Computer analysis of World Chess Champions

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

• Jeff Sonas, 2005
• rating scheme, based on tournament results from
  1840 to the present,
• ratings are calculated for each month
  separately, players 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
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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 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

III Jose Raul Capablanca, 1921 -1927
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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
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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 Craftys 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
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Average error
V Max Euwe, 1935 - 1937
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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
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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
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Complexity of a position
Euwe-Alekhine, 16th World Championship 1935
complexity 0.00
VII Vasily Smyslov, 1957 - 1958
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Complexity of a position
Euwe-Alekhine, 16th World Championship 1935
complexity 0.00
VII Vasily Smyslov, 1957 - 1958
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Complexity of a position
Euwe-Alekhine, 16th World Championship 1935
complexity 0.00
VII Vasily Smyslov, 1957 - 1958
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Complexity of a position
Euwe-Alekhine, 16th World Championship 1935
complexity 0.00
VII Vasily Smyslov, 1957 - 1958
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Complexity of a position
Euwe-Alekhine, 16th World Championship 1935
complexity 0.00
VII Vasily Smyslov, 1957 - 1958
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Complexity of a position
Euwe-Alekhine, 16th World Championship 1935
complexity 0.00
VII Vasily Smyslov, 1957 - 1958
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Complexity of a position
Euwe-Alekhine, 16th World Championship 1935
complexity 0.00
VII Vasily Smyslov, 1957 - 1958
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Complexity of a position
Euwe-Alekhine, 16th World Championship 1935
complexity 0.00
VII Vasily Smyslov, 1957 - 1958
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Complexity of a position
Euwe-Alekhine, 16th World Championship 1935
complexity 0.00
VII Vasily Smyslov, 1957 - 1958
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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
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Complexity of a position
Euwe-Alekhine, 16th World Championship 1935
complexity 0.14
VII Vasily Smyslov, 1957 - 1958
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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
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Complexity of a position
VII Vasily Smyslov, 1957 - 1958
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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
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Percentage of best moves played

• It alone does NOT reveal true strength of a
  player.

IX Tigran Petrosian, 1963 - 1969
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The difference in best move evaluations
X Boris Spassky, 1969 - 1972
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Percentage of best moves played...... and the
difference in best move evaluations
XI Robert James Fischer, 1972 - 1975
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Material
XII Anatoly Karpov, 1975 - 1985
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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
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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

XIV Vladimir Kramnik, 2000 -
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?
XIV Vladimir Kramnik, 2000 -