Chess piece point value

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In chess, the chess pieces are often assigned certain point values 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.

Contents

[edit] Standard valuations

The following is the most common assignment of point values (Capablanca and 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 infinite since 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 (Lasker 1934:73).

This system has some shortcomings. For instance, three minor pieces (nine points) are slightly stronger than two rooks (ten points) (Capablanca and de Firmian 2006:24), (Fine and Benko 2003:458).

[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 increases, and the value of bishops increases to a lesser extent. The knight loses power and the strength of the queen decreases somewhat. Some examples follow (Alburt and Krogius, 2005:402-3).

  • 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.

[edit] Alternate valuations

Grandmaster Larry Evans gives the values pawn = 1 point, knight = 3½ points, bishop = 3¾ points, rook = 5 points, and queen = 10 points (Evans 1967:73, 76). (He 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 (Evans 1967:73, 76). 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, and 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 knight = 3½, bishop = 3½, rook = 5, and queen = 9½. Another popular system is knight = 3, bishop = 3, rook = 4½, queen = 9 (Soltis 2004:6).

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 1/8 for each pawn above five of the side being valued, with the opposite adjustment for each pawn short of five." (Kaufman 1999)

[edit] Historical valuations

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

  • Knight 9.25
  • Bishop 9.75
  • Rook 15
  • Queen 23.75
  • King as attack piece (in the endgame) 6.5
  • Pawn 2 at the start, 3.75 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's The Chess-Player's Handbook gives these values, rounded slightly:

  • Pawn 1
  • Knight 3
  • Bishop 3.5
  • Rook 5.5
  • Queen 10

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 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 (Soltis 2004:10-12).

[edit] See also

[edit] References

  •   Lasker, Emanuel (1934). Lasker's Chess Primer. Billings (1988 reprint).
  • 80-Square Chess, E. Trice in ICGA Journal Vol. 27, No. 2 - June 2004, p. 81-96.

[edit] External links

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