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The centipawn is the unit of measure used in chess as measure of the advantage. A centipawn is equal to 1/100 of a pawn. Therefore 100 centipawns = 1 pawn. These values play no formal role in the game but are useful to players, and essential in computer chess to evaluate positions.
World Champion (from 1894 to 1921, and notable mathematician) Emanuel Lasker gave the following values:
- Pawn = 100 (on average)
- Knight = 350
- Bishop = 350 (on average)
- Rook = 500 (on average)
- Queen = 850
Lasker, in his book Chess Manual, gave more precise relative values for the early part of the game:
- Rook pawn: 50
- Knight pawn: 125
- Bishop pawn: 150
- Central pawn: 200
- Knight: 450 (either queenside or kingside)
- Queen bishop: 450
- King bishop: 500
- Queen rook: 600
- King rook: 700
- Queen: 1,100
By setting the average pawn value to be 100, we can renormalize Lasker measures as follows:
- Rook pawn: 38
- Knight pawn: 95
- Bishop pawn: 115
- Central pawn: 153
- Knight: 344 (either queenside or kingside)
- Queen bishop: 344
- King bishop: 382
- Queen rook: 458
- King rook: 534
- Queen: 840
Kingside bishop and rook are worth about 14% more than their queenside counterparts.
Statistically for castling, prob(O-O)=79% whereas prob(O-O-O)=9%, so prob(no_castling)=12% -- see https://blog.ebemunk.com/a-visual-look-at-2-million-chess-games -- interestingly, White and Black will castle on the same side 69% of the time.
For other alternative valuations, see: http://chess.wikia.com/wiki/Centipawn
The score is usually scaled to units of centipawns. So the first-move advantage for white might be expressed as 20 centipawns, however, for readability it is frequently written in decimal format, e.g. +0.20. A positive value means white is winning. A negative value means black is winning.
For the Stockfish engine, the score is an aggregate of various factors such as material, pawn structure, space advantage, mobility, two-bishops, king safety, etc. It is not a matter of just arithmetic material accounting of relative values. The reported score is a computational approximation given the state of the board and the evaluation of best possible moves -- for details, see https://chessprogramming.wikispaces.com/Evaluation
This chart show the probability of a move type being seen on any given turn. A typical game has an average move length of 40.77.
Detail images for World Champions: https://imgur.com/a/ydIt8
Shortcut to his page: https://git.io/chesswik | Last update : 2018-03-17