2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2023 The Stockfish developers (see AUTHORS file)
5 Stockfish is free software: you can redistribute it and/or modify
6 it under the terms of the GNU General Public License as published by
7 the Free Software Foundation, either version 3 of the License, or
8 (at your option) any later version.
10 Stockfish is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13 GNU General Public License for more details.
15 You should have received a copy of the GNU General Public License
16 along with this program. If not, see <http://www.gnu.org/licenses/>.
29 // Used to drive the king towards the edge of the board
30 // in KX vs K and KQ vs KR endgames.
31 // Values range from 27 (center squares) to 90 (in the corners)
32 inline int push_to_edge(Square s) {
33 int rd = edge_distance(rank_of(s)), fd = edge_distance(file_of(s));
34 return 90 - (7 * fd * fd / 2 + 7 * rd * rd / 2);
37 // Used to drive the king towards A1H8 corners in KBN vs K endgames.
38 // Values range from 0 on A8H1 diagonal to 7 in A1H8 corners
39 inline int push_to_corner(Square s) {
40 return abs(7 - rank_of(s) - file_of(s));
43 // Drive a piece close to or away from another piece
44 inline int push_close(Square s1, Square s2) { return 140 - 20 * distance(s1, s2); }
45 inline int push_away(Square s1, Square s2) { return 120 - push_close(s1, s2); }
48 bool verify_material(const Position& pos, Color c, Value npm, int pawnsCnt) {
49 return pos.non_pawn_material(c) == npm && pos.count<PAWN>(c) == pawnsCnt;
53 // Map the square as if strongSide is white and strongSide's only pawn
54 // is on the left half of the board.
55 Square normalize(const Position& pos, Color strongSide, Square sq) {
57 assert(pos.count<PAWN>(strongSide) == 1);
59 if (file_of(pos.square<PAWN>(strongSide)) >= FILE_E)
62 return strongSide == WHITE ? sq : flip_rank(sq);
70 std::pair<Map<Value>, Map<ScaleFactor>> maps;
88 add<KBPPKB>("KBPPKB");
89 add<KRPPKRP>("KRPPKRP");
94 /// Mate with KX vs K. This function is used to evaluate positions with
95 /// king and plenty of material vs a lone king. It simply gives the
96 /// attacking side a bonus for driving the defending king towards the edge
97 /// of the board, and for keeping the distance between the two kings small.
99 Value Endgame<KXK>::operator()(const Position& pos) const {
101 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
102 assert(!pos.checkers()); // Eval is never called when in check
104 // Stalemate detection with lone king
105 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
108 Square strongKing = pos.square<KING>(strongSide);
109 Square weakKing = pos.square<KING>(weakSide);
111 Value result = pos.non_pawn_material(strongSide)
112 + pos.count<PAWN>(strongSide) * PawnValueEg
113 + push_to_edge(weakKing)
114 + push_close(strongKing, weakKing);
116 if ( pos.count<QUEEN>(strongSide)
117 || pos.count<ROOK>(strongSide)
118 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
119 || ( (pos.pieces(strongSide, BISHOP) & ~DarkSquares)
120 && (pos.pieces(strongSide, BISHOP) & DarkSquares)))
121 result = std::min(result + VALUE_KNOWN_WIN, VALUE_TB_WIN_IN_MAX_PLY - 1);
123 return strongSide == pos.side_to_move() ? result : -result;
127 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
128 /// defending king towards a corner square that our bishop attacks.
130 Value Endgame<KBNK>::operator()(const Position& pos) const {
132 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
133 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
135 Square strongKing = pos.square<KING>(strongSide);
136 Square strongBishop = pos.square<BISHOP>(strongSide);
137 Square weakKing = pos.square<KING>(weakSide);
139 // If our bishop does not attack A1/H8, we flip the enemy king square
140 // to drive to opposite corners (A8/H1).
