2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
4 Copyright (C) 2008-2015 Marco Costalba, Joona Kiiski, Tord Romstad
5 Copyright (C) 2015-2020 Marco Costalba, Joona Kiiski, Gary Linscott, Tord Romstad
7 Stockfish is free software: you can redistribute it and/or modify
8 it under the terms of the GNU General Public License as published by
9 the Free Software Foundation, either version 3 of the License, or
10 (at your option) any later version.
12 Stockfish is distributed in the hope that it will be useful,
13 but WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 GNU General Public License for more details.
17 You should have received a copy of the GNU General Public License
18 along with this program. If not, see <http://www.gnu.org/licenses/>.
31 // Table used to drive the king towards the edge of the board
32 // in KX vs K and KQ vs KR endgames.
33 constexpr int PushToEdges[SQUARE_NB] = {
34 100, 90, 80, 70, 70, 80, 90, 100,
35 90, 70, 60, 50, 50, 60, 70, 90,
36 80, 60, 40, 30, 30, 40, 60, 80,
37 70, 50, 30, 20, 20, 30, 50, 70,
38 70, 50, 30, 20, 20, 30, 50, 70,
39 80, 60, 40, 30, 30, 40, 60, 80,
40 90, 70, 60, 50, 50, 60, 70, 90,
41 100, 90, 80, 70, 70, 80, 90, 100
44 // Table used to drive the king towards a corner square of the
45 // right color in KBN vs K endgames.
46 constexpr int PushToCorners[SQUARE_NB] = {
47 6400, 6080, 5760, 5440, 5120, 4800, 4480, 4160,
48 6080, 5760, 5440, 5120, 4800, 4480, 4160, 4480,
49 5760, 5440, 4960, 4480, 4480, 4000, 4480, 4800,
50 5440, 5120, 4480, 3840, 3520, 4480, 4800, 5120,
51 5120, 4800, 4480, 3520, 3840, 4480, 5120, 5440,
52 4800, 4480, 4000, 4480, 4480, 4960, 5440, 5760,
53 4480, 4160, 4480, 4800, 5120, 5440, 5760, 6080,
54 4160, 4480, 4800, 5120, 5440, 5760, 6080, 6400
57 // Drive a piece close to or away from another piece
58 inline int push_close(Square s1, Square s2) { return 140 - 20 * distance(s1, s2); }
59 inline int push_away(Square s1, Square s2) { return 120 - push_close(s1, s2); }
62 bool verify_material(const Position& pos, Color c, Value npm, int pawnsCnt) {
63 return pos.non_pawn_material(c) == npm && pos.count<PAWN>(c) == pawnsCnt;
67 // Map the square as if strongSide is white and strongSide's only pawn
68 // is on the left half of the board.
69 Square normalize(const Position& pos, Color strongSide, Square sq) {
71 assert(pos.count<PAWN>(strongSide) == 1);
73 if (file_of(pos.square<PAWN>(strongSide)) >= FILE_E)
76 return strongSide == WHITE ? sq : flip_rank(sq);
84 std::pair<Map<Value>, Map<ScaleFactor>> maps;
104 add<KBPPKB>("KBPPKB");
105 add<KRPPKRP>("KRPPKRP");
110 /// Mate with KX vs K. This function is used to evaluate positions with
111 /// king and plenty of material vs a lone king. It simply gives the
112 /// attacking side a bonus for driving the defending king towards the edge
113 /// of the board, and for keeping the distance between the two kings small.
115 Value Endgame<KXK>::operator()(const Position& pos) const {
117 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
118 assert(!pos.checkers()); // Eval is never called when in check
120 // Stalemate detection with lone king
121 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
124 Square winnerKSq = pos.square<KING>(strongSide);
125 Square loserKSq = pos.square<KING>(weakSide);
127 Value result = pos.non_pawn_material(strongSide)
128 + pos.count<PAWN>(strongSide) * PawnValueEg
129 + PushToEdges[loserKSq]
130 + push_close(winnerKSq, loserKSq);
132 if ( pos.count<QUEEN>(strongSide)
133 || pos.count<ROOK>(strongSide)
134 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
135 || ( (pos.pieces(strongSide, BISHOP) & ~DarkSquares)
136 && (pos.pieces(strongSide, BISHOP) & DarkSquares)))
137 result = std::min(result + VALUE_KNOWN_WIN, VALUE_TB_WIN_IN_MAX_PLY - 1);
139 return strongSide == pos.side_to_move() ? result : -result;
143 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
144 /// defending king towards a corner square that our bishop attacks.
