computer analysis of world chess champions

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, 1886 - 1894

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, 1894 -1921

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, 1921 -1927

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

designedAnalysed 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, 1927 -1935 and 1937 - 1946

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, 1935 - 1937

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

Average error

V Max Euwe, 1935 - 1937

Blunders

VI Mikhail Botvinnik, 1948 - 1957, 1958 - 1960, and 1961 - 1963

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, 1957 - 1958

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



depth 1st eval 2nd eval

2 Qc2 -0.09 Qc1 -0.17

3 Qc2 +0.24 Qc1 +0.16

4 Qc2 +0.08 Qc1 +0.00

5 Qc2 +0.35 Qc1 +0.30

6 Qc2 +0.07 Qc1 +0.02

7 Qc2 +0.57 Qc1 +0.55

8 Qc2 +0.72 Qc1 +0.60

9 Qc2 +0.96 Qc1 +0.87

10 Qc1 +1.30 Qc2 +1.16

11 Qc1 +1.52 Qc2 +1.26

12 Qd4 +4.46 Qc1 +1.60

complexity = 0.00

Euwe-Alekhine, 16th World Championship 1935




2 Qc2 -0.09 Qc1 -0.17

3 Qc2 +0.24 Qc1 +0.16

4 Qc2 +0.08 Qc1 +0.00

5 Qc2 +0.35 Qc1 +0.30

6 Qc2 +0.07 Qc1 +0.02

7 Qc2 +0.57 Qc1 +0.55

8 Qc2 +0.72 Qc1 +0.60

9 Qc2 +0.96 Qc1 +0.87

10 Qc1 +1.30 Qc2 +1.16

11 Qc1 +1.52 Qc2 +1.26

12 Qd4 +4.46 Qc1 +1.60

complexity = 0.00 + (1.30 – 1.16)


complexity = 0.14




2 Qc2 -0.09 Qc1 -0.17

3 Qc2 +0.24 Qc1 +0.16

4 Qc2 +0.08 Qc1 +0.00

5 Qc2 +0.35 Qc1 +0.30

6 Qc2 +0.07 Qc1 +0.02

7 Qc2 +0.57 Qc1 +0.55

8 Qc2 +0.72 Qc1 +0.60

9 Qc2 +0.96 Qc1 +0.87

10 Qc1 +1.30 Qc2 +1.16

11 Qc1 +1.52 Qc2 +1.26

12 Qd4 +4.46 Qc1 +1.60

complexity = 0.14





2 Qc2 -0.09 Qc1 -0.17

3 Qc2 +0.24 Qc1 +0.16

4 Qc2 +0.08 Qc1 +0.00

5 Qc2 +0.35 Qc1 +0.30

6 Qc2 +0.07 Qc1 +0.02

7 Qc2 +0.57 Qc1 +0.55

8 Qc2 +0.72 Qc1 +0.60

9 Qc2 +0.96 Qc1 +0.87

10 Qc1 +1.30 Qc2 +1.16

11 Qc1 +1.52 Qc2 +1.26

12 Qd4 +4.46 Qc1 +1.60

complexity = 0.14 + (4.46 – 1.60)


complexity = 0.14 + 2.86complexity = 3.00

Average error in equally complex positions

VIII Mikhail Tal, 1960 - 1961

How would players perform if they faced equally complex

positions? What would be their expected error if they were playing in

another style?

0

10

20

30

40

50

60

0,1 0,3 0,5 0,7 0,9 1,1

complexity

% o

f mov

es

average Capablanca Tal

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

0

10

20

30

40

50

60

70

80

1 11 21 31 41 51 61 71 81

move no.

mat

eria

l

Kramnik Petrosian Spassky Steinitz

-20

-15

-10

-5

0

5

10

1 11 21 31 41 51 61 71 81 91

move no.

devi

atio

n

Kramnik Petrosian Spassky Steinitz

Credibility of Crafty as an analysis tool

XIII Garry Kasparov, 1985 - 2000

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.

Deep Blue 0.0757 New York, 1997

Kasparov

Deep Fritz 0.0617 Bahrain, 2002 Kramnik

Deep Junior

0.0865 New York, 2003

Kasparov

FritzX3D 0.0904 New York, 2003

Kasparov

Hydra 0.0743 London, 2005 Adams

Conclusion

XIV Vladimir Kramnik, 2000 -

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 -

computer analysis of world chess champions

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