142 Value result = (VALUE_KNOWN_WIN + 3520)
143 + push_close(strongKing, weakKing)
144 + 420 * push_to_corner(opposite_colors(strongBishop, SQ_A1) ? flip_file(weakKing) : weakKing);
146 assert(abs(result) < VALUE_TB_WIN_IN_MAX_PLY);
147 return strongSide == pos.side_to_move() ? result : -result;
151 /// KP vs K. This endgame is evaluated with the help of a bitbase
153 Value Endgame<KPK>::operator()(const Position& pos) const {
155 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
156 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
158 // Assume strongSide is white and the pawn is on files A-D
159 Square strongKing = normalize(pos, strongSide, pos.square<KING>(strongSide));
160 Square strongPawn = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
161 Square weakKing = normalize(pos, strongSide, pos.square<KING>(weakSide));
163 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
165 if (!Bitbases::probe(strongKing, strongPawn, weakKing, us))
168 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(strongPawn));
170 return strongSide == pos.side_to_move() ? result : -result;
174 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
175 /// a bitbase. The function below returns drawish scores when the pawn is
176 /// far advanced with support of the king, while the attacking king is far
179 Value Endgame<KRKP>::operator()(const Position& pos) const {
181 assert(verify_material(pos, strongSide, RookValueMg, 0));
182 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
184 Square strongKing = pos.square<KING>(strongSide);
185 Square weakKing = pos.square<KING>(weakSide);
186 Square strongRook = pos.square<ROOK>(strongSide);
187 Square weakPawn = pos.square<PAWN>(weakSide);
188 Square queeningSquare = make_square(file_of(weakPawn), relative_rank(weakSide, RANK_8));
191 // If the stronger side's king is in front of the pawn, it's a win
192 if (forward_file_bb(strongSide, strongKing) & weakPawn)
193 result = RookValueEg - distance(strongKing, weakPawn);
195 // If the weaker side's king is too far from the pawn and the rook,
197 else if ( distance(weakKing, weakPawn) >= 3 + (pos.side_to_move() == weakSide)
198 && distance(weakKing, strongRook) >= 3)
199 result = RookValueEg - distance(strongKing, weakPawn);
201 // If the pawn is far advanced and supported by the defending king,
202 // the position is drawish
203 else if ( relative_rank(strongSide, weakKing) <= RANK_3
204 && distance(weakKing, weakPawn) == 1
205 && relative_rank(strongSide, strongKing) >= RANK_4
206 && distance(strongKing, weakPawn) > 2 + (pos.side_to_move() == strongSide))
207 result = Value(80) - 8 * distance(strongKing, weakPawn);
210 result = Value(200) - 8 * ( distance(strongKing, weakPawn + pawn_push(weakSide))
211 - distance(weakKing, weakPawn + pawn_push(weakSide))
212 - distance(weakPawn, queeningSquare));
214 return strongSide == pos.side_to_move() ? result : -result;
218 /// KR vs KB. This is very simple, and always returns drawish scores. The
219 /// score is slightly bigger when the defending king is close to the edge.
221 Value Endgame<KRKB>::operator()(const Position& pos) const {
223 assert(verify_material(pos, strongSide, RookValueMg, 0));
224 assert(verify_material(pos, weakSide, BishopValueMg, 0));
226 Value result = Value(push_to_edge(pos.square<KING>(weakSide)));
227 return strongSide == pos.side_to_move() ? result : -result;
231 /// KR vs KN. The attacking side has slightly better winning chances than
232 /// in KR vs KB, particularly if the king and the knight are far apart.
234 Value Endgame<KRKN>::operator()(const Position& pos) const {
236 assert(verify_material(pos, strongSide, RookValueMg, 0));
237 assert(verify_material(pos, weakSide, KnightValueMg, 0));
239 Square weakKing = pos.square<KING>(weakSide);
240 Square weakKnight = pos.square<KNIGHT>(weakSide);
241 Value result = Value(push_to_edge(weakKing) + push_away(weakKing, weakKnight));
242 return strongSide == pos.side_to_move() ? result : -result;
246 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
247 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
248 /// with a king positioned next to it can be a draw, so in that case, we only
249 /// use the distance between the kings.
