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Hub AI
Chess piece relative value AI simulator
(@Chess piece relative value_simulator)
Hub AI
Chess piece relative value AI simulator
(@Chess piece relative value_simulator)
Chess piece relative value
In chess, a relative value (or point value) is a numerical value conventionally assigned to each piece. Piece valuations have no role in the rules of chess but are useful as an aid to evaluating an exchange of pieces.
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 the queen. For instance, sacrificing a knight or bishop under such an evaluation can still be considered a fair exchange if one can ensure the capture of three or more pawns in return. But valuation systems provide only a rough guide; a piece's true value can vary significantly depending on its board position relative to a player's other pieces and the opponent's pieces.
Piece values exist because calculating to checkmate in most positions is beyond even 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.
The following table is the most common assignment of point values.
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 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 loss of the king due to checkmate trumps all other considerations. 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. 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.
This system has some shortcomings. Combinations of pieces are not always worth the sum of their parts; for instance, two bishops on opposite colours are usually more valuable than a bishop and 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 reduces stronger pieces' value in the presence of opponent weaker pieces, as the latter interdict access to part of the board for the former to prevent the value difference from evaporating by 1-for-1 trading. This effect causes three queens to badly lose to seven knights (when both start behind a wall of pawns), even though three times nine is six more than seven times three. In a less exotic case, 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 from the action on a large board is almost worthless).
The evaluation of the pieces depends on many parameters. Edward Lasker wrote, "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, the rook a minor piece plus one or two pawns, and the queen three minor pieces or two rooks. Kaufman suggests the following values in the middlegame:
Paired bishops are worth 7.5 pawns—half a pawn more than the values of the 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 were not tested. 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, pieces controlling the centre are worth more than average, trapped pieces (such as bad bishops) are worth less, etc.
Chess piece relative value
In chess, a relative value (or point value) is a numerical value conventionally assigned to each piece. Piece valuations have no role in the rules of chess but are useful as an aid to evaluating an exchange of pieces.
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 the queen. For instance, sacrificing a knight or bishop under such an evaluation can still be considered a fair exchange if one can ensure the capture of three or more pawns in return. But valuation systems provide only a rough guide; a piece's true value can vary significantly depending on its board position relative to a player's other pieces and the opponent's pieces.
Piece values exist because calculating to checkmate in most positions is beyond even 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.
The following table is the most common assignment of point values.
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 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 loss of the king due to checkmate trumps all other considerations. 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. 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.
This system has some shortcomings. Combinations of pieces are not always worth the sum of their parts; for instance, two bishops on opposite colours are usually more valuable than a bishop and 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 reduces stronger pieces' value in the presence of opponent weaker pieces, as the latter interdict access to part of the board for the former to prevent the value difference from evaporating by 1-for-1 trading. This effect causes three queens to badly lose to seven knights (when both start behind a wall of pawns), even though three times nine is six more than seven times three. In a less exotic case, 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 from the action on a large board is almost worthless).
The evaluation of the pieces depends on many parameters. Edward Lasker wrote, "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, the rook a minor piece plus one or two pawns, and the queen three minor pieces or two rooks. Kaufman suggests the following values in the middlegame:
Paired bishops are worth 7.5 pawns—half a pawn more than the values of the 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 were not tested. 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, pieces controlling the centre are worth more than average, trapped pieces (such as bad bishops) are worth less, etc.