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EspañolCHESS PIECE POINT VALUE
In chess, the chess pieces are often assigned certain 'point values' as a heuristic that help determine how valuable a piece is strategically. These values are useful to players, and are also used in computer chess to help the computer figure out what moves to make.
Calculations of the value of pieces provide only a rough idea of the state of play. The exact piece values will depend on the game situation, and can differ considerably from those given here.
The following is the most common assignment of point values .
The value of the king is undefined, as its loss causes the loss of the game. In the endgame, when there is little danger of checkmate, the fighting value of the king is about four points .
This system has some shortcomings. For instance, three minor pieces (nine points) are often slightly stronger than two rooks (ten points) or a queen (nine points) , .
Though the 1, 3, 3, 5, 9 system of point totals is generally accepted, many other systems of valuing pieces have been presented. They have mostly been received poorly, although the point system itself falls under similar criticism, as all systems are very rigid and generally fail to take positional factors into account.
An 1813 book (source unknown, perhaps by Jacob Sarratt) gives these valuations of the pieces:
★ Knight 9¼
★ Bishop 9¾
★ Rook 15
★ Queen 23¾
★ King as attack piece (in the endgame) 6½
★ Pawn 2 at the start, 3¾ in the endgame
If these values are divided by three and rounded, they are more in line with the valuations used now:
★ Knight 3.1
★ Bishop 3.3
★ Rook 5
★ Queen 7.9
★ King as attacking piece in the endgame 2.2
★ Pawn 0.7 in the beginning, 1.3 in the endgame
Howard Staunton in ''The Chess-Player's Handbook'' notes that piece values are dependent on the position and the phase of the game (the queen typically less valuable toward the endgame), but gives these values, without explaining how they were obtained :
★ Pawn 1.00
★ Knight 3.05
★ Bishop 3.50
★ Rook 5.48
★ Queen 9.94
In the 1817 edition of Philidor's ''Studies of Chess'', the editor (Peter Pratt) gave the same values.
The 1843 German book ''Handbuch des Schachspiels'' by Paul Rudolf von Bilguer gave
★ Pawn 1.5
★ Knight 5.3
★ Bishop 5.3
★ Rook 8.6
★ Queen 15.5
When standardizing so that a pawn equals one:
★ Pawn 1
★ Knight 3.5
★ Bishop 3.5
★ Rook 5.7
★ Queen 10.3
Yevgeny Gik gave these figures based only on average mobility:
★ Pawn 1
★ Knight 2.4
★ King 3 (as an attacking and defensive piece)
★ Bishop 4
★ Rook 6.4
★ Queen 10.4
but Andrew Soltis points out problems with that chart and other mathematical methods of evaluation .
Grandmaster Larry Evans gives the values:
★ pawn = 1 point
★ knight = 3½ points
★ bishop = 3¾ points
★ rook = 5 points
★ queen = 10 points .
(Evans initially gives the bishop a value of 3½ points but later changes it to 3¾ points.) A bishop is usually slightly more powerful than a knight, but not always—it depends on the position , .
Another system is used by Max Euwe and Hans Kramer in Volume 1 of their ''The Middlegame'', with values
★ pawn = 1 point
★ knight = 3½ points
★ bishop = 3½ points
★ rook = 5½ points
★ queen = 10 points.
Bobby Fischer gave the value of the bishop as 3¼ points (with the other pieces having the traditional value).
An early Soviet chess program used
★ pawn = 1
★ knight = 3½
★ bishop = 3½
★ rook = 5
★ queen = 9½.
Another popular system is
★ pawn = 1
★ knight = 3
★ bishop = 3
★ rook = 4½
★ queen = 9 .
International master Larry Kaufman performed a computer analysis of thousands of games by masters to determine the average relative value of the pieces. He determined (to the nearest ¼ point) the following:
★ pawn = 1 point
★ knight = 3¼ points
★ bishop = 3¼ points
★ rook = 5 points
★ queen = 9¾ points.
Add an additional ½ point for having both bishops. Kaufman elaborates about how the values of knights and rooks change, depending on the number of pawns on the board: ''"A further refinement would be to raise the knight's value by 1/16 and lower the rook's value by ⅛ for each pawn above five of the side being valued, with the opposite adjustment for each pawn short of five."''
