In chess, a relative value (or point value) is a standard value conventionally assigned to each piece. Piece valuations have no role in the rules of chess but are useful as an aid to evaluating a position.
The best-known system assigns 1 point to a pawn, 3 points to a knight or bishop, 5 points to a rook and 9 points to a queen. 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. Such piece values are valid for, and conceptually averaged over, tactically "quiet" positions where immediate tactical gain of material will not happen. [1]
The following table is the most common assignment of point values. [2] [3] [4] [5] [6]
Piece | |||||
Value | 1 | 3 | 3 | 5 | 9 |
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. [8] The value of the king is undefined as it cannot be captured or traded during the course of the game. Chess engines usually assign the king an arbitrary large value such as 200 points or more to indicate that the inevitable loss of the king due to checkmate trumps all other considerations. [9] During the endgame, as there is less danger of checkmate, the king will often assume a more active role. It is better at defending nearby pieces and pawns than the knight is and better at attacking them than the bishop is. [10] Overall, this makes the king more powerful than a minor piece but less powerful than a rook, so its fighting value is about four points. [11] [12]
This system has some shortcomings: namely, combinations of pieces do not always equal the sum of their parts; for instance, two bishops on opposite colours are usually worth slightly more than a bishop plus a knight, and three minor pieces (nine points) are often slightly stronger than two rooks (ten points) or a queen (nine points). [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. This effect causes 3 queens to badly lose against 7 knights (when both start behind a wall of pawns), even though the added piece values predict that the player with the seven knights is two knights short of equality. [15] [1] In a less exotic case, it explains why trading rooks in the presence of a queen-vs-3-minors imbalance favours the player with the queen, as the rooks hinder the movement of the queen more than of the minor pieces. Adding piece values is thus a first approximation, because piece cooperation must also be considered (e.g. opposite-coloured bishops cooperate very well) alongside each piece’s mobility (e.g. a short-range piece far away from the action on a large board is almost worthless). [1]
The evaluation of the pieces depends on many parameters. 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". Nevertheless, he valued the bishop and knight ( minor pieces ) equally, [16] the rook a minor piece plus one or two pawns, and the queen three minor pieces or two rooks. [17] Larry Kaufman suggests the following values in the middlegame:
Piece | |||||
Value | 1 | 3.5 | 3.5 | 5.25 | 10 |
The bishop pair is worth 7.5 pawns – half a pawn more than the values of its constituent bishops combined. Although it would be a very theoretical situation, there is no such bonus for a pair of same-coloured bishops. Per investigations by H. G. Muller, three light-squared bishops and one dark-squared bishop would receive only a 0.5-point bonus, while two on each colour would receive a 1-point bonus. More imbalanced combinations like 3:0 or 4:0, however, were not tested. [18] The position of each piece also makes a significant difference: pawns near the edges are worth less than those near the centre, pawns close to promotion are worth far more, [1] pieces controlling the centre are worth more than average, trapped pieces (such as bad bishops ) are worth less, etc.
Although the 1-3-3-5-9 system of point totals is the most commonly given, many other systems of valuing pieces have been proposed. Several systems treat the bishop as slightly more powerful than a knight. [19] [20]
Note: Where a value for the king is given, this is used when considering piece development, its power in the endgame, etc.
Source | Date | Comment | |||||
---|---|---|---|---|---|---|---|
3.1 | 3.3 | 5.0 | 7.9 | 2.2 | Sarratt [ verification needed ] | 1813 | (rounded) pawns vary from 0.7 to 1.3 [21] |
3.05 | 3.50 | 5.48 | 9.94 | Philidor | 1817 | also given by Staunton in 1847 [22] | |
3 | 3 | 5 | 10 | Peter Pratt | early 19th century | [23] | |
3.5 | 3.5 | 5.7 | 10.3 | Bilguer | 1843 | (rounded) [23] [24] | |
3 | 3 | 5 | 9–10 | 4 | Em. Lasker | 1934 | [25] [26] |