251 Value Endgame<KQKP>::operator()(const Position& pos) const {
253 assert(verify_material(pos, strongSide, QueenValueMg, 0));
254 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
256 Square strongKing = pos.square<KING>(strongSide);
257 Square weakKing = pos.square<KING>(weakSide);
258 Square weakPawn = pos.square<PAWN>(weakSide);
260 Value result = Value(push_close(strongKing, weakKing));
262 if ( relative_rank(weakSide, weakPawn) != RANK_7
263 || distance(weakKing, weakPawn) != 1
264 || ((FileBBB | FileDBB | FileEBB | FileGBB) & weakPawn))
265 result += QueenValueEg - PawnValueEg;
267 return strongSide == pos.side_to_move() ? result : -result;
271 /// KQ vs KR. This is almost identical to KX vs K: we give the attacking
272 /// king a bonus for having the kings close together, and for forcing the
273 /// defending king towards the edge. If we also take care to avoid null move for
274 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
276 Value Endgame<KQKR>::operator()(const Position& pos) const {
278 assert(verify_material(pos, strongSide, QueenValueMg, 0));
279 assert(verify_material(pos, weakSide, RookValueMg, 0));
281 Square strongKing = pos.square<KING>(strongSide);
282 Square weakKing = pos.square<KING>(weakSide);
284 Value result = QueenValueEg
286 + push_to_edge(weakKing)
287 + push_close(strongKing, weakKing);
289 return strongSide == pos.side_to_move() ? result : -result;
293 /// KNN vs KP. Very drawish, but there are some mate opportunities if we can
294 /// press the weakSide King to a corner before the pawn advances too much.
296 Value Endgame<KNNKP>::operator()(const Position& pos) const {
298 assert(verify_material(pos, strongSide, 2 * KnightValueMg, 0));
299 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
301 Square weakKing = pos.square<KING>(weakSide);
302 Square weakPawn = pos.square<PAWN>(weakSide);
304 Value result = PawnValueEg
305 + 2 * push_to_edge(weakKing)
306 - 10 * relative_rank(weakSide, weakPawn);
308 return strongSide == pos.side_to_move() ? result : -result;
312 /// Some cases of trivial draws
313 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
316 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
317 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
318 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
321 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
323 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
324 assert(pos.count<PAWN>(strongSide) >= 1);
326 // No assertions about the material of weakSide, because we want draws to
327 // be detected even when the weaker side has some pawns.
329 Bitboard strongPawns = pos.pieces(strongSide, PAWN);
330 Bitboard allPawns = pos.pieces(PAWN);
332 Square strongBishop = pos.square<BISHOP>(strongSide);
333 Square weakKing = pos.square<KING>(weakSide);
334 Square strongKing = pos.square<KING>(strongSide);
336 // All strongSide pawns are on a single rook file?
337 if (!(strongPawns & ~FileABB) || !(strongPawns & ~FileHBB))
339 Square queeningSquare = relative_square(strongSide, make_square(file_of(lsb(strongPawns)), RANK_8));
341 if ( opposite_colors(queeningSquare, strongBishop)
342 && distance(queeningSquare, weakKing) <= 1)
343 return SCALE_FACTOR_DRAW;
346 // If all the pawns are on the same B or G file, then it's potentially a draw
347 if ((!(allPawns & ~FileBBB) || !(allPawns & ~FileGBB))
348 && pos.non_pawn_material(weakSide) == 0
349 && pos.count<PAWN>(weakSide) >= 1)
351 // Get the least advanced weakSide pawn
352 Square weakPawn = frontmost_sq(strongSide, pos.pieces(weakSide, PAWN));
354 // There's potential for a draw if our pawn is blocked on the 7th rank,
355 // the bishop cannot attack it or they only have one pawn left.