146 Value Endgame<KBNK>::operator()(const Position& pos) const {
148 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
149 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
151 Square winnerKSq = pos.square<KING>(strongSide);
152 Square loserKSq = pos.square<KING>(weakSide);
153 Square bishopSq = pos.square<BISHOP>(strongSide);
155 // If our bishop does not attack A1/H8, we flip the enemy king square
156 // to drive to opposite corners (A8/H1).
158 Value result = VALUE_KNOWN_WIN
159 + push_close(winnerKSq, loserKSq)
160 + PushToCorners[opposite_colors(bishopSq, SQ_A1) ? ~loserKSq : loserKSq];
162 assert(abs(result) < VALUE_TB_WIN_IN_MAX_PLY);
163 return strongSide == pos.side_to_move() ? result : -result;
167 /// KP vs K. This endgame is evaluated with the help of a bitbase
169 Value Endgame<KPK>::operator()(const Position& pos) const {
171 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
172 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
174 // Assume strongSide is white and the pawn is on files A-D
175 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
176 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
177 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
179 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
181 if (!Bitbases::probe(wksq, psq, bksq, us))
184 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
186 return strongSide == pos.side_to_move() ? result : -result;
190 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
191 /// a bitbase. The function below returns drawish scores when the pawn is
192 /// far advanced with support of the king, while the attacking king is far
195 Value Endgame<KRKP>::operator()(const Position& pos) const {
197 assert(verify_material(pos, strongSide, RookValueMg, 0));
198 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
200 Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
201 Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
202 Square rsq = relative_square(strongSide, pos.square<ROOK>(strongSide));
203 Square psq = relative_square(strongSide, pos.square<PAWN>(weakSide));
205 Square queeningSq = make_square(file_of(psq), RANK_1);
208 // If the stronger side's king is in front of the pawn, it's a win
209 if (forward_file_bb(WHITE, wksq) & psq)
210 result = RookValueEg - distance(wksq, psq);
212 // If the weaker side's king is too far from the pawn and the rook,
214 else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
215 && distance(bksq, rsq) >= 3)
216 result = RookValueEg - distance(wksq, psq);
218 // If the pawn is far advanced and supported by the defending king,
219 // the position is drawish
220 else if ( rank_of(bksq) <= RANK_3
221 && distance(bksq, psq) == 1
222 && rank_of(wksq) >= RANK_4
223 && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
224 result = Value(80) - 8 * distance(wksq, psq);
227 result = Value(200) - 8 * ( distance(wksq, psq + SOUTH)
228 - distance(bksq, psq + SOUTH)
229 - distance(psq, queeningSq));
231 return strongSide == pos.side_to_move() ? result : -result;
235 /// KR vs KB. This is very simple, and always returns drawish scores. The
236 /// score is slightly bigger when the defending king is close to the edge.
238 Value Endgame<KRKB>::operator()(const Position& pos) const {
240 assert(verify_material(pos, strongSide, RookValueMg, 0));
241 assert(verify_material(pos, weakSide, BishopValueMg, 0));
243 Value result = Value(PushToEdges[pos.square<KING>(weakSide)]);
244 return strongSide == pos.side_to_move() ? result : -result;
248 /// KR vs KN. The attacking side has slightly better winning chances than
249 /// in KR vs KB, particularly if the king and the knight are far apart.
251 Value Endgame<KRKN>::operator()(const Position& pos) const {
253 assert(verify_material(pos, strongSide, RookValueMg, 0));
254 assert(verify_material(pos, weakSide, KnightValueMg, 0));
256 Square bksq = pos.square<KING>(weakSide);
257 Square bnsq = pos.square<KNIGHT>(weakSide);
258 Value result = Value(PushToEdges[bksq] + push_away(bksq, bnsq));
259 return strongSide == pos.side_to_move() ? result : -result;
263 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
264 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
265 /// with a king positioned next to it can be a draw, so in that case, we only
266 /// use the distance between the kings.
