Chess piece point value

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Image:Chess qll44.png Image:Chess rll44.png Image:Chess bll44.png Image:Chess nll44.png Image:Chess pll44.png

In chess, the chess pieces are often assigned certain point values as a heuristic that helps determine how valuable a piece is strategically. These values play no formal role in the game but are useful to players, and are also used in computer chess to help the computer evaluate positions.

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. In some positions, a well-placed piece might be much more valuable than indicated by heuristics, while a badly-placed piece may be completely trapped and, thus, almost worthless.

Valuations almost always assign the value 1 point to pawns (typically as the average value of a pawn in the starting position). Computer programs often represent the values of pieces and positions in terms of 'centipawns', where 100 centipawns = 1 pawn, which allows strategic features of the position, worth less than a single pawn, to be evaluated without requiring fractions.

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[edit] Standard valuations

The following is the most common assignment of point values (Capablanca & de Firmian 2006:24-25) (Soltis 2004:6).

Piece Value  
Queen 9 Image:Chess qld44.png Image:Chess qdl44.png
Rook 5 Image:Chess rll44.png Image:Chess rdd44.png
Bishop 3 Image:Chess bld44.png Image:Chess bdl44.png
Knight 3 Image:Chess nll44.png Image:Chess ndd44.png
Pawn 1 Image:Chess pld44.png Image:Chess pdl44.png

The value of the king is undefined as it cannot be captured, let alone traded, during the course of the game. Some early computer chess programs gave the king an arbitrary large value (such as 200 points or 1,000,000,000 points) to indicate that the inevitable loss of the king due to checkmate trumps all other considerations (Levy & Newborn 1991:45). In the endgame, when there is little danger of checkmate, the fighting value of the king is about four points (Lasker 1934:73). The king is good at attacking and defending nearby pieces and pawns. It is better at defending such pieces than the knight is, and it is better at attacking them than the bishop is (Ward 1996:13).

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) (Capablanca & de Firmian 2006:24), (Fine & Benko 2003:458, 582).

[edit] 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.

[edit] Historical valuations

An 1813 book (source unknown, perhaps by Jacob Sarratt) gives these valuations of the pieces:

  • pawn 2 at the start, 3¾ in the endgame
  • knight 9¼
  • bishop 9¾
  • rook 15
  • queen 23¾
  • king as attack piece (in the endgame) 6½

If these values are divided by three and rounded, they are more in line with the valuations used now:

  • pawn 0.7 in the beginning, 1.3 in the endgame
  • knight 3.1
  • bishop 3.3
  • rook 5
  • queen 7.9
  • king as attacking piece in the endgame 2.2

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 (Staunton 1870, 30–31):

  • 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 normalizing 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
  • bishop 4
  • rook 6.4
  • queen 10.4
  • king 3 (as an attacking and defensive piece)

but Andrew Soltis points out problems with that chart and other mathematical methods of evaluation (Soltis 2004:10-12).

Emanuel Lasker gave these approximate values: (Lasker 1934:73)

  • Knight = 3 pawns (3 points)
  • Bishop = knight (3 points)
  • Rook = knight plus 2 pawns (5 points)
  • queen = 2 rooks = 3 knights (10 or 9 points)
  • king = knight + pawn (4 points)

[edit] More recent evaluations

World Champion Emanuel Lasker (Lasker 1947:107) gave the following values (here scaled and rounded so pawn = 1 point):

  • pawn = 1 (on average)
  • knight = 3½
  • bishop = 3½ (on average)
  • rook = 5 (on average)
  • queen = 8½.

However Lasker adjusts some of these depending on the starting positions, with pawns nearer the centre, and bishops/rooks on the King's side, being worth more:

  • centre (d/e-file) pawn = 1½ points, a/h-file pawn = ½ point
  • c-file bishop = 3½ points, f-file bishop = 3¾ points
  • a-file rook = 4½ points, h-file rook = 5¼ points.

Grandmaster Larry Evans gives the values:

  • pawn = 1
  • knight = 3½
  • bishop = 3¾
  • rook = 5
  • queen = 10 (Evans 1967:73, 76).

(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 (Evans 1967:73, 76), (Mayer 1997:7). A chess-playing program was given the value of 3 for the knight and 3.4 for the bishop, but that difference was acknowledged to not be real (Mayer 1997:5).

Another system is used by Max Euwe and Hans Kramer in Volume 1 of their The Middlegame, with values

  • pawn = 1
  • knight = 3½
  • bishop = 3½
  • rook = 5½
  • queen = 10.

Bobby Fischer gave the values:

An early Soviet chess program used

  • pawn = 1
  • knight = 3½
  • bishop = 3½
  • rook = 5
  • queen = 9½ (Soltis 2004:6).

Another popular system is

  • pawn = 1
  • knight = 3
  • bishop = 3
  • rook = 4½
  • queen = 9 (Soltis 2004:6).

[edit] 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
  • knight = 3¼
  • bishop = 3¼
  • rook = 5
  • queen = 9¾.

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." (Kaufman 1999).

[edit] 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 (Berliner 1999:14-18).

Image:chess zhor 26.png
Image:chess zver 26.png a8 __ b8 __ c8 __ d8 __ e8 __ f8 __ g8 __ h8 __ Image:chess zver 26.png
a7 __ b7 pd c7 __ d7 __ e7 __ f7 __ g7 __ h7 __
a6 pd b6 __ c6 __ d6 __ e6 pd f6 pd g6 __ h6 pd
a5 __ b5 __ c5 __ d5 __ e5 __ f5 __ g5 __ h5 __
a4 __ b4 __ c4 __ d4 __ e4 __ f4 __ g4 __ h4 __
a3 __ b3 pl c3 pl d3 __ e3 __ f3 pl g3 __ h3 pl
a2 __ b2 pl c2 __ d2 __ e2 __ f2 pl g2 __ h2 pl
a1 __ b1 __ c1 __ d1 __ e1 __ f1 __ g1 __ h1 __
Image:chess zhor 26.png
Different types of doubled pawns (from Berliner).

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 (Berliner 1999:18-20).

Value of non-passed pawn in the opening
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
Value of non-passed pawn in the endgame
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
Value of an advanced pawn
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

[edit] 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 (Alburt & Krogius 2005:402-3).
  • 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 (Seirawan 2003:ix).
  • 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 (Berliner 1999:16-20).

C.J.S. Purdy gave minor pieces a value of 3½ points in the opening and middlegame but 3 points in the endgame (Purdy 2003:146, 151).

[edit] See also

[edit] References

[edit] External links