356 if ( relative_rank(strongSide, weakPawn) == RANK_7
357 && (strongPawns & (weakPawn + pawn_push(weakSide)))
358 && (opposite_colors(strongBishop, weakPawn) || !more_than_one(strongPawns)))
360 int strongKingDist = distance(weakPawn, strongKing);
361 int weakKingDist = distance(weakPawn, weakKing);
363 // It's a draw if the weak king is on its back two ranks, within 2
364 // squares of the blocking pawn and the strong king is not
365 // closer. (I think this rule only fails in practically
366 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
367 // and positions where qsearch will immediately correct the
368 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w).
369 if ( relative_rank(strongSide, weakKing) >= RANK_7
371 && weakKingDist <= strongKingDist)
372 return SCALE_FACTOR_DRAW;
376 return SCALE_FACTOR_NONE;
380 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
381 /// the third rank defended by a pawn.
383 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
385 assert(verify_material(pos, strongSide, QueenValueMg, 0));
386 assert(pos.count<ROOK>(weakSide) == 1);
387 assert(pos.count<PAWN>(weakSide) >= 1);
389 Square strongKing = pos.square<KING>(strongSide);
390 Square weakKing = pos.square<KING>(weakSide);
391 Square weakRook = pos.square<ROOK>(weakSide);
393 if ( relative_rank(weakSide, weakKing) <= RANK_2
394 && relative_rank(weakSide, strongKing) >= RANK_4
395 && relative_rank(weakSide, weakRook) == RANK_3
396 && ( pos.pieces(weakSide, PAWN)
397 & attacks_bb<KING>(weakKing)
398 & pawn_attacks_bb(strongSide, weakRook)))
399 return SCALE_FACTOR_DRAW;
401 return SCALE_FACTOR_NONE;
405 /// KRP vs KR. This function knows a handful of the most important classes of
406 /// drawn positions, but is far from perfect. It would probably be a good idea
407 /// to add more knowledge in the future.
409 /// It would also be nice to rewrite the actual code for this function,
410 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
412 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
414 assert(verify_material(pos, strongSide, RookValueMg, 1));
415 assert(verify_material(pos, weakSide, RookValueMg, 0));
417 // Assume strongSide is white and the pawn is on files A-D
418 Square strongKing = normalize(pos, strongSide, pos.square<KING>(strongSide));
419 Square strongRook = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
420 Square strongPawn = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
421 Square weakKing = normalize(pos, strongSide, pos.square<KING>(weakSide));
422 Square weakRook = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
424 File pawnFile = file_of(strongPawn);
425 Rank pawnRank = rank_of(strongPawn);
426 Square queeningSquare = make_square(pawnFile, RANK_8);
427 int tempo = (pos.side_to_move() == strongSide);
429 // If the pawn is not too far advanced and the defending king defends the
430 // queening square, use the third-rank defence.
431 if ( pawnRank <= RANK_5
432 && distance(weakKing, queeningSquare) <= 1
433 && strongKing <= SQ_H5
434 && (rank_of(weakRook) == RANK_6 || (pawnRank <= RANK_3 && rank_of(strongRook) != RANK_6)))
435 return SCALE_FACTOR_DRAW;
437 // The defending side saves a draw by checking from behind in case the pawn
438 // has advanced to the 6th rank with the king behind.
439 if ( pawnRank == RANK_6
440 && distance(weakKing, queeningSquare) <= 1
441 && rank_of(strongKing) + tempo <= RANK_6
442 && (rank_of(weakRook) == RANK_1 || (!tempo && distance<File>(weakRook, strongPawn) >= 3)))
443 return SCALE_FACTOR_DRAW;
445 if ( pawnRank >= RANK_6
446 && weakKing == queeningSquare
447 && rank_of(weakRook) == RANK_1
448 && (!tempo || distance(strongKing, strongPawn) >= 2))
449 return SCALE_FACTOR_DRAW;
451 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
452 // and the black rook is behind the pawn.
453 if ( strongPawn == SQ_A7
454 && strongRook == SQ_A8
455 && (weakKing == SQ_H7 || weakKing == SQ_G7)
456 && file_of(weakRook) == FILE_A
457 && (rank_of(weakRook) <= RANK_3 || file_of(strongKing) >= FILE_D || rank_of(strongKing) <= RANK_5))
458 return SCALE_FACTOR_DRAW;
460 // If the defending king blocks the pawn and the attacking king is too far
461 // away, it's a draw.
