In Kotov’s great book “Think Like a Grandmaster” he taught the average chess player the inner workings of how a chess master thinks about a position by creating a tree of candidates and then proceeding along the tree. While there is much to learn from Kotov’s work, I have always been facinated how computers can evaluate positions and how their positional play is derived from these material evaluation algorithms. I believe that the way chess engines derive material evaluations might help the lower rated amateur improve their evaluation skills.
Below is a combination of the Crafty chess engine algorithms as well as Larry Kaufman’s material evaluation processes which is used by the Rybka engine.
Pawns
Pawn = 1
isolated pawn penalty based on file:
a-pawn : -.12
b-pawn : -.14
c-pawn : -.16
d-pawn : -.20
e-pawn : -.20
f-pawn : -.16
g-pawn : -.14
h-pawn : -.12
Doubled pawn (and not also isolated) penalty of -.12 plus add isolated pawn penalty
Backward pawns -.06 penalty +.04 bonus for attack on backward pawn on semi-open file.
Pawn advance in center +.04 / rank increasing to about +.08 / rank in the endgame
Development
Rook pawn is worth 15% less than a regular pawn (.85 of a pawn) (L.Kaufman)
Knights
Knights = 3.25
Centralized knight: +.30
In outpost : +.08
Unpaired knight is worth approximately 3.14 pawns (worth less) (L.Kaufman)
Bishops
Bishops = 3.25
Bishop in endgame +.10
Bad bishop : -.04
Corner bishop : 0.0
Center bishop: +.3
Attacking / good bishop: +.18
Attack against King: +.05
The Bishop Pair
Bishop pair: +.50 Bishop pair is worth .50 more if not pieces exist to exchange them (L.Kaufman)
Bishop pair is worth less than .50 a pawn when most or all of the pawns are on the board, and more than .50 pawns when half or more of the pawns are gone (L.Kaufman)
If you have the bishop pair, and your opponent’s single bishop is a bad bishop (hemmed in by his own pawns), you already have full compensation for 1 pawn (L.Kaufman)
Unpaired bishop is worth approximately 3.14 pawns (worth less) (L.Kaufman)
Rooks
Rooks = 5
Attacking on open-file: +.20
One semi-open file: +.10
On open-file: +.14
Rook and Bishop is better than the Rook and Knight. (L.Kaufman)
Queen
Queen = 9.75
Queen and Knight is slightly better than Queen and Bishop
King
Centralized in opening: -.24
Centralized in endgame: +.36
On open file in opening: -.23
No adjacent pawns: -.08
Special Cases
Hanging pieces: -.10
Exchanges favor the side with a material advantage
Minor pieces lose their value as the endgame approaches
In endgames with no other piece the bishop is worth about 2.5 and the knight 2.25 with other pieces the minors are worth about 3.25
Rooks gain value as the endgame approaches
Note: I have modified the Crafty point values to reflect the Kaufman values.
Resources
Evaluation of Material Imbalances in Chess
GNU Chess Positional Heuristics
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