BishBosh.Evaluation.Fitness

AUTHOR

Dr. Alistair Ward

DESCRIPTION

• Quantifies the fitness of a game.
• By measuring the fitness from the perspective of the player who just moved (rather than the next player to move), an automated player can test various moves & select the fittest.

Types

Constants

maximumDefended :: NPieces

• The constant maximum total number of times the pieces of either side, can be defended.
• Assumes all Pawns have been Queened.
• CAVEAT: assuming the optimal arrangement of pieces:

RQQB = 3 + 7 + 3 + 2 = 15 QQQN = 4 + 6 + 8 + 4 = 22 NQQK = 4 + 8 + 6 + 0 = 18 BQQR = 2 + 3 + 7 + 3 = 15 = 70

Functions

measurePieceSquareValue :: Num pieceSquareValue => PieceSquareByCoordinatesByRank pieceSquareValue -> Game -> pieceSquareValue

Measures the piece-square value from the perspective of the last player to move.

measurePieceSquareValueIncrementally

Arguments

:: Num pieceSquareValue

=> pieceSquareValue

The value before the last move was applied, & therefore also from the perspective of the previous player.

-> PieceSquareByCoordinatesByRank pieceSquareValue

-> Game

-> pieceSquareValue

• Measures the piece-square value from the perspective of the last player to move.
• The previous value is provided, to enable calculation by difference.
• N.B.: because of diminishing returns, the piece-square value for everything but quiet moves is calculated from scratch.

measureValueOfMaterial

Arguments

:: RankValues

-> RankValue

Maximum total rank-value.

-> Game

-> CriterionValue

Measure the arithmetic difference between the total rank-value of the pieces currently held by either side; https://www.chessprogramming.org/Material.

measureValueOfCastlingPotential :: Game -> CriterionValue

Measure the arithmetic difference between the potential to Castle, on either side.

measureValueOfDefence :: Game -> CriterionValue

• Measure the normalised arithmetic difference between the number of pieces defending each of one's own, on either side.
• N.B. the rank-value of the defended piece is irrelevant because; it's the unknown value of the attacker that counts, since that's what the defender has the opportunity to counter-strike. CAVEAT: the validity of this depends on the duration of the battle.
• N.B. defence of the King is irrelevent, because it can't be taken.
• N.B. it's the total number of defenders which is relevant, rather than whether each piece has some protection, since it's not the individual battles but the war which counts.
• CAVEAT: this criterion competes with mobility, since each defended piece blocks the path of the defender.

measureValueOfDoubledPawns :: Game -> CriterionValue

• Measure the arithmetic difference between the number of doubled Pawns on either side; https://www.chessprogramming.org/Doubled_Pawn.
• N.B.: measures tripled Pawns as equivalent to two doubled Pawns.
• CAVEAT: this is a negative attribute, so the weighted normalised value shouldn't exceed the reduction due to measureValueOfMaterial resulting from a Pawn-sacrifice.

measureValueOfIsolatedPawns :: Game -> CriterionValue

• Measure the arithmetic difference between the number of isolated Pawns on either side; https://www.chessprogramming.org/Isolated_Pawn.
• CAVEAT: this is a negative attribute, so the weighted normalised value shouldn't exceed the reduction due to measureValueOfMaterial resulting from a Pawn-sacrifice.

measureValueOfPassedPawns :: Game -> CriterionValue

Measure the arithmetic difference between the number of passed Pawns on either side; https://www.chessprogramming.org/Passed_Pawn.

evaluateFitness

Arguments

:: (Fractional pieceSquareValue, Real pieceSquareValue)

=> Maybe pieceSquareValue

An optional value for the specified game.

-> Game

-> Reader pieceSquareValue WeightedMeanAndCriterionValues

• Evaluates the fitness of the board from the perspective of the last player to move. If the game has ended, the fitness is maximum for checkmate or zero for a draw, but otherwise is the weighted mean of various criteria; https://www.chessprogramming.org/Evaluation.
• Also returns the break-down of those criterion-values with a non-zero criterion-weight.
• Besides measuring the difference between the total rank-value on either side, other criteria are selected to represent known attributes of a good position.
• Many possible criteria aren't measured because they're, either currently or imminently, represented by those that are, typically by measureValueOfMaterial.