268 Value Endgame<KQKP>::operator()(const Position& pos) const {
270 assert(verify_material(pos, strongSide, QueenValueMg, 0));
271 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
273 Square winnerKSq = pos.square<KING>(strongSide);
274 Square loserKSq = pos.square<KING>(weakSide);
275 Square pawnSq = pos.square<PAWN>(weakSide);
277 Value result = Value(push_close(winnerKSq, loserKSq));
279 if ( relative_rank(weakSide, pawnSq) != RANK_7
280 || distance(loserKSq, pawnSq) != 1
281 || ((FileBBB | FileDBB | FileEBB | FileGBB) & pawnSq))
282 result += QueenValueEg - PawnValueEg;
284 return strongSide == pos.side_to_move() ? result : -result;
288 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
289 /// king a bonus for having the kings close together, and for forcing the
290 /// defending king towards the edge. If we also take care to avoid null move for
291 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
293 Value Endgame<KQKR>::operator()(const Position& pos) const {
295 assert(verify_material(pos, strongSide, QueenValueMg, 0));
296 assert(verify_material(pos, weakSide, RookValueMg, 0));
298 Square winnerKSq = pos.square<KING>(strongSide);
299 Square loserKSq = pos.square<KING>(weakSide);
301 Value result = QueenValueEg
303 + PushToEdges[loserKSq]
304 + push_close(winnerKSq, loserKSq);
306 return strongSide == pos.side_to_move() ? result : -result;
310 /// KNN vs KP. Very drawish, but there are some mate opportunities if we can
311 // press the weakSide King to a corner before the pawn advances too much.
313 Value Endgame<KNNKP>::operator()(const Position& pos) const {
315 assert(verify_material(pos, strongSide, 2 * KnightValueMg, 0));
316 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
318 Value result = PawnValueEg
319 + 2 * PushToEdges[pos.square<KING>(weakSide)]
320 - 10 * relative_rank(weakSide, pos.square<PAWN>(weakSide));
322 return strongSide == pos.side_to_move() ? result : -result;
326 /// Some cases of trivial draws
327 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
330 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
331 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
332 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
335 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
337 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
338 assert(pos.count<PAWN>(strongSide) >= 1);
340 // No assertions about the material of weakSide, because we want draws to
341 // be detected even when the weaker side has some pawns.
343 Bitboard strongpawns = pos.pieces(strongSide, PAWN);
344 Bitboard allpawns = pos.pieces(PAWN);
346 // All strongSide pawns are on a single rook file?
347 if (!(strongpawns & ~FileABB) || !(strongpawns & ~FileHBB))
349 Square bishopSq = pos.square<BISHOP>(strongSide);
350 Square queeningSq = relative_square(strongSide, make_square(file_of(lsb(strongpawns)), RANK_8));
351 Square weakkingSq = pos.square<KING>(weakSide);
353 if ( opposite_colors(queeningSq, bishopSq)
354 && distance(queeningSq, weakkingSq) <= 1)
355 return SCALE_FACTOR_DRAW;
358 // If all the pawns are on the same B or G file, then it's potentially a draw
359 if ((!(allpawns & ~FileBBB) || !(allpawns & ~FileGBB))
360 && pos.non_pawn_material(weakSide) == 0
361 && pos.count<PAWN>(weakSide) >= 1)
363 // Get the least advanced weakSide pawn
364 Square weakPawnSq = frontmost_sq(strongSide, pos.pieces(weakSide, PAWN));
366 Square strongKingSq = pos.square<KING>(strongSide);
367 Square weakKingSq = pos.square<KING>(weakSide);
368 Square bishopSq = pos.square<BISHOP>(strongSide);
370 // There's potential for a draw if our pawn is blocked on the 7th rank,
371 // the bishop cannot attack it or they only have one pawn left
372 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
373 && (strongpawns & (weakPawnSq + pawn_push(weakSide)))
374 && (opposite_colors(bishopSq, weakPawnSq) || !more_than_one(strongpawns)))
376 int strongKingDist = distance(weakPawnSq, strongKingSq);
377 int weakKingDist = distance(weakPawnSq, weakKingSq);
379 // It's a draw if the weak king is on its back two ranks, within 2
380 // squares of the blocking pawn and the strong king is not
381 // closer. (I think this rule only fails in practically
382 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
383 // and positions where qsearch will immediately correct the
384 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
385 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
387 && weakKingDist <= strongKingDist)
388 return SCALE_FACTOR_DRAW;
392 return SCALE_FACTOR_NONE;
396 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
397 /// the third rank defended by a pawn.
