Two more parameters eliminated

RedundantRook and RedundantQueen replaced by simple
variable RedundantMajor. Also the SameColor coefficient
for Queen<->Queen has been set by definition to 0.

The remaining 5 parameters:

LinearCoefficients[ROOK]
LinearCoefficients[QUEEN]
QuadraticCoefficientsSameColor[ROOK][ROOK]
QuadraticCoefficientsSameColor[QUEEN][ROOK]
RedundantMajor

are sufficient to equate the material imbalances for the
5 common material configurations of R, RR, Q, QR and QRR
to any desired values simultaneously.

With the chosen parameters there should be no functional
change unless one side has more than 2 rooks or more
than 1 queen. For example bench from the start position
using the commands:

./stockfish
go depth 16

produces identical output except for one extra node
in the last iteration.

bench: 8198094

diff --git a/src/material.cpp b/src/material.cpp
index 4fd125de25bc5e1740f774e2eff0e07a7871a05f..b9b4bb63988ec28f6425592b937d8118b6ce2205 100644 (file)
--- a/src/material.cpp
+++ b/src/material.cpp
@@ -35,11 +35,10 @@ namespace {
   const int NoPawnsSF[4] = { 6, 12, 32 };
 
   // Polynomial material balance parameters
-  const Value RedundantQueen = Value(320);
-  const Value RedundantRook  = Value(554);
+  const Value RedundantMajor = Value(160);
 
   //                                  pair  pawn knight bishop rook queen
-  const int LinearCoefficients[6] = { 1852, -162, -1122, -183,  105,  26 };
+  const int LinearCoefficients[6] = { 1852, -162, -1122, -183,  302,  1 };
 
   const int QuadraticCoefficientsSameColor[][PIECE_TYPE_NB] = {
     // pair pawn knight bishop rook queen
@@ -47,8 +46,8 @@ namespace {
     {  39,    2                         }, // Pawn
     {  35,  271,  -4                    }, // Knight
     {   0,  105,   4,    0              }, // Bishop
-    { -27,   -2,  46,   100,   56       }, // Rook
-    {  58,   29,  83,   148,   -3,  -25 }  // Queen
+    { -27,   -2,  46,   100,  -141      }, // Rook
+    {  58,   29,  83,   148,  -163,   0 }  // Queen
   };
 
   const int QuadraticCoefficientsOppositeColor[][PIECE_TYPE_NB] = {
@@ -106,11 +105,9 @@ namespace {
     int pt1, pt2, pc, v;
     int value = 0;
 
-    // Redundancy of major pieces, formula based on Kaufman's paper
-    // "The Evaluation of Material Imbalances in Chess"
-    if (pieceCount[Us][ROOK] > 0)
-        value -=  RedundantRook * (pieceCount[Us][ROOK] - 1)
-                + RedundantQueen * pieceCount[Us][QUEEN];
+    // Penalty for major piece redundancy
+    if (pieceCount[Us][ROOK] + pieceCount[Us][QUEEN] > 1)
+        value -= RedundantMajor;
 
     // Second-degree polynomial material imbalance by Tord Romstad
     for (pt1 = NO_PIECE_TYPE; pt1 <= QUEEN; ++pt1)