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50-399: White prepares to exchange the bishop for Black's knight, inflicting doubled pawns upon Black in the process. This is not a lethal threat; Black can choose to fall in with White's plan. The Trompowsky is a popular alternative to the more common lines after 1.d4 Nf6 beginning 2.c4 or 2.Nf3. By playing 2.Bg5, White sidesteps immense bodies of opening theory of various Indian Defences like

100-433: A bad bishop . 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

150-405: A passed pawn . Exchanges of pawns or other pieces are often made or avoided to prevent such deficiencies or to obtain a pawn structure advantage. If an opponent moves a pawn into a position diagonally adjacent to a player's pawn, effectively offering an exchange of pawns, sometimes it is possible to avoid a disadvantageous pawn exchange by moving the attacked pawn directly forward instead of taking

200-403: A queen is valued at about 9. Since the king is indispensable, it has infinite value. Pieces, especially as distinguished by their value, are often referred to collectively as material in chess. These values are not absolute because the usefulness of a piece also depends on its position in a particular game, commonly in a way hard to quantify. For example, an advanced passed pawn with

250-415: 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 assessing 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 . However, valuation systems provide only a rough guide and the true value of

300-655: A sacrifice is the deliberate giving up of a piece by a player, allowing or forcing an opponent to capture the piece or exchange it for a lower value piece. In a desperado situation, a trapped piece which would inevitably be lost can sometimes be exchanged for another piece, even if it has lower value, in order to minimize net material loss for the player having the inevitably lost piece. Exchanges of chess pieces are commonly involved in chess tactics and strategy. Exchanges can appear in connection with practically any kind of attacking or defensive chess tactic or combination of tactics. Such tactics can involve checkmating

350-415: 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). 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

400-541: A bishop to have slightly more value than a knight, especially in open positions, or consider that a knight is better than a bishop in closed positions, and may make or avoid exchanges accordingly. Exchanges may be made to clear out pieces to be relieved from cramped situations or incur other positional advantages or avoid positional disadvantages. Pawn structure is commonly important in positional chess. Deficiencies in pawn structure can include having doubled pawns or isolated pawns . A positional advantage can be having

450-433: 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

500-407: A game. The exchange of a rook for bishop or knight is an uneven exchange because a rook is generally more valuable than a bishop or knight . A minor exchange is a less commonly used term which refers to the exchange of a bishop for a knight. A player's objective in a chess game is to checkmate the opponent's king and/or to avoid checkmate of his own king. In this ultimate sense,

550-520: A good probability of promotion is commonly more valuable in a particular situation than a backward or isolated pawn that is not a passed pawn. A forced exchange is an exchange in a position where one of the players is required to initiate or undergo an exchange, either because no alternative play is allowed by chess rules or because the consequence of not making the exchange would be unacceptably detrimental to that player's game. Many exchanges can be offered, but they are not forced. In such cases,

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600-407: A king, rook, and bishop or knight may try to exchange rooks leading to a draw because a king and lone bishop or knight cannot force checkmate. Often an exchange or a series of them are used to set up a tactic. Often an attacking player initiates an attack by making the first capture in a series of exchanges leading to a tactical trap; the opponent recaptures to avoid material loss but can fall prey to

650-663: A number of ways to meet the Trompowsky, some of which avoid doubled pawns, while others allow them. The most common Black responses are discussed here. White can also play 2.Bg5 after 1.d4 d5. This is known as the Pseudo-Trompowsky, Hodgson Attack , Levitsky Attack, Queen's Bishop Attack, and Bishop Attack, and is covered in ECO code D00. Play transposes to the Trompowsky if Black plays 2...Nf6. Exchange (chess) In chess , an exchange or trade of chess pieces

700-501: A piece is very position dependent. Piece values exist because calculating all the way to checkmate in most positions is beyond the reach even of top computers. Thus players aim primarily to create a material advantage, and to chase this goal it is necessary 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. The following table

750-461: A specific square is defended by one or more of his other pieces. This typically means that if an opponent's piece captures the defended piece, the capturing piece would be subject to recapture by a defending piece ( defender ). An opponent's piece in a position to capture a given piece could be considered an attacking piece ( attacker ). Positions could develop where a player's piece on a square has one or more attackers and one or more defenders. This