399 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
401 assert(verify_material(pos, strongSide, QueenValueMg, 0));
402 assert(pos.count<ROOK>(weakSide) == 1);
403 assert(pos.count<PAWN>(weakSide) >= 1);
405 Square kingSq = pos.square<KING>(weakSide);
406 Square rsq = pos.square<ROOK>(weakSide);
408 if ( relative_rank(weakSide, kingSq) <= RANK_2
409 && relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
410 && relative_rank(weakSide, rsq) == RANK_3
411 && ( pos.pieces(weakSide, PAWN)
412 & pos.attacks_from<KING>(kingSq)
413 & pos.attacks_from<PAWN>(rsq, strongSide)))
414 return SCALE_FACTOR_DRAW;
416 return SCALE_FACTOR_NONE;
420 /// KRP vs KR. This function knows a handful of the most important classes of
421 /// drawn positions, but is far from perfect. It would probably be a good idea
422 /// to add more knowledge in the future.
424 /// It would also be nice to rewrite the actual code for this function,
425 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
427 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
429 assert(verify_material(pos, strongSide, RookValueMg, 1));
430 assert(verify_material(pos, weakSide, RookValueMg, 0));
432 // Assume strongSide is white and the pawn is on files A-D
433 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
434 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
435 Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
436 Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
437 Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
439 File f = file_of(wpsq);
440 Rank r = rank_of(wpsq);
441 Square queeningSq = make_square(f, RANK_8);
442 int tempo = (pos.side_to_move() == strongSide);
444 // If the pawn is not too far advanced and the defending king defends the
445 // queening square, use the third-rank defence.
447 && distance(bksq, queeningSq) <= 1
449 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
450 return SCALE_FACTOR_DRAW;
452 // The defending side saves a draw by checking from behind in case the pawn
453 // has advanced to the 6th rank with the king behind.
455 && distance(bksq, queeningSq) <= 1
456 && rank_of(wksq) + tempo <= RANK_6
457 && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
458 return SCALE_FACTOR_DRAW;
461 && bksq == queeningSq
462 && rank_of(brsq) == RANK_1
463 && (!tempo || distance(wksq, wpsq) >= 2))
464 return SCALE_FACTOR_DRAW;
466 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
467 // and the black rook is behind the pawn.
470 && (bksq == SQ_H7 || bksq == SQ_G7)
471 && file_of(brsq) == FILE_A
472 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
473 return SCALE_FACTOR_DRAW;
475 // If the defending king blocks the pawn and the attacking king is too far
476 // away, it's a draw.
478 && bksq == wpsq + NORTH
479 && distance(wksq, wpsq) - tempo >= 2
480 && distance(wksq, brsq) - tempo >= 2)
481 return SCALE_FACTOR_DRAW;
483 // Pawn on the 7th rank supported by the rook from behind usually wins if the
484 // attacking king is closer to the queening square than the defending king,
485 // and the defending king cannot gain tempi by threatening the attacking rook.
488 && file_of(wrsq) == f
489 && wrsq != queeningSq
490 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
491 && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
492 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
494 // Similar to the above, but with the pawn further back
496 && file_of(wrsq) == f
498 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
499 && (distance(wksq, wpsq + NORTH) < distance(bksq, wpsq + NORTH) - 2 + tempo)
500 && ( distance(bksq, wrsq) + tempo >= 3
501 || ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
502 && (distance(wksq, wpsq + NORTH) < distance(bksq, wrsq) + tempo))))
503 return ScaleFactor( SCALE_FACTOR_MAX
504 - 8 * distance(wpsq, queeningSq)
505 - 2 * distance(wksq, queeningSq));
507 // If the pawn is not far advanced and the defending king is somewhere in
508 // the pawn's path, it's probably a draw.
