Updated KNNKP endgame.

This is a patch that significantly improves playing KNNKP endgames:

```
Score of 2553 vs master: 132 - 38 - 830 [0.547] 1000
Elo difference: 32.8 +/- 8.7, LOS: 100.0 %, DrawRatio: 83.0 %
```

At the same time it reduces the evaluation of this mostly draw engame
from ~7.5 to ~1.5

This patch does not regress against master in normal games:

STC
LLR: 2.94 (-2.94,2.94) {-1.50,0.50}
Total: 96616 W: 18459 L: 18424 D: 59733
Ptnml(0-2): 1409, 10812, 23802, 10905, 1380
http://tests.stockfishchess.org/tests/view/5e49dfe6f8d1d52b40cd31bc

LTC
LLR: 2.95 (-2.94,2.94) {-1.50,0.50}
Total: 49726 W: 6340 L: 6304 D: 37082
Ptnml(0-2): 239, 4227, 15906, 4241, 250
http://tests.stockfishchess.org/tests/view/5e4ab9ee16fb3df8c4cc01d0

Theory: KNNK is a dead draw, however the presence of the additional weakSide pawn opens up some mate opportunities. The idea is to block the pawn (preferably behind the Troitsky line) with one of the knights and press the weakSide king into a corner. If we can stalemate the king, we release the pawn with the knight (to avoid actual stalemate), and use the knight to complete the mate before the pawn promotes. This is also why there is an additional penalty for advancement of the pawn.

closes https://github.com/official-stockfish/Stockfish/pull/2553

Bench: 4981770

diff --git a/src/endgame.cpp b/src/endgame.cpp
index 6745ee2664c612689646c283f78833355d509dcf..74e16fa6941b0e5e6196c4b319cbd122d6fa5940 100644 (file)
--- a/src/endgame.cpp
+++ b/src/endgame.cpp
@@ -310,16 +310,17 @@ Value Endgame<KQKR>::operator()(const Position& pos) const {
 }
 
 
-/// KNN vs KP. Simply push the opposing king to the corner
+/// KNN vs KP. Very drawish, but there are some mate opportunities if we can
+//  press the weakSide King to a corner before the pawn advances too much.
 template<>
 Value Endgame<KNNKP>::operator()(const Position& pos) const {
 
   assert(verify_material(pos, strongSide, 2 * KnightValueMg, 0));
   assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
 
-  Value result =  2 * KnightValueEg
-                - PawnValueEg
-                + PushToEdges[pos.square<KING>(weakSide)];
+  Value result =      PawnValueEg
+               +  2 * PushToEdges[pos.square<KING>(weakSide)]
+               - 10 * relative_rank(weakSide, pos.square<PAWN>(weakSide));
 
   return strongSide == pos.side_to_move() ? result : -result;
 }