800-508: Is V = 33 N + 0.7 N 2 {\displaystyle V=33N+0.7{N}^{2}} . The quadratic term reflects the possibility of cooperation between moves. 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

850-406: Is a common way in which exchanges could occur, although there are other ways also. In such positions, a player with the attacking piece(s) may decide whether it is worthwhile for him to initiate a capture likely to result in recapture, likely decided by the value of the pieces to be taken in the ensuing exchange. Pinned pieces often cannot be counted on being attackers or defenders. In chess,

900-401: Is a series of closely related moves, typically sequential, in which the two players capture each other's pieces. Any type of pieces except the kings may possibly be exchanged, i.e. captured in an exchange, although a king can capture an opponent's piece. Either the player of the white or the black pieces may make the first capture of the other player's piece in an exchange, followed by

950-438: 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 V {\displaystyle V} in centipawns of a short-range leaper with N {\displaystyle N} moves on an 8 × 8 board

1000-435: Is better at defending such pieces than the knight is, and it is better at attacking them than the bishop is. Overall, this makes it more powerful than a minor piece but less powerful than a rook, so its fighting value is worth about four points. This system has some shortcomings. Combinations of pieces do not always equal the sum of their parts; for instance, two bishops on opposite colors are usually worth slightly more than

1050-468: Is difficult to compare the relative value of different pieces, as so much depends on the peculiarities of the position...". Nevertheless, he said that the bishop and knight ( minor pieces ) are equal, the rook is worth a minor piece plus one or two pawns, and the queen is worth three minor pieces or two rooks. Larry Kaufman suggests the following values in the middlegame : Pawn Knight Bishop Rook Queen The bishop pair

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1100-504: Is equal in a certain situation, some players may consider that having two bishops, which can cover both dark and light squares, is advantageous over having just one bishop which can cover only half the squares, and so may exchange or avoid exchange to obtain or maintain such an advantage. A player may decide to take an opponent's well-posted or well- developed pieces in exchange for undeveloped, poorly developed, immobile, or otherwise poorly posted pieces of his/her own. Some may consider

1150-491: Is the most common assignment of point values. 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 and is partially based on the earlier work of Pietro Carrera . The value of the king is undefined as it cannot be captured, let alone traded, during

1200-445: Is worth 7.5 pawns – half a pawn more than the individual 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 one would receive only a 0.5-point bonus, while two on each colour would receive a 1-point bonus. Thus, one could rather think of it as penalising

1250-524: 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. As already noted when the standard values were first formulated, 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

1300-461: 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

1350-576: The Queen's Indian , King's Indian , Nimzo-Indian , as well as the Grünfeld Defence . The opening is named after the one-time Brazilian champion Octávio Trompowsky (1897–1984) who played it in the 1930s and 1940s. Chess master Karel Opočenský (1892–1975) also played it in the 1930s, and the opening is also known as the Opočenský Opening. Also, chess master William Allen Ruth developed

1400-430: The middlegame . 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

1450-423: 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 have the bishop as usually being slightly more powerful than a knight. Note: Where a value for the king is given, this is used when considering piece development, its power in the endgame, etc. Lasker adjusts some of these depending on the starting positions, with pawns nearer

1500-409: The absence of a piece, though more imbalanced combinations like 3:0 or 4:0 were not tested.) The position of the pieces also makes a significant difference, e.g. pawns near the edges are worth less than those near the centre, pawns close to promotion are worth far more, pieces controlling the centre are worth more than average, trapped pieces (such as bad bishops ) are worth less, etc. Although

1550-442: 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. 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

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1600-476: 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. 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

1650-409: 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. The endgame is a different story, as there is less danger of checkmate , allowing the king to take a more active role. The king is good at attacking and defending nearby pieces and pawns. It

1700-428: The endgame. There are shortcomings of giving each type of piece a single, static value. Two minor pieces plus two pawns are sometimes as good as a queen. Two rooks are sometimes better than a queen and pawn. Many of the systems have a 2-point difference between the rook and a minor piece , but most theorists put that difference at about 1 + 1 ⁄ 2 points (see The exchange (chess) § Value of