509 if (r <= RANK_4 && bksq > wpsq)
511 if (file_of(bksq) == file_of(wpsq))
512 return ScaleFactor(10);
513 if ( distance<File>(bksq, wpsq) == 1
514 && distance(wksq, bksq) > 2)
515 return ScaleFactor(24 - 2 * distance(wksq, bksq));
517 return SCALE_FACTOR_NONE;
521 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
523 assert(verify_material(pos, strongSide, RookValueMg, 1));
524 assert(verify_material(pos, weakSide, BishopValueMg, 0));
526 // Test for a rook pawn
527 if (pos.pieces(PAWN) & (FileABB | FileHBB))
529 Square ksq = pos.square<KING>(weakSide);
530 Square bsq = pos.square<BISHOP>(weakSide);
531 Square psq = pos.square<PAWN>(strongSide);
532 Rank rk = relative_rank(strongSide, psq);
533 Direction push = pawn_push(strongSide);
535 // If the pawn is on the 5th rank and the pawn (currently) is on
536 // the same color square as the bishop then there is a chance of
537 // a fortress. Depending on the king position give a moderate
538 // reduction or a stronger one if the defending king is near the
539 // corner but not trapped there.
540 if (rk == RANK_5 && !opposite_colors(bsq, psq))
542 int d = distance(psq + 3 * push, ksq);
544 if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
545 return ScaleFactor(24);
547 return ScaleFactor(48);
550 // When the pawn has moved to the 6th rank we can be fairly sure
551 // it's drawn if the bishop attacks the square in front of the
552 // pawn from a reasonable distance and the defending king is near
555 && distance(psq + 2 * push, ksq) <= 1
556 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
557 && distance<File>(bsq, psq) >= 2)
558 return ScaleFactor(8);
561 return SCALE_FACTOR_NONE;
564 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
565 /// pawns and the defending king is actively placed, the position is drawish.
567 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
569 assert(verify_material(pos, strongSide, RookValueMg, 2));
570 assert(verify_material(pos, weakSide, RookValueMg, 1));
572 Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
573 Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
574 Square bksq = pos.square<KING>(weakSide);
576 // Does the stronger side have a passed pawn?
577 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
578 return SCALE_FACTOR_NONE;
580 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
582 if ( distance<File>(bksq, wpsq1) <= 1
583 && distance<File>(bksq, wpsq2) <= 1
584 && relative_rank(strongSide, bksq) > r)
586 assert(r > RANK_1 && r < RANK_7);
587 return ScaleFactor(7 * r);
589 return SCALE_FACTOR_NONE;
593 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
594 /// are on the same rook file and are blocked by the defending king, it's a draw.
596 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
598 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
599 assert(pos.count<PAWN>(strongSide) >= 2);
600 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
602 Square ksq = pos.square<KING>(weakSide);
603 Bitboard pawns = pos.pieces(strongSide, PAWN);
605 // If all pawns are ahead of the king, on a single rook file and
606 // the king is within one file of the pawns, it's a draw.
607 if ( !(pawns & ~forward_ranks_bb(weakSide, ksq))
608 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
609 && distance<File>(ksq, lsb(pawns)) <= 1)
610 return SCALE_FACTOR_DRAW;
612 return SCALE_FACTOR_NONE;
616 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
617 /// path of the pawn, and the square of the king is not of the same color as the
618 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
619 /// it's almost always a draw.
621 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
623 assert(verify_material(pos, strongSide, BishopValueMg, 1));
624 assert(verify_material(pos, weakSide, BishopValueMg, 0));
626 Square pawnSq = pos.square<PAWN>(strongSide);
627 Square strongBishopSq = pos.square<BISHOP>(strongSide);
628 Square weakBishopSq = pos.square<BISHOP>(weakSide);
629 Square weakKingSq = pos.square<KING>(weakSide);
631 // Case 1: Defending king blocks the pawn, and cannot be driven away
632 if ( file_of(weakKingSq) == file_of(pawnSq)
633 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
634 && ( opposite_colors(weakKingSq, strongBishopSq)
635 || relative_rank(strongSide, weakKingSq) <= RANK_6))
636 return SCALE_FACTOR_DRAW;
638 // Case 2: Opposite colored bishops
639 if (opposite_colors(strongBishopSq, weakBishopSq))
640 return SCALE_FACTOR_DRAW;
642 return SCALE_FACTOR_NONE;
646 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
648 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
650 assert(verify_material(pos, strongSide, BishopValueMg, 2));
651 assert(verify_material(pos, weakSide, BishopValueMg, 0));
653 Square wbsq = pos.square<BISHOP>(strongSide);
654 Square bbsq = pos.square<BISHOP>(weakSide);
656 if (!opposite_colors(wbsq, bbsq))
657 return SCALE_FACTOR_NONE;
659 Square ksq = pos.square<KING>(weakSide);
660 Square psq1 = pos.squares<PAWN>(strongSide)[0];
661 Square psq2 = pos.squares<PAWN>(strongSide)[1];
662 Square blockSq1, blockSq2;
664 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
666 blockSq1 = psq1 + pawn_push(strongSide);
667 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
671 blockSq1 = psq2 + pawn_push(strongSide);
672 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
675 switch (distance<File>(psq1, psq2))
678 // Both pawns are on the same file. It's an easy draw if the defender firmly
679 // controls some square in the frontmost pawn's path.
