of a position VII Vasily Smyslov, 1957 - 1958

Average error in equally complex positions • How would players perform if they faced equally complex positions? • What would be their expected error if they were playing in another style? VIII Mikhail Tal, 1960 - 1961

Percentage of best moves played • It alone does NOT reveal true strength of a player. IX Tigran Petrosian, 1963 - 1969

The difference in best move evaluations X Boris Spassky, 1969 - 1972

Percentage of best moves played...... and the difference in best move evaluations XI Robert James Fischer, 1972 - 1975

Material XII Anatoly Karpov, 1975 - 1985

Credibility of Crafty as an analysis tool • By limiting search depth we achieved automatic adaptation of time used to the complexity of a given position. • Occasional errors cancel out through statistical averaging (around 1.400 analyses were applied, altogether over 37.000 positions). Using another program instead of Crafty... • An open source program was required for the modification of the program. • Analyses of “Man against the machine” matches indicate that Crafty competently appreciates the strength of the strongest chess programs. XIII Garry Kasparov, 1985 - 2000

Conclusion • Slightly modified chess program Crafty was applied as tool for computer analysis aiming at an objective comparison of chess players of different eras. • Several criteria for evaluation were designed: • average difference between moves played and best evaluated moves • rate of blunders (big errors) • expected error in equally complex positions • rate of best moves played & difference in best moves evaluations • A method to assess the difficulty of positions was designed, in order to bring all players to a “common denominator”. • The results might appear quite surprising. Overall, they can be nicely interpreted by a chess expert. XIV Vladimir Kramnik, 2000 -

? XIV Vladimir Kramnik, 2000 -

Computer analysis of World Chess Champions