World Correspondence Chess Champion Hans Berliner gives the following valuations, based on experience and computer experiments:
★ pawn = 1
★ knight = 3.2
★ bishop = 3.33
★ rook = 5.1
★ queen = 8.8
There are adjustments for the rank and file of a pawn and adjustments for the pieces depending on how open or closed the position is. Bishops, rooks, and queens gain up to 10 percent more value in open positions and lose up to 20 percent in closed positions. Knights gain up to 50 percent in closed positions and lose up to 30 percent in the corners and edges of the board. The value of a good bishop may be 10 percent or more than that of a bad bishop .
There are different types of doubled pawns, see the diagram. White's doubled pawns on the b-file are the best situation in the diagram, since advancing the pawns and exchanging can get them un-doubled and mobile. The doubled b-pawn is worth 0.75 points. If the black pawn on a6 was on c6, it would not be possible to dissolve the doubled pawn, and it would be worth only 0.5 points. The doubled pawn on the f2 is worth about 0.5 points. The second white pawn on the h-file is worth only 0.33 points, and additional pawns on the file would be worth only 0.2 points .
The relative value of pieces changes as a game progresses to the endgame. The relative value of pawns and rooks may increase, and the value of bishops may increase also, though usually to a lesser extent. The knight tends to lose some power, and the strength of the queen may be slightly lessened, as well. Some examples follow.
★ A queen versus two rooks
:
★ In the middlegame they are equal
:
★ In the endgame, the two rooks are somewhat more powerful. With no other pieces on the board, two rooks are equal to a queen and a pawn
★ A rook versus two minor pieces
:
★ In the opening and middlegame, a rook and ''two'' pawns are weaker than two bishops; equal to or slightly weaker than a bishop and knight; and equal to two knights
:
★ In the endgame, a rook and ''one'' pawn are equal to two knights; and equal or slightly weaker than a bishop and knight. A rook and ''two'' pawns are equal to two bishops .
★ Bishops are often more powerful than rooks in the opening. Rooks are usually more powerful than bishops in the middlegame, and rooks dominate the minor pieces in the endgame .
★ As the tables in Berliner's system show, the values of pawns changes dramatically in the endgame. In the opening and middlegame, pawns on the central files are more valuable. In the late middlegame and endgame the situation reverses, and pawns on the wings become more valuable due to their likelihood of becoming an outside passed pawn and threatening to promote. When there is about fourteen points of material on both sides, the value of pawns on any file is about equal. After that, wing pawns become more valuable .
★ The exchange (chess)
★ Computer chess
★ Claude Elwood Shannon
★ Evaluation function
★
★
★
★
★
★ The Evaluation of Material Imbalances, Kaufman, Larry, , , Chess Life, 1999
★
★
★
★
★
★ ''80-Square Chess'', E. Trice in ICGA Journal Vol. 27, No. 2 - June 2004, p. 81-96.
★ Relative Value of Chess Pieces
★ Relative Value of Pieces and Principles of Play from ''The Modern Chess Instructor'' by Wilhelm Steinitz
★ About the Values of Chess Pieces by Ralph Betza, 1996.
★ Larry Kaufman article
★ some historical evaluations
Calculations of the value of pieces provide only a rough idea of the state of play. The exact piece values will depend on the game situation, and can differ considerably from those given here.
Standard valuations
The following is the most common assignment of point values .
| Piece | Value | |
|---|---|---|
| Queen | 9 |  Chess qld44.png  Chess qdl44.png |
| Rook | 5 |  Chess rll44.png  Chess rdd44.png |
| Bishop | 3 |  Chess bld44.png  Chess bdl44.png |
| Knight | 3 |  Chess nll44.png  Chess ndd44.png |
| Pawn | 1 |  Chess pld44.png  Chess pdl44.png |
The value of the king is undefined, as its loss causes the loss of the game. In the endgame, when there is little danger of checkmate, the fighting value of the king is about four points .