462 if ( pawnRank <= RANK_5
463 && weakKing == strongPawn + NORTH
464 && distance(strongKing, strongPawn) - tempo >= 2
465 && distance(strongKing, weakRook) - tempo >= 2)
466 return SCALE_FACTOR_DRAW;
468 // Pawn on the 7th rank supported by the rook from behind usually wins if the
469 // attacking king is closer to the queening square than the defending king,
470 // and the defending king cannot gain tempi by threatening the attacking rook.
471 if ( pawnRank == RANK_7
472 && pawnFile != FILE_A
473 && file_of(strongRook) == pawnFile
474 && strongRook != queeningSquare
475 && (distance(strongKing, queeningSquare) < distance(weakKing, queeningSquare) - 2 + tempo)
476 && (distance(strongKing, queeningSquare) < distance(weakKing, strongRook) + tempo))
477 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(strongKing, queeningSquare));
479 // Similar to the above, but with the pawn further back
480 if ( pawnFile != FILE_A
481 && file_of(strongRook) == pawnFile
482 && strongRook < strongPawn
483 && (distance(strongKing, queeningSquare) < distance(weakKing, queeningSquare) - 2 + tempo)
484 && (distance(strongKing, strongPawn + NORTH) < distance(weakKing, strongPawn + NORTH) - 2 + tempo)
485 && ( distance(weakKing, strongRook) + tempo >= 3
486 || ( distance(strongKing, queeningSquare) < distance(weakKing, strongRook) + tempo
487 && (distance(strongKing, strongPawn + NORTH) < distance(weakKing, strongPawn) + tempo))))
488 return ScaleFactor( SCALE_FACTOR_MAX
489 - 8 * distance(strongPawn, queeningSquare)
490 - 2 * distance(strongKing, queeningSquare));
492 // If the pawn is not far advanced and the defending king is somewhere in
493 // the pawn's path, it's probably a draw.
494 if (pawnRank <= RANK_4 && weakKing > strongPawn)
496 if (file_of(weakKing) == file_of(strongPawn))
497 return ScaleFactor(10);
498 if ( distance<File>(weakKing, strongPawn) == 1
499 && distance(strongKing, weakKing) > 2)
500 return ScaleFactor(24 - 2 * distance(strongKing, weakKing));
502 return SCALE_FACTOR_NONE;
506 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
508 assert(verify_material(pos, strongSide, RookValueMg, 1));
509 assert(verify_material(pos, weakSide, BishopValueMg, 0));
511 // Test for a rook pawn
512 if (pos.pieces(PAWN) & (FileABB | FileHBB))
514 Square weakKing = pos.square<KING>(weakSide);
515 Square weakBishop = pos.square<BISHOP>(weakSide);
516 Square strongKing = pos.square<KING>(strongSide);
517 Square strongPawn = pos.square<PAWN>(strongSide);
518 Rank pawnRank = relative_rank(strongSide, strongPawn);
519 Direction push = pawn_push(strongSide);
521 // If the pawn is on the 5th rank and the pawn (currently) is on
522 // the same color square as the bishop then there is a chance of
523 // a fortress. Depending on the king position give a moderate
524 // reduction or a stronger one if the defending king is near the
525 // corner but not trapped there.
526 if (pawnRank == RANK_5 && !opposite_colors(weakBishop, strongPawn))
528 int d = distance(strongPawn + 3 * push, weakKing);
530 if (d <= 2 && !(d == 0 && weakKing == strongKing + 2 * push))
531 return ScaleFactor(24);
533 return ScaleFactor(48);
536 // When the pawn has moved to the 6th rank we can be fairly sure
537 // it's drawn if the bishop attacks the square in front of the
538 // pawn from a reasonable distance and the defending king is near
540 if ( pawnRank == RANK_6
541 && distance(strongPawn + 2 * push, weakKing) <= 1
542 && (attacks_bb<BISHOP>(weakBishop) & (strongPawn + push))
543 && distance<File>(weakBishop, strongPawn) >= 2)
544 return ScaleFactor(8);
547 return SCALE_FACTOR_NONE;
550 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
551 /// pawns and the defending king is actively placed, the position is drawish.
