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

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. I Wilhelm Steinitz, 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. Computers...  Were so far mostly used as a tool for statistical analysis of players’ results.

Related work II Emanuel Lasker, 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.

Our approach III Jose Raul Capablanca,  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 players vs 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

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. IV Alexander Alekhine, and 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.

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. V Max Euwe,  Positional players are expected to commit less errors due to somewhat less complex positions, than tactical players.

Average error V Max Euwe,

Blunders VI Mikhail Botvinnik, , , and  Big mistakes can be quite reliably detected with a computer.  We label a move as a blunder when the numerical error exceeds 1.00.

Complexity of a position VII Vasily Smyslov, 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| best i ≠ best i - 1

Complexity of a position VII Vasily Smyslov, depth1steval2ndeval 2Qc2-0.09Qc Qc2+0.24Qc Qc2+0.08Qc Qc2+0.35Qc Qc2+0.07Qc Qc2+0.57Qc Qc2+0.72Qc Qc2+0.96Qc Qc1+1.30Qc Qc1+1.52Qc Qd4+4.46Qc complexity = 0.00 Euwe-Alekhine, 16th World Championship 1935

Complexity of a position VII Vasily Smyslov, depth1steval2ndeval 2Qc2-0.09Qc Qc2+0.24Qc Qc2+0.08Qc Qc2+0.35Qc Qc2+0.07Qc Qc2+0.57Qc Qc2+0.72Qc Qc2+0.96Qc Qc1+1.30Qc Qc1+1.52Qc Qd4+4.46Qc complexity = 0.00 Euwe-Alekhine, 16th World Championship 1935

Complexity of a position VII Vasily Smyslov, depth1steval2ndeval 2Qc2-0.09Qc Qc2+0.24Qc Qc2+0.08Qc Qc2+0.35Qc Qc2+0.07Qc Qc2+0.57Qc Qc2+0.72Qc Qc2+0.96Qc Qc1+1.30Qc Qc1+1.52Qc Qd4+4.46Qc complexity = 0.00 Euwe-Alekhine, 16th World Championship 1935

Complexity of a position VII Vasily Smyslov, depth1steval2ndeval 2Qc2-0.09Qc Qc2+0.24Qc Qc2+0.08Qc Qc2+0.35Qc Qc2+0.07Qc Qc2+0.57Qc Qc2+0.72Qc Qc2+0.96Qc Qc1+1.30Qc Qc1+1.52Qc Qd4+4.46Qc complexity = 0.00 Euwe-Alekhine, 16th World Championship 1935

Complexity of a position VII Vasily Smyslov, depth1steval2ndeval 2Qc2-0.09Qc Qc2+0.24Qc Qc2+0.08Qc Qc2+0.35Qc Qc2+0.07Qc Qc2+0.57Qc Qc2+0.72Qc Qc2+0.96Qc Qc1+1.30Qc Qc1+1.52Qc Qd4+4.46Qc complexity = 0.00 Euwe-Alekhine, 16th World Championship 1935

Complexity of a position VII Vasily Smyslov, depth1steval2ndeval 2Qc2-0.09Qc Qc2+0.24Qc Qc2+0.08Qc Qc2+0.35Qc Qc2+0.07Qc Qc2+0.57Qc Qc2+0.72Qc Qc2+0.96Qc Qc1+1.30Qc Qc1+1.52Qc Qd4+4.46Qc complexity = 0.00 Euwe-Alekhine, 16th World Championship 1935

Complexity of a position VII Vasily Smyslov, depth1steval2ndeval 2Qc2-0.09Qc Qc2+0.24Qc Qc2+0.08Qc Qc2+0.35Qc Qc2+0.07Qc Qc2+0.57Qc Qc2+0.72Qc Qc2+0.96Qc Qc1+1.30Qc Qc1+1.52Qc Qd4+4.46Qc complexity = 0.00 Euwe-Alekhine, 16th World Championship 1935

Complexity of a position VII Vasily Smyslov, depth1steval2ndeval 2Qc2-0.09Qc Qc2+0.24Qc Qc2+0.08Qc Qc2+0.35Qc Qc2+0.07Qc Qc2+0.57Qc Qc2+0.72Qc Qc2+0.96Qc Qc1+1.30Qc Qc1+1.52Qc Qd4+4.46Qc complexity = 0.00 Euwe-Alekhine, 16th World Championship 1935

Complexity of a position VII Vasily Smyslov, depth1steval2ndeval 2Qc2-0.09Qc Qc2+0.24Qc Qc2+0.08Qc Qc2+0.35Qc Qc2+0.07Qc Qc2+0.57Qc Qc2+0.72Qc Qc2+0.96Qc Qc1+1.30Qc Qc1+1.52Qc Qd4+4.46Qc complexity = 0.00 Euwe-Alekhine, 16th World Championship 1935

Complexity of a position VII Vasily Smyslov, depth1steval2ndeval 2Qc2-0.09Qc Qc2+0.24Qc Qc2+0.08Qc Qc2+0.35Qc Qc2+0.07Qc Qc2+0.57Qc Qc2+0.72Qc Qc2+0.96Qc Qc1+1.30Qc Qc1+1.52Qc Qd4+4.46Qc complexity = (1.30 – 1.16) Euwe-Alekhine, 16th World Championship 1935 complexity = 0.14

Complexity of a position VII Vasily Smyslov, depth1steval2ndeval 2Qc2-0.09Qc Qc2+0.24Qc Qc2+0.08Qc Qc2+0.35Qc Qc2+0.07Qc Qc2+0.57Qc Qc2+0.72Qc Qc2+0.96Qc Qc1+1.30Qc Qc1+1.52Qc Qd4+4.46Qc complexity = 0.14 Euwe-Alekhine, 16th World Championship 1935

Complexity of a position VII Vasily Smyslov, depth1steval2ndeval 2Qc2-0.09Qc Qc2+0.24Qc Qc2+0.08Qc Qc2+0.35Qc Qc2+0.07Qc Qc2+0.57Qc Qc2+0.72Qc Qc2+0.96Qc Qc1+1.30Qc Qc1+1.52Qc Qd4+4.46Qc complexity = (4.46 – 1.60) Euwe-Alekhine, 16th World Championship 1935 complexity = complexity = 3.00

Complexity of a position VII Vasily Smyslov,

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

Percentage of best moves played  It alone does NOT reveal true strength of a player. IX Tigran Petrosian,

The difference in best move evaluations X Boris Spassky,

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

Material XII Anatoly Karpov,

Credibility of Crafty as an analysis tool XIII Garry Kasparov,  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 analyses were applied, altogether over 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. Deep Blue0.0757New York, 1997Kasparov Deep Fritz0.0617Bahrain, 2002Kramnik Deep Junior0.0865New York, 2003Kasparov FritzX3D0.0904New York, 2003Kasparov Hydra0.0743London, 2005Adams

Conclusion XIV Vladimir Kramnik,  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,