Chess piece point value - AbsoluteAstronomy.com

Chess

Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...

, the chess piece relative value system conventionally assigns a point value to each piece when assessing its relative strength in potential exchanges

Exchange (chess)

In the tactics and strategy in the board game of chess, an exchange or trade of chess pieces is series of closely related moves, typically sequential, in which the two players capture each others pieces. Any types of pieces except the kings may possibly be exchanged, i. e. captured in an...

. These values are used as a heuristic

Heuristic

Heuristic refers to experience-based techniques for problem solving, learning, and discovery. Heuristic methods are used to speed up the process of finding a satisfactory solution, where an exhaustive search is impractical...

that helps determine how valuable a piece is strategically. They play no formal role in the game but are useful to players, and are also used in computer chess

Computer chess

Computer chess is computer architecture encompassing hardware and software capable of playing chess autonomously without human guidance. Computer chess acts as solo entertainment , as aids to chess analysis, for computer chess competitions, and as research to provide insights into human...

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'(cp), where 100 cp = 1 pawn, which allows strategic features of the position, worth less than a single pawn, to be evaluated without requiring fractions.

Edward Lasker

Edward Lasker

Edward Lasker was a leading German-American chess and Go player. He was awarded the title of International Master of chess by FIDE. Lasker was an engineer by profession, and an author.-Background:...

said "It is difficult to compare the relative value of different pieces, as so much depends on the peculiarities of the position...". Nevertheless, he said that bishops and knights (minor pieces) were equal, rooks are worth a minor piece plus one or two pawns, and a queen is worth three minor pieces or two rooks .

Standard valuations

The following is the most common assignment of point values , , , .

Pieces	Symbol	Value
pawn Pawn (chess) The pawn is the most numerous and weakest piece in the game of chess, historically representing infantry, or more particularly armed peasants or pikemen. Each player begins the game with eight pawns, one on each square of the rank immediately in front of the other pieces...		1
knight Knight (chess) The knight is a piece in the game of chess, representing a knight . It is normally represented by a horse's head and neck. Each player starts with two knights, which begin on the row closest to the player, one square from the corner...		3
bishop Bishop (chess) A bishop is a piece in the board game of chess. Each player begins the game with two bishops. One starts between the king's knight and the king, the other between the queen's knight and the queen...		3
rook Rook (chess) A rook is a piece in the strategy board game of chess. Formerly the piece was called the castle, tower, marquess, rector, and comes...		5
queen Queen (chess) The queen is the most powerful piece in the game of chess, able to move any number of squares vertically, horizontally, or diagonally. Each player starts the game with one queen, placed in the middle of the first rank next to the king. With the chessboard oriented correctly, the white queen starts...		9

The oldest derivation of the standard values is due to the Modenese School (Ercole del Rio

Ercole del Rio

Domenico Ercole del Rio was an Italian lawyer and author. He published an 110-page chess book in 1750 which was the basis of a work by Giambattista Lolli thirteen years later. He composed many chess problems. He was one of the Modenese Masters.-References:...

, Giambattista Lolli

Giambattista Lolli

Giambattista Lolli was an Italian chess player. Lolli was one of the most important chess theoreticians of his time. He is most famous for his book Osservazioni teorico-pratiche sopra il giuoco degli scacchi , published 1763 in Bologna...

, and Domenico Lorenzo Ponziani

Domenico Lorenzo Ponziani

Domenico Lorenzo Ponziani was an 18th-century Italian law professor, priest, chess player, composer and theoretician. He is best known today for his chess writing.-Life:...

) in the 18th century and is partially based on the earlier work of Pietro Carrera

Pietro Carrera

Pietro Carrera, chess player, historian, priest and author, born in Sicily, in Militello in Val di Catania , located in the Valley of Noto; here he grew up in the old colony of San Vito. He was born on July 12, 1573, he was the son of Donna Antonia Severino and Mariano Carrera, a traditional...

. The value of the king

King (chess)

In chess, the king is the most important piece. The object of the game is to trap the opponent's king so that its escape is not possible . 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 on the next move. If this cannot be...

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 . In the endgame, when there is little danger of checkmate, the fighting value of the king is about four points . 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 .

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

Although 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.

Several systems give the bishop slightly more value than the knight. A bishop is usually slightly more powerful than a knight, but not always – it depends on the position , . A chess-playing program was given the value of 3 for the knight and 3.4 for the bishop, but that large of a difference was acknowledged to not be real .