This system has some shortcomings. For instance, three minor pieces (nine points) are often slightly stronger than two rooks (ten points) or a queen (nine points) , .
Alternate valuations
Though the 1, 3, 3, 5, 9 system of point totals is generally accepted, many other systems of valuing pieces have been presented. They have mostly been received poorly, although the point system itself falls under similar criticism, as all systems are very rigid and generally fail to take positional factors into account.
Historical valuations
An 1813 book (source unknown, perhaps by Jacob Sarratt) gives these valuations of the pieces:
★ Knight 9¼
★ Bishop 9¾
★ Rook 15
★ Queen 23¾
★ King as attack piece (in the endgame) 6½
★ Pawn 2 at the start, 3¾ in the endgame
If these values are divided by three and rounded, they are more in line with the valuations used now:
★ Knight 3.1
★ Bishop 3.3
★ Rook 5
★ Queen 7.9
★ King as attacking piece in the endgame 2.2
★ Pawn 0.7 in the beginning, 1.3 in the endgame
Howard Staunton in ''The Chess-Player's Handbook'' notes that piece values are dependent on the position and the phase of the game (the queen typically less valuable toward the endgame), but gives these values, without explaining how they were obtained :
★ Pawn 1.00
★ Knight 3.05
★ Bishop 3.50
★ Rook 5.48
★ Queen 9.94
In the 1817 edition of Philidor's ''Studies of Chess'', the editor (Peter Pratt) gave the same values.
The 1843 German book ''Handbuch des Schachspiels'' by Paul Rudolf von Bilguer gave
★ Pawn 1.5
★ Knight 5.3
★ Bishop 5.3
★ Rook 8.6
★ Queen 15.5
When standardizing so that a pawn equals one:
★ Pawn 1
★ Knight 3.5
★ Bishop 3.5
★ Rook 5.7
★ Queen 10.3
Yevgeny Gik gave these figures based only on average mobility:
★ Pawn 1
★ Knight 2.4
★ King 3 (as an attacking and defensive piece)
★ Bishop 4
★ Rook 6.4
★ Queen 10.4
but Andrew Soltis points out problems with that chart and other mathematical methods of evaluation .
More recent point evaluations
Grandmaster Larry Evans gives the values:
★ pawn = 1 point
★ knight = 3½ points
★ bishop = 3¾ points
★ rook = 5 points
★ queen = 10 points .
(Evans initially gives the bishop a value of 3½ points but later changes it to 3¾ points.) A bishop is usually slightly more powerful than a knight, but not always—it depends on the position , .
Another system is used by Max Euwe and Hans Kramer in Volume 1 of their ''The Middlegame'', with values
★ pawn = 1 point
★ knight = 3½ points
★ bishop = 3½ points
★ rook = 5½ points
★ queen = 10 points.
Bobby Fischer gave the value of the bishop as 3¼ points (with the other pieces having the traditional value).
An early Soviet chess program used
★ pawn = 1
★ knight = 3½
★ bishop = 3½
★ rook = 5
★ queen = 9½.
Another popular system is
★ pawn = 1
★ knight = 3
★ bishop = 3
★ rook = 4½
★ queen = 9 .
Larry Kaufman's research
International master Larry Kaufman performed a computer analysis of thousands of games by masters to determine the average relative value of the pieces. He determined (to the nearest ¼ point) the following:
★ pawn = 1 point
★ knight = 3¼ points
★ bishop = 3¼ points
★ rook = 5 points
★ queen = 9¾ points.
Add an additional ½ point for having both bishops. Kaufman elaborates about how the values of knights and rooks change, depending on the number of pawns on the board: ''"A further refinement would be to raise the knight's value by 1/16 and lower the rook's value by ⅛ for each pawn above five of the side being valued, with the opposite adjustment for each pawn short of five."''
Hans Berliner's system
World Correspondence Chess Champion Hans Berliner gives the following valuations, based on experience and computer experiments:
★ pawn = 1
★ knight = 3.2
★ bishop = 3.33
★ rook = 5.1
★ queen = 8.8
There are adjustments for the rank and file of a pawn and adjustments for the pieces depending on how open or closed the position is. Bishops, rooks, and queens gain up to 10 percent more value in open positions and lose up to 20 percent in closed positions. Knights gain up to 50 percent in closed positions and lose up to 30 percent in the corners and edges of the board. The value of a good bishop may be 10 percent or more than that of a bad bishop .