1750-404: The endgame: In the threshold case (queen versus other pieces): In the middlegame case: The above is written for around ten pawns on the board (a normal number); the value of the rooks goes down as pawns are added, and goes up as pawns are removed. 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

1800-406: The exchange ). In some open positions, a rook plus a pair of bishops are stronger than two rooks plus a knight. 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

1850-477: The game. Pachman also notes that the bishop pair is almost always better than a rook and pawn. 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. Three minor pieces are almost as strong as two rooks. In this position, Black

1900-402: The higher-valued piece can be said to be up the exchange or wins the exchange , while the opponent who captures the lower-valued piece is down the exchange or loses the exchange . Exchanges occur very frequently in chess, in almost every game and usually multiple times per game. Exchanges are often related to the tactics or strategy in a chess game, but often simply occur over the course of

1950-490: The offered pawn. However, one may also consider making exchanges of pawns or other pieces to open up a file for one's rooks and queen or opening up a diagonal for one's bishop and queen, even if a pawn deficiency is incurred. If a player gains material superiority in a game, a strategy can involve making even exchanges to eliminate other pieces for simplification to make the superiority more decisive. The opponent with less material may try to avoid exchanges, but then

2000-633: The opening simultaneously in the 1930s, and it was well-known by locals in Pennsylvania as the Ruth Opening. The Trompowsky has also been called the Zot. Julian Hodgson , Antoaneta Stefanova , and Arjun Erigaisi are among several grandmasters who often employ the Trompowsky. World Champion Magnus Carlsen has occasionally employed the Trompowsky, notably in the first game of the 2016 World Chess Championship against Sergey Karjakin . Black has

2050-411: The opponent, avoiding checkmate, gaining a material advantage, avoid losing more material than necessary, helping a pawn to promote, preventing an opponent's pawn promotion, or setting up a draw by any of a couple methods. Some tactics can lead to draw by stalemate , threefold repetition , or insufficient material to checkmate. For example, a player with a king and rook against an opponent with

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2100-405: The other player capturing a piece of the first player, often referred to as a recapture . Commonly, the word "exchange" is used when the pieces exchanged are of the same type or of about equal value, which is an even exchange . According to chess tactics , a bishop and a knight are usually of about equal value. If the values of the pieces exchanged are not equal, then the player who captures

2150-410: The player presented with the possibility of an exchange may decide to make the initial capture, may decline making the initial capture, or may even move to avoid the exchange. The player can weigh the advantages and disadvantages of each move to decide. For a prospective uneven exchange, the values of the pieces are often the deciding factor. Chess positions are often set up where a player's piece on

2200-419: The player with more material may try to force exchanges anyway. Strong players commonly play a materially even game with each other, often clearing out their pieces with even exchanges to transition from middlegame to the endgame . An exchange variation is a type of opening in which there is an early, voluntary exchange of pawns and/or other pieces. Chess piece relative value In chess ,

2250-414: The queen's value in the middlegame or endgame cases, since in these cases both sides have the same number of queens and it cancels out.) 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: In conclusion: In

2300-423: The queen, but not so much the minors. Adding piece values thus is a first approximation, because one must also consider how well pieces cooperate with each other (e.g. opposite-coloured bishops cooperate very well), and how fast the piece travels (e.g. a short-range piece far away from the action on a large board is almost worthless). The evaluation of the pieces depends on many parameters. Edward Lasker said, "It

2350-411: 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

2400-465: The trap. Exchanges are often made to try to improve a position from a strategic point of view. Since positional advantages are often smaller than those due to difference in material value, exchanges to gain a positional advantage are commonly even exchanges in terms of material. A player may undertake an exchange to capture an opponent's piece having better positional value than the piece that will be lost. For example, even if overall material count

2450-408: 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 knights player is two knights short of equality. In a less exotic case it explains why trading rooks in the presence of a queen-vs-3-minors imbalance favors the queen player, as the rooks hinder

2500-402: The value of chess pieces remaining in a game does not matter. Although no official score is kept of the value of pieces on the board for each player, much experience in chess play has determined approximate average strategic and tactical value of various pieces relative to a pawn , which is given a value of 1. Bishops and knights have about the same value at 3, rooks are valued at about 5, and

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