Alternate systems, with pawn = 1
					Source	Date	Comment
3.1	3.3	5.0	7.9	2.2	Sarratt? Jacob Sarratt Jacob Henry Sarratt was one of the top English chess players of the late 18th and early 19th century. Sarratt was renowned as a player and author and adopted the title "Professor of Chess" . He was the first professional player to teach chess in England...	1813	(rounded) pawns vary from 0.7 to 1.3
3.05	3.50	5.48	9.94		Philidor François-André Danican Philidor François-André Danican Philidor , often referred to as André Danican Philidor during his lifetime, was a French composer and chess player. He contributed to the early development of the opéra comique...	1817	also given by Staunton in 1847
3	3	5	10		Peter Pratt	early 19th century
3.5	3.5	5.7	10.3		Bilguer Paul Rudolf von Bilguer Paul Rudolf von Bilguer was a German chess master and chess theoretician from Ludwigslust, Mecklenburg-Schwerin....	1843	(rounded)
3	3	5	9-10	4	Lasker Emanuel Lasker Emanuel Lasker was a German chess player, mathematician, and philosopher who was World Chess Champion for 27 years...	1934
3½	3½	5½	10		Euwe Max Euwe Machgielis Euwe was a Dutch chess Grandmaster, mathematician, and author. He was the fifth player to become World Chess Champion . Euwe also served as President of FIDE, the World Chess Federation, from 1970 to 1978.- Early years :Euwe was born in Watergraafsmeer, near Amsterdam...	1944
3½	3½	5	8½	4	Lasker	1947	(rounded) Kingside rooks and bishops are valued more, queenside ones less
3	3+	5	9		Horowitz	1951	The bishop is "3 plus small fraction"
3½	3½+	5	10	4	Evans Larry Evans For the football player of the same name, see Larry Evans .Larry Melvyn Evans was an American chess grandmaster, author, and journalist. He won or shared the U.S. Chess Championship five times and the U.S. Open Chess Championship four times...	1958	Bishop is 3¾ if in the bishop pair
3	3¼	5	9		Fischer Bobby Fischer Robert James "Bobby" Fischer was an American chess Grandmaster and the 11th World Chess Champion. He is widely considered one of the greatest chess players of all time. Fischer was also a best-selling chess author...	1972
3	3	4½	8½		European Committee on Computer Chess, Euwe	1970s
3	3	5	9-10		Soviet chess encyclopedia	1990	A queen equals three minor pieces or two rooks
3¼	3¼	5	9¾		Kaufman Larry Kaufman Lawrence C. "Larry" Kaufman is a Grandmaster of chess. He is also a mathematics professor and currently lives in Potomac, Maryland. In 2008, as an International Master, Kaufman won the World Senior Championship which automatically earned him the Grandmaster title.A long time researcher in...	1999	Add ½ point for the bishop pair
3.20	3.33	5.10	8.80		Berliner Hans Berliner Hans Jack Berliner , a Professor of , is a former World Correspondence Chess Champion, from 1965–68. He is a Grandmaster of Correspondence Chess, and an International Master for over-the-board chess. He directed the construction of the chess computer HiTech. Berliner is also a chess writer.-Life...	1999	plus adjustments for openness of position, rank & file
3½	3½	5	9		Kurzdorfer	2003
3½	3½	5	9½				early Soviet chess program
3	3	4½	9				another popular system
4	3½	7	13½	4	used by a computer		Two bishops are worth more
2.4	4.0	6.4	10.4	3.0	Yevgeny Gik		based on average mobility; pointed out problems with this type of analysis

Hans Berliner's system

World Correspondence Chess

Correspondence chess

Correspondence chess is chess played by various forms of long-distance correspondence, usually through a correspondence chess server, through email or by the postal system; less common methods which have been employed include fax and homing pigeon...

Champion Hans Berliner

Hans Berliner

Hans Jack Berliner , a Professor of , is a former World Correspondence Chess Champion, from 1965–68. He is a Grandmaster of Correspondence Chess, and an International Master for over-the-board chess. He directed the construction of the chess computer HiTech. Berliner is also a chess writer.-Life...

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 at least 10 percent higher than that of a bad bishop .
There are different types of doubled pawns

Doubled pawns

In chess, doubled pawns are two pawns of the same color residing on the same file. Pawns can become doubled only when one pawn captures onto a file on which another friendly pawn resides. In the diagram, the pawns on the b-file and e-file are doubled...

