Simplify pawnless endgame evaluation

Retire KmmKm evaluation function. Instead give a very drawish
scale factor when the material advantage is small and not much
material remains.

Retire NoPawnsSF array. Pawnless endgames without a bishop will
now be scored higher. Pawnless endgames with a bishop pair will
be scored lower. The effect of this is hopefully small.

Consistent results both at short TC (fixed games):
ELO: -0.00 +-2.1 (95%) LOS: 50.0%
Total: 40000 W: 7405 L: 7405 D: 25190

And long TC (fixed games):
ELO: 0.77 +-1.9 (95%) LOS: 78.7%
Total: 39690 W: 6179 L: 6091 D: 27420

bench: 7213723

src/endgame.cpp

@@ -349,7 +349,6 @@ Value Endgame<KQKR>::operator()(const Position& pos) const {
 
 /// Some cases of trivial draws
 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
-template<> Value Endgame<KmmKm>::operator()(const Position&) const { return VALUE_DRAW; }
 
 
 /// KB and one or more pawns vs K. It checks for draws with rook pawns and

src/endgame.h

@@ -42,7 +42,6 @@ enum EndgameType {
   KRKN,  // KR vs KN
   KQKP,  // KQ vs KP
   KQKR,  // KQ vs KR
-  KmmKm, // K and two minors vs K and one or two minors
 
 
   // Scaling functions

src/material.cpp

@@ -31,9 +31,6 @@ namespace {
   const Value MidgameLimit = Value(15581);
   const Value EndgameLimit = Value(3998);
 
-  // Scale factors used when one side has no more pawns
-  const int NoPawnsSF[4] = { 6, 12, 32 };
-
   // Polynomial material balance parameters
 
   //                                  pair  pawn knight bishop rook queen
@@ -62,7 +59,6 @@ namespace {
 
   // Endgame evaluation and scaling functions are accessed directly and not through
   // the function maps because they correspond to more than one material hash key.
-  Endgame<KmmKm> EvaluateKmmKm[] = { Endgame<KmmKm>(WHITE), Endgame<KmmKm>(BLACK) };
   Endgame<KXK>   EvaluateKXK[]   = { Endgame<KXK>(WHITE),   Endgame<KXK>(BLACK) };
 
   Endgame<KBPsK>  ScaleKBPsK[]  = { Endgame<KBPsK>(WHITE),  Endgame<KBPsK>(BLACK) };
@@ -165,21 +161,6 @@ Entry* probe(const Position& pos, Table& entries, Endgames& endgames) {
       return e;
   }
 
-  if (!pos.pieces(PAWN) && !pos.pieces(ROOK) && !pos.pieces(QUEEN))
-  {
-      // Minor piece endgame with at least one minor piece per side and
-      // no pawns. Note that the case KmmK is already handled by KXK.
-      assert((pos.pieces(WHITE, KNIGHT) | pos.pieces(WHITE, BISHOP)));
-      assert((pos.pieces(BLACK, KNIGHT) | pos.pieces(BLACK, BISHOP)));
-
-      if (   pos.count<BISHOP>(WHITE) + pos.count<KNIGHT>(WHITE) <= 2
-          && pos.count<BISHOP>(BLACK) + pos.count<KNIGHT>(BLACK) <= 2)
-      {
-          e->evaluationFunction = &EvaluateKmmKm[pos.side_to_move()];
-          return e;
-      }
-  }
-
   // OK, we didn't find any special evaluation function for the current
   // material configuration. Is there a suitable scaling function?
   //
@@ -233,17 +214,16 @@ Entry* probe(const Position& pos, Table& entries, Endgames& endgames) {
   }
 
   // No pawns makes it difficult to win, even with a material advantage. This
-  // catches some trivial draws like KK, KBK and KNK
+  // catches some trivial draws like KK, KBK and KNK and gives a very drawish
+  // scale factor for cases such as KRKBP and KmmKm (except for KBBKN).
   if (!pos.count<PAWN>(WHITE) && npm_w - npm_b <= BishopValueMg)
   {
-      e->factor[WHITE] = (uint8_t)
-      (npm_w == npm_b || npm_w < RookValueMg ? 0 : NoPawnsSF[std::min(pos.count<BISHOP>(WHITE), 2)]);
+      e->factor[WHITE] = npm_w < RookValueMg ? 0 : npm_b <= BishopValueMg ? 4 : 12;
   }
 
   if (!pos.count<PAWN>(BLACK) && npm_b - npm_w <= BishopValueMg)
   {
-      e->factor[BLACK] = (uint8_t)
-      (npm_w == npm_b || npm_b < RookValueMg ? 0 : NoPawnsSF[std::min(pos.count<BISHOP>(BLACK), 2)]);
+      e->factor[BLACK] = npm_b < RookValueMg ? 0 : npm_w <= BishopValueMg ? 4 : 12;
   }
 
   if (pos.count<PAWN>(WHITE) == 1 && npm_w - npm_b <= BishopValueMg)