Valuation systems, however, provide only a rough guide; the true value of a piece can vary significantly depending on position.
Piece values exist because calculating to checkmate in most positions is beyond reach even for top computers.
Thus, players aim primarily to create a material advantage; to pursue this goal, it is normally helpful to quantitatively approximate the strength of an army of pieces.
[2][3][4][5][6] Pawn Knight Bishop Rook Queen The oldest derivation of the standard values is due to the Modenese School (Ercole del Rio, Giambattista Lolli, and Domenico Lorenzo Ponziani) in the 18th century[7] and is partially based on the earlier work of Pietro Carrera.
[13][14] Chess-variant theorist Ralph Betza identified the 'leveling effect', which causes reduction of the value of stronger pieces in the presence of opponent weaker pieces, due to the latter interdicting access to part of the board for the former in order to prevent the value difference from evaporating by 1-for-1 trading.
Edward Lasker stated that "It is difficult to compare the relative value of different pieces, as so much depends on the peculiarities of the position".
Lasker adjusts some of these depending on the starting positions, with pawns nearer the centre, with bishops and rooks on the kingside, being worth more: Larry Kaufman in 2021 gives a more detailed system based on his experience working with chess engines, depending on the presence or absence of queens.
According to Kaufman, the difference is small in the endgame (when queens are absent), but in the middlegame (when queens are present) the difference is substantial:[49] In conclusion:[49] In the endgame:[49] In the threshold case (queen versus other pieces):[49] In the middlegame case:[49] The above is written for around ten pawns on the board (a typical number); the value of the rooks goes down as pawns are added, and goes up as pawns are removed.
[49] World Correspondence Chess Champion Hans Berliner gives the following valuations, based on experience and computer experiments: Pawn Knight Bishop Rook Queen 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.
[51] As already noted when the standard values were first formulated,[52] the relative strength of the pieces will change as a game progresses to the endgame.
Knights lose value as their unique mobility becomes a detriment to crossing an empty board.
Rooks and (to a lesser extent) bishops gain value as their lines of movement and attack are less obstructed.
Queens slightly lose value as their high mobility becomes less proportionally useful when there are fewer pieces to attack and defend.
Positions in which a bishop and knight can be exchanged for a rook and pawn are fairly common (see diagram).
White is better because three minor pieces are usually better than a queen because of their greater mobility, and Black's extra pawn is not important enough to change the situation.
It is also valuable for a piece to have moves to squares that are orthogonally adjacent, as this enables it to wipe out lone passed pawns (and also checkmate the king, but this is less important as usually enough pawns survive to the late endgame to allow checkmate to be achieved via promotion).
As many games are decided by promotion, the effectiveness of a piece in opposing or supporting pawns is a major part of its value.