There are different types of doubled pawns, see the diagram. White's doubled pawns on the b-file are the best situation in the diagram, since advancing the pawns and exchanging can get them un-doubled and mobile. The doubled b-pawn is worth 0.75 points. If the black pawn on a6 was on c6, it would not be possible to dissolve the doubled pawn, and it would be worth only 0.5 points. The doubled pawn on the f2 is worth about 0.5 points. The second white pawn on the h-file is worth only 0.33 points, and additional pawns on the file would be worth only 0.2 points .
| Rank | a & h file | b & g file | c & f file | d & e file |
|---|---|---|---|---|
| 2 | 0.90 | 0.95 | 1.05 | 1.10 |
| 3 | 0.90 | 0.95 | 1.05 | 1.15 |
| 4 | 0.90 | 0.95 | 1.10 | 1.20 |
| 5 | 0.97 | 1.03 | 1.17 | 1.27 |
| 6 | 1.06 | 1.12 | 1.25 | 1.40 |
| Rank | a & h file | b & g file | c & f file | d & e file |
|---|---|---|---|---|
| 2 | 1.20 | 1.05 | 0.95 | 0.90 |
| 3 | 1.20 | 1.05 | 0.95 | 0.90 |
| 4 | 1.25 | 1.10 | 1.00 | 0.95 |
| 5 | 1.33 | 1.17 | 1.07 | 1.00 |
| 6 | 1.45 | 1.29 | 1.16 | 1.05 |
| Rank | Isolated | Connected | Passed | Passed & connected |
|---|---|---|---|---|
| 4 | 1.05 | 1.15 | 1.30 | 1.55 |
| 5 | 1.30 | 1.35 | 1.55 | 2.3 |
| 6 | 2.1 | x | x | 3.5 |
Changing valuations in the endgame
The relative value of pieces changes as a game progresses to the endgame. The relative value of pawns and rooks may increase, and the value of bishops may increase also, though usually to a lesser extent. The knight tends to lose some power, and the strength of the queen may be slightly lessened, as well. Some examples follow.
★ A queen versus two rooks
:
★ In the middlegame they are equal
:
★ In the endgame, the two rooks are somewhat more powerful. With no other pieces on the board, two rooks are equal to a queen and a pawn
★ A rook versus two minor pieces
:
★ In the opening and middlegame, a rook and ''two'' pawns are weaker than two bishops; equal to or slightly weaker than a bishop and knight; and equal to two knights
:
★ In the endgame, a rook and ''one'' pawn are equal to two knights; and equal or slightly weaker than a bishop and knight. A rook and ''two'' pawns are equal to two bishops .
★ Bishops are often more powerful than rooks in the opening. Rooks are usually more powerful than bishops in the middlegame, and rooks dominate the minor pieces in the endgame .
★ As the tables in Berliner's system show, the values of pawns changes dramatically in the endgame. In the opening and middlegame, pawns on the central files are more valuable. In the late middlegame and endgame the situation reverses, and pawns on the wings become more valuable due to their likelihood of becoming an outside passed pawn and threatening to promote. When there is about fourteen points of material on both sides, the value of pawns on any file is about equal. After that, wing pawns become more valuable .
See also
★ The exchange (chess)
★ Computer chess
★ Claude Elwood Shannon
★ Evaluation function
References
★
★
★
★
★
★ The Evaluation of Material Imbalances, Kaufman, Larry, , , Chess Life, 1999
★
★
★
★
★
★ ''80-Square Chess'', E. Trice in ICGA Journal Vol. 27, No. 2 - June 2004, p. 81-96.
External links
★ Relative Value of Chess Pieces
★ Relative Value of Pieces and Principles of Play from ''The Modern Chess Instructor'' by Wilhelm Steinitz
★ About the Values of Chess Pieces by Ralph Betza, 1996.
★ Larry Kaufman article
★ some historical evaluations
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