553 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
555 assert(verify_material(pos, strongSide, RookValueMg, 2));
556 assert(verify_material(pos, weakSide, RookValueMg, 1));
558 Square strongPawn1 = lsb(pos.pieces(strongSide, PAWN));
559 Square strongPawn2 = msb(pos.pieces(strongSide, PAWN));
560 Square weakKing = pos.square<KING>(weakSide);
562 // Does the stronger side have a passed pawn?
563 if (pos.pawn_passed(strongSide, strongPawn1) || pos.pawn_passed(strongSide, strongPawn2))
564 return SCALE_FACTOR_NONE;
566 Rank pawnRank = std::max(relative_rank(strongSide, strongPawn1), relative_rank(strongSide, strongPawn2));
568 if ( distance<File>(weakKing, strongPawn1) <= 1
569 && distance<File>(weakKing, strongPawn2) <= 1
570 && relative_rank(strongSide, weakKing) > pawnRank)
572 assert(pawnRank > RANK_1 && pawnRank < RANK_7);
573 return ScaleFactor(7 * pawnRank);
575 return SCALE_FACTOR_NONE;
579 /// K and two or more pawns vs K. There is just a single rule here: if all pawns
580 /// are on the same rook file and are blocked by the defending king, it's a draw.
582 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
584 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
585 assert(pos.count<PAWN>(strongSide) >= 2);
586 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
588 Square weakKing = pos.square<KING>(weakSide);
589 Bitboard strongPawns = pos.pieces(strongSide, PAWN);
591 // If all pawns are ahead of the king on a single rook file, it's a draw.
592 if ( !(strongPawns & ~(FileABB | FileHBB))
593 && !(strongPawns & ~passed_pawn_span(weakSide, weakKing)))
594 return SCALE_FACTOR_DRAW;
596 return SCALE_FACTOR_NONE;
600 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
601 /// path of the pawn, and the square of the king is not of the same color as the
602 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
603 /// it's almost always a draw.
605 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
607 assert(verify_material(pos, strongSide, BishopValueMg, 1));
608 assert(verify_material(pos, weakSide, BishopValueMg, 0));
610 Square strongPawn = pos.square<PAWN>(strongSide);
611 Square strongBishop = pos.square<BISHOP>(strongSide);
612 Square weakBishop = pos.square<BISHOP>(weakSide);
613 Square weakKing = pos.square<KING>(weakSide);
615 // Case 1: Defending king blocks the pawn, and cannot be driven away
616 if ( (forward_file_bb(strongSide, strongPawn) & weakKing)
617 && ( opposite_colors(weakKing, strongBishop)
618 || relative_rank(strongSide, weakKing) <= RANK_6))
619 return SCALE_FACTOR_DRAW;
621 // Case 2: Opposite colored bishops
622 if (opposite_colors(strongBishop, weakBishop))
623 return SCALE_FACTOR_DRAW;
625 return SCALE_FACTOR_NONE;
629 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
631 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
633 assert(verify_material(pos, strongSide, BishopValueMg, 2));
634 assert(verify_material(pos, weakSide, BishopValueMg, 0));
636 Square strongBishop = pos.square<BISHOP>(strongSide);
637 Square weakBishop = pos.square<BISHOP>(weakSide);
639 if (!opposite_colors(strongBishop, weakBishop))
640 return SCALE_FACTOR_NONE;
642 Square weakKing = pos.square<KING>(weakSide);
643 Square strongPawn1 = lsb(pos.pieces(strongSide, PAWN));
644 Square strongPawn2 = msb(pos.pieces(strongSide, PAWN));
645 Square blockSq1, blockSq2;
647 if (relative_rank(strongSide, strongPawn1) > relative_rank(strongSide, strongPawn2))
649 blockSq1 = strongPawn1 + pawn_push(strongSide);
650 blockSq2 = make_square(file_of(strongPawn2), rank_of(strongPawn1));
654 blockSq1 = strongPawn2 + pawn_push(strongSide);
655 blockSq2 = make_square(file_of(strongPawn1), rank_of(strongPawn2));
658 switch (distance<File>(strongPawn1, strongPawn2))
661 // Both pawns are on the same file. It's an easy draw if the defender firmly
662 // controls some square in the frontmost pawn's path.