3.5 | 3.5 | 5.5 | 10 | Euwe | 1944 | [27] | |
3.5 | 3.5 | 5.0 | 8.5 | 4 | Em. Lasker | 1947 | (rounded) Kingside rooks and bishops are valued more, queenside ones less [28] [29] 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:
|
3 | 3+ | 5 | 9 | Horowitz | 1951 | The bishop is "3 plus small fraction". [31] [32] | |
3 | 3.5 | 5 | 10 | Turing | 1953 | [33] | |
3.5 | 3.5–3.75 | 5 | 10 | 4 | Evans | 1958 | Bishop is 3.75 if part of a bishop pair [34] [35] |
3.5 | 3.5 | 5 | 9.5 | Styeklov (early Soviet chess program) | 1961 | [36] [37] | |
3 | 3.25 | 5 | 9 | ∞ | Fischer | 1972 | The king's value represents its importance, not its strength. [38] |
3 | 3 | 4.25 | 8.5 | European Committee on Computer Chess, Euwe | 1970s | [39] | |
3 | 3.15 | 4.5 | 9 | Kasparov | 1986 | [40] | |
3 | 3 | 5 | 9–10 | Soviet chess encyclopedia | 1990 | A queen equals three minor pieces or two rooks. [23] | |
4 | 3.5 | 7 | 13.5 | 4 | used by a computer | 1992 | Two bishops are worth more. [23] |
3.20 | 3.33 | 5.10 | 8.80 | Berliner | 1999 | plus adjustments for openness of position, rank & file . [41] | |
3.25 | 3.25 | 5 | 9.75 | Kaufman | 1999 | Add 0.5 points for the bishop pair [42] [43] | |
3.5 | 3.5 | 5.25 | 10 | Kaufman | 2011 | Add 0.5 points for the bishop pair. The values given apply to the middlegame phase only. [44]
| |
3.5 | 3.5 | 5 | 9 | Kurzdorfer | 2003 | [45] | |
3 | 3 | 4.5 | 9 | another popular system | 2004 | [46] | |
2.4 | 4.0 | 6.4 | 10.4 | 3.0 | Yevgeny Gik | 2004 | Based on average mobility; Soltis points out problems with this type of analysis. [47] |
3.05 | 3.33 | 5.63 | 9.5 | AlphaZero | 2020 |
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. He uses "middlegame" to mean positions where both queens are on the board, "threshold" for positions where there is an imbalance (one queen versus none, or two queens versus one), and "endgame" for positions without queens. (Kaufman did not give the queen's value in the middlegame or endgame cases, since in these cases both sides have the same number of queens and their values cancel.) [48]
Game phase | Comments | ||||||||
---|---|---|---|---|---|---|---|---|---|
pawn | knight | bishop | bishop pair bonus | first rook | second rook | queen | second queen | ||
Middlegame | 0.8 | 3.2 | 3.3 | +0.3 | 4.7 | 4.5 | – | – | (both sides have a queen) |
Threshold | 0.9 | 3.2 | 3.3 | +0.4 | 4.8 | 4.9 | 9.4 | 8.7 | (one queen vs. zero, or two queens vs. one) |
Endgame | 1.0 | 3.2 | 3.3 | +0.5 | 5.3 | 5.0 | – | – | (no queens) |
The file of a pawn is also important, because this cannot change except by capture. 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: [48]
centre pawn | bishop pawn | knight pawn | rook pawn |
1 | 0.95 | 0.85 | 0.7 |
In conclusion: [48]
In the endgame: [48]
In the threshold case (queen versus other pieces): [48]
In the middlegame case: [48]
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. [48]
Finally, Kaufman proposes a simplified version that avoids decimals: use the traditional values P = 1, N = 3, B = 3+, and R = 5 with queens off the board, but use P = 1, N = 4, B = 4+, R = 6, Q = 11 when at least one player has a queen. The point is to show that two minor pieces equal rook and two pawns with queens on the board, but only rook and one pawn without queens. [48]
World Correspondence Chess Champion Hans Berliner gives the following valuations, based on experience and computer experiments:
Piece | |||||
Value | 1 | 3.2 | 3.33 | 5.1 | 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 at least 10 percent higher than that of a bad bishop . [49]
a | b | c | d | e | f | g | h | ||
8 | 8 | ||||||||
7 | 7 | ||||||||
6 | 6 | ||||||||
5 | 5 | ||||||||
4 | 4 | ||||||||
3 | 3 | ||||||||
2 | 2 | ||||||||
1 | 1 | ||||||||
a | b | c | d | e | f | g | h |
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 were 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 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. [50]
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 | — | — | 3.5 |
|
|
As already noted when the standard values were first formulated, [51] the relative strength of the pieces will change as a game progresses to the endgame. Pawns gain value as their path towards promotion becomes clear, and strategy begins to revolve around either defending or capturing them before they can promote. 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. Some examples follow.
