Values of Chessmen
by Bill Wall
When I first learned chess, I was told (or read) that the value of the pieces are one point for a pawn, 3 points for a knight, a little bit more than 3 points for a bishop, 5 points for a rook, and 9 points for a queen. These are approximations of the average values of pieces since their actual value depends of the position (a locked bishop is no longer worth 3 points, for example).
In the 19th century, Howard Staunton, in his Chess-Player’s Handbook, gave the value of the pieces as 1 for the pawn, 2.75 for the knight, 3.25 for the bishop, 5 for the rook and 9 for the queen. Later, Bilguer, in his chess handbook, gave the values as 1 for the pawn, 3.25 for the knight, 3.50 for the bishop, 5 for the rook, and 9 for the queen. Steinitz gave the value as 1 for the pawn, 3.05 for the knight, 3.50 for the bishop, 5.48 for the rook, and 9.94 for the queen. Emanuel Lasker gave the value of 2 for the d-pawn and e-pawn, 1.5 for the bishop pawn, 1.25 for the knight pawn, 0.5 for the rook pawn, 4.5 for the knight, 4.5 for the Queen’s bishop, 5.0 for the King’s bishop, 6 for the Queen’s rook, 7 for the King’s rook, and 11 for the queen. Max Euwe gave the value of 1 to the pawn, 3.5 for the knight, 3.5 for the bishop, 5.5 for the rook, and 10 for the queen. Bobby Fischer gave the value of 1 for the pawn, 3 for the knight, 3.25 for the bishop, 5 for the rook, and 9 for the queen. Dr. Hans Berliner gave the value of 1 for the pawn, 3.20 for the knight, 3.33 for the bishop, 5.10 for the rook, and 8.80 for the queen.
Looking at simple mobility, one can give the value of the pawn as 1, 2 for the knight, 3.25 for the bishop, 5 for the rook, and 8.25 for the queen. For restricted mobility, the value is 1 for the pawn, 2.50 for the knight, 2.75 for the bishop, 5 for the rook, and 7.75 for the queen.
Modern day analysis with computers shows that the value of the pawn is 1, 3.25 for the knight, 3.50 for the bishop, 5 for the rook, and 9.75 for the queen.
The value of the rook pawn is, on average, 15% less than the average value of other pawns. Rook pawns are easily stopped from queening in the endgame. Also, it can only capture in one direction rather than in two directions.
The value of doubled pawns as about ½ pawn less than two individual pawns together. However, when the pawns are doubled, there is also a semi-open file that could help change the value of the major pieces, such as a rook on an open file. With both rooks on the board, the value of doubled pawns is 1/16th less than two connected pawns.
Isolated doubled pawns on semi-open files are not worth that much more than a single sound pawn. When they are on a closed file, the doubled pawns are worth about ½ a pawn.
The average value of a bishop is greater than that of a knight. On average, single bishops and knights have the same value of 3.25 pawns. The bishop is a little bit stronger against a rook or pawns in the endgame than the knight. The side with a single knight has a slight advantage when there are 6 or more pawns per side. The knight and the bishop have similar value when there are 5 pawns per side. The bishop has the advantage when there are 4 pawns or less per side in the endgame.
The average value of a rook against a knight or bishop is about 1.37 of a pawn. If one side has a rook against a knight and two pawns, the side with the rook is about ¼ of a pawn behind in value. In an open position, a rook and a pair of bishops is stronger than two rooks and a knight.
The average value of the queen is a rook, a minor piece (bishop or knight) and 1.5 pawns. The knight is slightly stronger than the bishop when supporting the rook against the enemy queen.
The value of a queen and pawn is the same as two rook if no minor pieces are present.