, 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 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 .

Value of non-passed pawn
Passed pawn
In chess, a passed pawn is a pawn with no opposing pawns to prevent it from advancing to the eighth rank, i.e. there are no opposing pawns in front of it on the same file nor on an adjacent file. A passed pawn is sometimes colloquially called a passer...

in the opening
Chess opening
A chess opening is the group of initial moves of a chess game. Recognized sequences of opening moves are referred to as openings as initiated by White or defenses, as created in reply by Black. There are many dozens of different openings, and hundreds of named variants. The Oxford Companion to...
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 pawn advances (multiplier of base amount)>

Rank	Isolated Isolated pawn In chess, an isolated pawn is a pawn which has no friendly pawn on an adjacent file. An isolated queen's pawn is often called an isolani. Isolated pawns are usually a weakness because they cannot be protected by other pawns...	Connected Connected pawns In chess, connected pawns are two or more pawns of the same color on adjacent files, as distinct from isolated pawns. These pawns are instrumental in creating pawn structure because, when diagonally adjacent, like the two rightmost white pawns, they form a pawn chain, a chain where the one behind...	Passed Passed pawn In chess, a passed pawn is a pawn with no opposing pawns to prevent it from advancing to the eighth rank, i.e. there are no opposing pawns in front of it on the same file nor on an adjacent file. A passed pawn is sometimes colloquially called a passer...	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

As already noted when the standard values were firstly formulated , the relative strength of the pieces changes as a game progresses to the endgame. The value of pawns, rooks and, to a lesser extent, bishops may increase. 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
Chess opening
A chess opening is the group of initial moves of a chess game. Recognized sequences of opening moves are referred to as openings as initiated by White or defenses, as created in reply by Black. There are many dozens of different openings, and hundreds of named variants. The Oxford Companion to...

. 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
Promotion (chess)
Promotion is a chess rule describing the transformation of a pawn that reaches its eighth rank into the player's choice of a queen, knight, rook, or bishop of the same color . The new piece replaces the pawn on the same square and is part of the move. Promotion is not limited to pieces that have...

. 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 .

C.J.S. Purdy

Cecil Purdy

Cecil John Seddon Purdy was an Australian chess International Master and inaugural World Correspondence Chess champion. Purdy earned the Grandmaster title at Correspondence Chess in 1953...

gave minor pieces a value of 3½ points in the opening and middlegame but 3 points in the endgame .

Shortcomings of the system

There are shortcomings of the system. For instance, 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.

1. Nxf7? Rxf7

2. Bxf7+ Kxf7

This seems like an even exchange (six points for six points), but it is not because two minor pieces are better than a rook and pawn in the middlegame . Pachman

Ludek Pachman

Luděk Pachman was a Czechoslovak-German chess grandmaster, chess writer, and political activist. In 1972, after being imprisoned and tortured almost to death by the Communist regime in Czechoslovakia, he was allowed to emigrate to West Germany...

also notes that two bishops are almost always better than a rook and pawn .

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. Rooks are usually developed later and are often blocked by pawns until later in the game .
This situation in this position is not very common, but White has exchanged a queen (nine points) for three minor pieces and a pawn (ten points). Three minor pieces are usually better than a queen because of their greater mobility, and the extra pawn is not important enough to change the situation . Three minor pieces are almost as strong as two rooks .

Two minor pieces plus two pawns are almost always as good as a queen. Two rooks are better than a queen and pawn .

Many of the systems have a two-point difference between the rook and a minor piece, but most theorists

Chess theory

The game of chess is commonly divided into three phases: the opening, middlegame, and endgame. As to each of these phases, especially the opening and endgame, there is a large body of theory as how the game should be played...

put that difference at about 1½ points, see The exchange (chess)#Value of the exchange.

In open positions, a rook plus a pair of bishops is stronger than two rooks plus a knight .

External links

Relative Value of Chess Pieces
Relative Value of Pieces and Principles of Play from The Modern Chess Instructor by Wilhelm Steinitz
Wilhelm Steinitz
Wilhelm Steinitz was an Austrian and then American chess player and the first undisputed world chess champion from 1886 to 1894. From the 1870s onwards, commentators have debated whether Steinitz was effectively the champion earlier...
About the Values of Chess Pieces by Ralph Betza, 1996.
Larry Kaufman article
some historical evaluations