C.J.S. Purdy gave minor pieces a value of 3+1⁄2 points in the opening and middlegame but 3 points in the endgame. [55]
There are shortcomings of giving each type of piece a single, static value.
a | b | c | d | e | f | g | h | ||
8 | 8 | ||||||||
7 | 7 | ||||||||
6 | 6 | ||||||||
5 | 5 | ||||||||
4 | 4 | ||||||||
3 | 3 | ||||||||
2 | 2 | ||||||||
1 | 1 | ||||||||
a | b | c | d | e | f | g | h |
Positions in which a bishop and knight can be exchanged for a rook and pawn are fairly common (see diagram). In this position, White should not do that, e.g.:
This seems like an even exchange (6 points for 6 points), but it is not, as two minor pieces are better than a rook and pawn in the middlegame. [58]
In most openings, two minor pieces are better than a rook and pawn and are usually at least as good as a rook and two pawns until the position is greatly simplified (i.e. late middlegame or endgame). Minor pieces get into play earlier than rooks, and they coordinate better, especially when there are many pieces and pawns on the board. On the other hand, rooks are usually blocked by pawns until later in the game. [59] Pachman also notes that the bishop pair is almost always better than a rook and pawn. [60]
a | b | c | d | e | f | g | h | ||
8 | 8 | ||||||||
7 | 7 | ||||||||
6 | 6 | ||||||||
5 | 5 | ||||||||
4 | 4 | ||||||||
3 | 3 | ||||||||
2 | 2 | ||||||||
1 | 1 | ||||||||
a | b | c | d | e | f | g | h |
In this position, White has exchanged a queen and a pawn (10 points) for three minor pieces (9 points). 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. [61] Three minor pieces are almost as strong as two rooks. [62]
a | b | c | d | e | f | g | h | ||
8 | 8 | ||||||||
7 | 7 | ||||||||
6 | 6 | ||||||||
5 | 5 | ||||||||
4 | 4 | ||||||||
3 | 3 | ||||||||
2 | 2 | ||||||||
1 | 1 | ||||||||
a | b | c | d | e | f | g | h |
In this position, Black is ahead in material, but White is better. White's queenside is completely defended, and Black's additional queen has no target; additionally, White is much more active than Black and can gradually build up pressure on Black's weak kingside.
In general, the approximate value in centipawns of a short-range leaper with moves on an 8 × 8 board is . The quadratic term reflects the possibility of cooperation between moves. [1]
If pieces are asymmetrical, moves going forward are about twice as valuable as move going sideways or backward, presumably because enemy pieces can generally be found in the forward direction. Similarly, capturing moves are usually twice as valuable as noncapturing moves (of relevance for pieces that do not capture the same way they move). There also seems to be significant value in reaching different squares (e.g. ignoring the board edges, a king and knight both have 8 moves, but in one or two moves a knight can reach 40 squares whereas a king can only reach 24). 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. [1]
An unexpected result from empirical computer studies is that the princess (a bishop-knight compound) and empress (a rook-knight compound) have almost exactly the same value, even though the lone rook is two pawns stronger than the lone bishop. The empress is about 50 centipawns weaker than the queen, and the princess 75 centipawns weaker than the queen. This does not appear to have much to do with the bishop's colourboundedness being masked in the compound, because adding a non-capturing backward step turns out to benefit the bishop about as much as the knight; and it also does not have much to do with the bishop's lack of mating potential being so masked, because adding a backward step (capturing and non-capturing) to the bishop benefits it about as much as adding such a step to the knight as well. A more likely explanation seems to be the large number of orthogonal contacts in the move pattern of the princess, with 16 such contacts for the princess compared to 8 for the empress and queen each: such orthogonal contacts would explain why even in cylindrical chess, the rook is still stronger than the bishop even though they now have the same mobility. This makes the princess extremely good at annihilating pawn chains, because it can attack a pawn as well as the square in front of it. [1]
Chess strategy is the aspect of chess play concerned with evaluation of chess positions and setting goals and long-term plans for future play. While evaluating a position strategically, a player must take into account such factors as the relative value of the pieces on the board, pawn structure, king safety, position of pieces, and control of key squares and groups of squares. Chess strategy is distinguished from chess tactics, which is the aspect of play concerned with the move-by-move setting up of threats and defenses. Some authors distinguish static strategic imbalances, which tend to persist for many moves, from dynamic imbalances, which are temporary. This distinction affects the immediacy with which a sought-after plan should take effect. Until players reach the skill level of "master", chess tactics tend to ultimately decide the outcomes of games more often than strategy. Many chess coaches thus emphasize the study of tactics as the most efficient way to improve one's results in serious chess play.
The king is the most important piece in the game of chess. It may move to any adjoining square; it may also perform, in tandem with the rook, a special move called castling. If a player's king is threatened with capture, it is said to be in check, and the player must remove the threat of capture immediately. If this cannot be done, the king is said to be in checkmate, resulting in a loss for that player. A player cannot make any move that places their own king in check. Despite this, the king can become a strong offensive piece in the endgame or, rarely, the middlegame.
