These PST values were determined from ~450,000 long time control engine vs engine matches (2700+ CCRL Elo), using Larry Kaufman's "The Evaluation of Material Imbalances" as a guideline.
I found the average score for White when a White piece occupied a square for 6 plies during a game after leaving the opening book, and the same for the same Black piece in its comparable square. I adjusted the scores to remove White advantage, then converted to Elo. Then I assumed that 1 Elo equals 1 centipawn.
For midgame values, I looked at moves 12 through 40, with at least 1 rook,2 minors, and 4 pawns on each side and no material imbalance. For the endgame, only after move 40 was considered and no more than 1 rook, 2 minors, and 4 pawns on each side (no material imbalance).
The endgame statistics for some pieces/squares was sparse. So, for the endgame tables I used the more statistically significant information to find 3 dimensional surfaces to model the PST values.
I used the values with Dan Honeycutt's engine Cupcake, which has some but not much chess knowledge encoded (on purpose). In one test (see below), they seemed to be worth about 19 Elo over Cupcake's original PSTs.
I doubt these values would work for a more advanced engine, but they may work well for an engine with no knowledge.
Code: Select all
#define PAWN_VAL 100
#define KNIGHT_VAL 300
#define BISHOP_VAL 300
#define ROOK_VAL 500
#define ROOK_VAL 950
const int pstPawnMg[64] =
{
//A1 H1
0, 0, 0, 0, 0, 0, 0, 0
-1, -7, -11, -35, -13, 5, 3, -5
1, 1, -6, -19, -6, -7, -4, 10
1, 14, 8, 4, 5, 4, 10, 7
9, 30, 23, 31, 31, 23, 17, 11
21, 54, 72, 56, 77, 95, 71, 11
118, 121, 173, 168, 107, 82, -16, 22
0, 0, 0, 0, 0, 0, 0, 0
//A8 H8
};
const int pstPawnEg[64] =
{
0, 0, 0, 0, 0, 0, 0, 0
-17, -17, -17, -17, -17, -17, -17, -17
-11, -11, -11, -11, -11, -11, -11, -11
-7, -7, -7, -7, -7, -7, -7, -7
16, 16, 16, 16, 16, 16, 16, 16
55, 55, 55, 55, 55, 55, 55, 55
82, 82, 82, 82, 82, 82, 82, 82
0, 0, 0, 0, 0, 0, 0, 0
};
const int pstKnightMg[64] =
{
-99, -30, -66, -64, -29, -19, -61, -81
-56, -31, -28, -1, -7, -20, -42, -11
-38, -16, 0, 14, 8, 3, 3, -42
-14, 0, 2, 3, 19, 12, 33, -7
-14, -4, 25, 33, 10, 33, 14, 43
-22, 18, 60, 64, 124, 143, 55, 6
-34, 24, 54, 74, 60, 122, 2, 29
-60, 0, 0, 0, 0, 0, 0, 0
};
const int pstKnightEg[64] =
{
-99, -99, -94, -88, -88, -94, -99, -99
-81, -62, -49, -43, -43, -49, -62, -81
-46, -27, -15, -9, -9, -15, -27, -46
-22, -3, 10, 16, 16, 10, -3, -22
-7, 12, 25, 31, 31, 25, 12, -7
-2, 17, 30, 36, 36, 30, 17, -2
-7, 12, 25, 31, 31, 25, 12, -7
-21, -3, 10, 16, 16, 10, -3, -21
};
const int pstBishopMg[64] =
{
-7, 12, -8, -37, -31, -8, -45, -67
15, 5, 13, -10, 1, 2, 0, 15
5, 12, 14, 13, 10, -1, 3, 4
1, 5, 23, 32, 21, 8, 17, 4
-1, 16, 29, 27, 37, 27, 17, 4
7, 27, 20, 56, 91, 108, 53, 44
-24, -23, 30, 58, 65, 61, 69, 11
0, 0, 0, 0, 0, 0, 0, 0
};
const int pstBishopEg[64] =
{
-27, -21, -17, -15, -15, -17, -21, -27
-10, -4, 0, 2, 2, 0, -4, -10
2, 8, 12, 14, 14, 12, 8, 2
11, 17, 21, 23, 23, 21, 17, 11
14, 20, 24, 26, 26, 24, 20, 14
13, 19, 23, 25, 25, 23, 19, 13
8, 14, 18, 20, 20, 18, 14, 8
-2, 4, 8, 10, 10, 8, 4, -2
};
const int pstRookMg[64] =
{
-2, -1, 3, 1, 2, 1, 4, -8
-26, -6, 2, -2, 2, -10, -1, -29
-16, 0, 3, -3, 8, -1, 12, 3
-9, -5, 8, 14, 18, -17, 13, -13
19, 33, 46, 57, 53, 39, 53, 16
24, 83, 54, 75, 134, 144, 85, 75
46, 33, 64, 62, 91, 89, 70, 104
84, 0, 0, 37, 124, 0, 0, 153
};
const int pstRookEg[64] =
{
-32, -31, -30, -29, -29, -30, -31, -32
-27, -25, -24, -24, -24, -24, -25, -27
-15, -13, -12, -12, -12, -12, -13, -15
1, 2, 3, 4, 4, 3, 2, 1
15, 17, 18, 18, 18, 18, 17, 15
25, 27, 28, 28, 28, 28, 27, 25
27, 28, 29, 30, 30, 29, 28, 27
16, 17, 18, 19, 19, 18, 17, 16
};
const int pstQueenMg[64] =
{
1, -10, -11, 3, -15, -51, -83, -13
-7, 3, 2, 5, -1, -10, -7, -2
-11, 0, 12, 2, 8, 11, 7, -6
-9, 5, 7, 9, 18, 17, 26, 4
-6, 0, 15, 25, 32, 9, 26, 12
-16, 10, 13, 25, 37, 30, 15, 26
1, 11, 35, 0, 16, 55, 39, 57
-13, 6, -42, 0, 29, 0, 0, 102
};
const int pstQueenEg[64] =
{
-61, -55, -52, -50, -50, -52, -55, -61
-31, -26, -22, -21, -21, -22, -26, -31
-8, -3, 1, 3, 3, 1, -3, -8
9, 14, 17, 19, 19, 17, 14, 9
19, 24, 28, 30, 30, 28, 24, 19
23, 28, 32, 34, 34, 32, 28, 23
21, 26, 30, 31, 31, 30, 26, 21
12, 17, 21, 23, 23, 21, 17, 12
};
const int pstKingMg[64] =
{
0, 0, 0, -9, 0, -9, 25, 0
-9, -9, -9, -9, -9, -9, -9, -9
-9, -9, -9, -9, -9, -9, -9, -9
-9, -9, -9, -9, -9, -9, -9, -9
-9, -9, -9, -9, -9, -9, -9, -9
-9, -9, -9, -9, -9, -9, -9, -9
-9, -9, -9, -9, -9, -9, -9, -9
-9, -9, -9, -9, -9, -9, -9, -9
};
const int pstKingEg[64] =
{
-34, -30, -28, -27, -27, -28, -30, -34
-17, -13, -11, -10, -10, -11, -13, -17
-2, 2, 4, 5, 5, 4, 2, -2
11, 15, 17, 18, 18, 17, 15, 11
22, 26, 28, 29, 29, 28, 26, 22
31, 34, 37, 38, 38, 37, 34, 31
38, 41, 44, 45, 45, 44, 41, 38
42, 46, 48, 50, 50, 48, 46, 42
};