663 if ( file_of(weakKing) == file_of(blockSq1)
664 && relative_rank(strongSide, weakKing) >= relative_rank(strongSide, blockSq1)
665 && opposite_colors(weakKing, strongBishop))
666 return SCALE_FACTOR_DRAW;
668 return SCALE_FACTOR_NONE;
671 // Pawns on adjacent files. It's a draw if the defender firmly controls the
672 // square in front of the frontmost pawn's path, and the square diagonally
673 // behind this square on the file of the other pawn.
674 if ( weakKing == blockSq1
675 && opposite_colors(weakKing, strongBishop)
676 && ( weakBishop == blockSq2
677 || (attacks_bb<BISHOP>(blockSq2, pos.pieces()) & pos.pieces(weakSide, BISHOP))
678 || distance<Rank>(strongPawn1, strongPawn2) >= 2))
679 return SCALE_FACTOR_DRAW;
681 else if ( weakKing == blockSq2
682 && opposite_colors(weakKing, strongBishop)
683 && ( weakBishop == blockSq1
684 || (attacks_bb<BISHOP>(blockSq1, pos.pieces()) & pos.pieces(weakSide, BISHOP))))
685 return SCALE_FACTOR_DRAW;
687 return SCALE_FACTOR_NONE;
690 // The pawns are not on the same file or adjacent files. No scaling.
691 return SCALE_FACTOR_NONE;
696 /// KBP vs KN. There is a single rule: if the defending king is somewhere along
697 /// the path of the pawn, and the square of the king is not of the same color as
698 /// the stronger side's bishop, it's a draw.
700 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
702 assert(verify_material(pos, strongSide, BishopValueMg, 1));
703 assert(verify_material(pos, weakSide, KnightValueMg, 0));
705 Square strongPawn = pos.square<PAWN>(strongSide);
706 Square strongBishop = pos.square<BISHOP>(strongSide);
707 Square weakKing = pos.square<KING>(weakSide);
709 if ( file_of(weakKing) == file_of(strongPawn)
710 && relative_rank(strongSide, strongPawn) < relative_rank(strongSide, weakKing)
711 && ( opposite_colors(weakKing, strongBishop)
712 || relative_rank(strongSide, weakKing) <= RANK_6))
713 return SCALE_FACTOR_DRAW;
715 return SCALE_FACTOR_NONE;
719 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
720 /// KP vs K bitbase: if the weakest side has a draw without the pawn, it probably
721 /// has at least a draw with the pawn as well. The exception is when the stronger
722 /// side's pawn is far advanced and not on a rook file; in this case it is often
723 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
725 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
727 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
728 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
730 // Assume strongSide is white and the pawn is on files A-D
731 Square strongKing = normalize(pos, strongSide, pos.square<KING>(strongSide));
732 Square weakKing = normalize(pos, strongSide, pos.square<KING>(weakSide));
733 Square strongPawn = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
735 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
737 // If the pawn has advanced to the fifth rank or further, and is not a
738 // rook pawn, it's too dangerous to assume that it's at least a draw.
739 if (rank_of(strongPawn) >= RANK_5 && file_of(strongPawn) != FILE_A)
740 return SCALE_FACTOR_NONE;
742 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
743 // it's probably at least a draw even with the pawn.
744 return Bitbases::probe(strongKing, strongPawn, weakKing, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;
747 } // namespace Stockfish