The bishop is a piece in the game of chess. It moves and captures along diagonals without jumping over interfering pieces. Each player begins the game with two bishops. The starting squares are c1 and f1 for White's bishops, and c8 and f8 for Black's bishops.
A chess piece, or chessman, is a game piece that is placed on a chessboard to play the game of chess. It can be either white or black, and it can be one of six types: king, queen, rook, bishop, knight, or pawn.
The endgame is the final stage of a chess game which occurs after the middlegame. It begins when few pieces are left on the board.
This glossary of chess explains commonly used terms in chess, in alphabetical order. Some of these terms have their own pages, like fork and pin. For a list of unorthodox chess pieces, see Fairy chess piece; for a list of terms specific to chess problems, see Glossary of chess problems; for a list of named opening lines, see List of chess openings; for a list of chess-related games, see List of chess variants; for a list of terms general to board games, see Glossary of board games.
Zugzwang is a situation found in chess and other turn-based games wherein one player is put at a disadvantage because of their obligation to make a move; a player is said to be "in zugzwang" when any legal move will worsen their position.
Checkmate is any game position in chess and other chess-like games in which a player's king is in check and there is no possible escape. Checkmating the opponent wins the game.
The middlegame is the portion of a chess game between the opening and the endgame. It is generally considered to begin when each player has completed the development of all or most of their pieces and brought their king to relative safety, and it is generally considered to end when only a few pieces remain on the board. However, there is no clear line between the opening and middlegame or between the middlegame and endgame. At master level, the opening analysis may go well into the middlegame; likewise, the middlegame blends into the endgame.
In chess, a tactic is a sequence of moves that each makes one or more immediate threats – a check, a material threat, a checkmating sequence threat, or the threat of another tactic – that culminates in the opponent's being unable to respond to all of the threats without making some kind of concession. Most often, the immediate benefit takes the form of a material advantage or mating attack; however, some tactics are used for defensive purposes and can salvage material that would otherwise be lost, or to induce stalemate in an otherwise lost position.
In chess, an isolated pawn is a pawn that has no friendly pawn on an adjacent file. Isolated pawns are usually a weakness because they cannot be protected by other pawns. The square in front of the pawn may become a good outpost for the opponent to anchor pieces. Isolated pawns most often become weaker in the endgame, as there are fewer pieces available to protect the pawn.
The empress is a fairy chess piece that can move like a rook or a knight. It cannot jump over other pieces when moving as a rook but may do so when moving as a knight. The piece has acquired many names and is frequently called a chancellor or a marshal.
The princess is a fairy chess piece that can move like a bishop or a knight. It cannot jump over other pieces when moving as a bishop but may do so when moving as a knight. The piece has acquired many names and is frequently called an archbishop, a cardinal, or a dragon; it may also simply be called the bishop+knight compound.
In chess, the exchange is the material difference of a rook for a minor piece. Having a rook for a minor piece is generally advantageous, since the rook is usually more valuable. A player who has a rook for a minor piece is said to be up the exchange, and the other player is down the exchange. A player who wins a rook for a minor piece is said to have won the exchange, while the other player has lost the exchange. The opposing captures often happen on consecutive moves, but this is not strictly necessary. Although it is generally detrimental to lose the exchange, one may occasionally find reason to purposely do so; the result is an exchange sacrifice.
In chess, a fortress is an endgame drawing technique in which the side behind in material sets up a zone of protection that the opponent cannot penetrate. This might involve keeping the enemy king out of one's position, or a safe zone the enemy cannot force one out of. An elementary fortress is a theoretically drawn position with reduced material in which a passive defense will maintain the draw.
A pawnless chess endgame is a chess endgame in which only a few pieces remain, and no pawns. The basic checkmates are types of pawnless endgames. Endgames without pawns do not occur very often in practice except for the basic checkmates of king and queen versus king, king and rook versus king, and queen versus rook. Other cases that occur occasionally are (1) a rook and minor piece versus a rook and (2) a rook versus a minor piece, especially if the minor piece is a bishop.
Much literature about chess endgames has been produced in the form of books and magazines. A bibliography of endgame books is below.
The game of chess is commonly divided into three phases: the opening, middlegame, and endgame. There is a large body of theory regarding how the game should be played in each of these phases, especially the opening and endgame. Those who write about chess theory, who are often also eminent players, are referred to as "chess theorists" or "chess theoreticians".
In chess, several checkmate patterns occur frequently enough to have acquired specific names in chess commentary. By definition, a checkmate pattern is a recognizable/particular/studied arrangements of pieces that delivers checkmate. The diagrams that follow show these checkmates with White checkmating Black.
The following outline is provided as an overview of and topical guide to chess:
Bibliography