680 if ( file_of(ksq) == file_of(blockSq1)
681 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
682 && opposite_colors(ksq, wbsq))
683 return SCALE_FACTOR_DRAW;
685 return SCALE_FACTOR_NONE;
688 // Pawns on adjacent files. It's a draw if the defender firmly controls the
689 // square in front of the frontmost pawn's path, and the square diagonally
690 // behind this square on the file of the other pawn.
692 && opposite_colors(ksq, wbsq)
693 && ( bbsq == blockSq2
694 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
695 || distance<Rank>(psq1, psq2) >= 2))
696 return SCALE_FACTOR_DRAW;
698 else if ( ksq == blockSq2
699 && opposite_colors(ksq, wbsq)
700 && ( bbsq == blockSq1
701 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
702 return SCALE_FACTOR_DRAW;
704 return SCALE_FACTOR_NONE;
707 // The pawns are not on the same file or adjacent files. No scaling.
708 return SCALE_FACTOR_NONE;
713 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
714 /// the path of the pawn, and the square of the king is not of the same color as
715 /// the stronger side's bishop, it's a draw.
717 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
719 assert(verify_material(pos, strongSide, BishopValueMg, 1));
720 assert(verify_material(pos, weakSide, KnightValueMg, 0));
722 Square pawnSq = pos.square<PAWN>(strongSide);
723 Square strongBishopSq = pos.square<BISHOP>(strongSide);
724 Square weakKingSq = pos.square<KING>(weakSide);
726 if ( file_of(weakKingSq) == file_of(pawnSq)
727 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
728 && ( opposite_colors(weakKingSq, strongBishopSq)
729 || relative_rank(strongSide, weakKingSq) <= RANK_6))
730 return SCALE_FACTOR_DRAW;
732 return SCALE_FACTOR_NONE;
736 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
737 /// and the defending king prevents the pawn from advancing, the position is drawn.
739 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
741 assert(verify_material(pos, strongSide, KnightValueMg, 1));
742 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
744 // Assume strongSide is white and the pawn is on files A-D
745 Square pawnSq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
746 Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
748 if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
749 return SCALE_FACTOR_DRAW;
751 return SCALE_FACTOR_NONE;
755 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
756 /// Otherwise the position is drawn.
758 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
760 assert(verify_material(pos, strongSide, KnightValueMg, 1));
761 assert(verify_material(pos, weakSide, BishopValueMg, 0));
763 Square pawnSq = pos.square<PAWN>(strongSide);
764 Square bishopSq = pos.square<BISHOP>(weakSide);
765 Square weakKingSq = pos.square<KING>(weakSide);
767 // King needs to get close to promoting pawn to prevent knight from blocking.
768 // Rules for this are very tricky, so just approximate.
769 if (forward_file_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
770 return ScaleFactor(distance(weakKingSq, pawnSq));
772 return SCALE_FACTOR_NONE;
776 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
777 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
778 /// has at least a draw with the pawn as well. The exception is when the stronger
779 /// side's pawn is far advanced and not on a rook file; in this case it is often
780 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
782 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
784 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
785 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
787 // Assume strongSide is white and the pawn is on files A-D
788 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
789 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
790 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
792 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
794 // If the pawn has advanced to the fifth rank or further, and is not a
795 // rook pawn, it's too dangerous to assume that it's at least a draw.
796 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
797 return SCALE_FACTOR_NONE;
799 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
800 // it's probably at least a draw even with the pawn.
801 return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;