const Value BishopPairMidgameBonus = Value(109);
const Value BishopPairEndgameBonus = Value(97);
- Key KNNKMaterialKey, KKNNMaterialKey;
+ // Polynomial material balance parameters
+ const Value RedundantQueenPenalty = Value(358);
+ const Value RedundantRookPenalty = Value(536);
+ const int LinearCoefficients[6] = { 1740, -146, -1246, -197, 206, -7 };
+
+ const int QuadraticCoefficientsSameColor[][6] = {
+ { 0, 0, 0, 0, 0, 0 }, { 31, -4, 0, 0, 0, 0 }, { 14, 267, -21, 0, 0, 0 },
+ { 0, 7, -26, 0, 0, 0 }, { -3, -1, 69, 162, 80, 0 }, { 40, 27, 119, 174, -64, -49 } };
+
+ const int QuadraticCoefficientsOppositeColor[][6] = {
+ { 0, 0, 0, 0, 0, 0 }, { -9, 0, 0, 0, 0, 0 }, { 49, 32, 0, 0, 0, 0 },
+ { -25, 19, -5, 0, 0, 0 }, { 97, -6, 39, -88, 0, 0 }, { 77, 69, -42, 104, 116, 0 } };
// Unmapped endgame evaluation and scaling functions, these
// are accessed direcly and not through the function maps.
ScalingFunction<KQKRP> ScaleKQKRP(WHITE), ScaleKRPKQ(BLACK);
ScalingFunction<KPsK> ScaleKPsK(WHITE), ScaleKKPs(BLACK);
ScalingFunction<KPKP> ScaleKPKPw(WHITE), ScaleKPKPb(BLACK);
+
+ Key KNNKMaterialKey, KKNNMaterialKey;
}
// Evaluate the material balance
- Color c;
+ const int bishopsPair_count[2] = { pos.piece_count(WHITE, BISHOP) > 1, pos.piece_count(BLACK, BISHOP) > 1 };
+ Color c, them;
int sign;
- Value egValue = Value(0);
- Value mgValue = Value(0);
+ int matValue = 0;
for (c = WHITE, sign = 1; c <= BLACK; c++, sign = -sign)
{
}
}
- // Bishop pair
- if (pos.piece_count(c, BISHOP) >= 2)
- {
- mgValue += sign * BishopPairMidgameBonus;
- egValue += sign * BishopPairEndgameBonus;
- }
-
- // Knights are stronger when there are many pawns on the board. The
- // formula is taken from Larry Kaufman's paper "The Evaluation of Material
- // Imbalances in Chess":
+ // Redundancy of major pieces, formula based on Kaufman's paper
+ // "The Evaluation of Material Imbalances in Chess"
// http://mywebpages.comcast.net/danheisman/Articles/evaluation_of_material_imbalance.htm
- mgValue += sign * Value(pos.piece_count(c, KNIGHT)*(pos.piece_count(c, PAWN)-5)*16);
- egValue += sign * Value(pos.piece_count(c, KNIGHT)*(pos.piece_count(c, PAWN)-5)*16);
-
- // Redundancy of major pieces, again based on Kaufman's paper:
if (pos.piece_count(c, ROOK) >= 1)
+ matValue -= sign * ((pos.piece_count(c, ROOK) - 1) * RedundantRookPenalty + pos.piece_count(c, QUEEN) * RedundantQueenPenalty);
+
+ // Second-degree polynomial material imbalance by Tord Romstad
+ //
+ // We use NO_PIECE_TYPE as a place holder for the bishop pair "extended piece",
+ // this allow us to be more flexible in defining bishop pair bonuses.
+ them = opposite_color(c);
+ for (PieceType pt1 = NO_PIECE_TYPE; pt1 <= QUEEN; pt1++)
{
- Value v = Value((pos.piece_count(c, ROOK) - 1) * 32 + pos.piece_count(c, QUEEN) * 16);
- mgValue -= sign * v;
- egValue -= sign * v;
+ int c1, c2, c3;
+ c1 = sign * (pt1 != NO_PIECE_TYPE ? pos.piece_count(c, pt1) : bishopsPair_count[c]);
+ if (!c1)
+ continue;
+
+ matValue += c1 * LinearCoefficients[pt1];
+
+ for (PieceType pt2 = NO_PIECE_TYPE; pt2 <= pt1; pt2++)
+ {
+ c2 = (pt2 != NO_PIECE_TYPE ? pos.piece_count(c, pt2) : bishopsPair_count[c]);
+ c3 = (pt2 != NO_PIECE_TYPE ? pos.piece_count(them, pt2) : bishopsPair_count[them]);
+ matValue += c1 * c2 * QuadraticCoefficientsSameColor[pt1][pt2];
+ matValue += c1 * c3 * QuadraticCoefficientsOppositeColor[pt1][pt2];
+ }
}
}
- mi->mgValue = int16_t(mgValue);
- mi->egValue = int16_t(egValue);
+
+ mi->value = int16_t(matValue / 16);
return mi;
}