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/>.
29 // Used to drive the king towards the edge of the board
30 // in KX vs K and KQ vs KR endgames.
31 inline int push_to_edge(Square s) {
32 int rd = edge_distance(rank_of(s)), fd = edge_distance(file_of(s));
33 return 90 - (7 * fd * fd / 2 + 7 * rd * rd / 2);
36 // Used to drive the king towards A1H8 corners in KBN vs K endgames.
37 inline int push_to_corner(Square s) {
38 return abs(7 - rank_of(s) - file_of(s));
41 // Drive a piece close to or away from another piece
42 inline int push_close(Square s1, Square s2) { return 140 - 20 * distance(s1, s2); }
43 inline int push_away(Square s1, Square s2) { return 120 - push_close(s1, s2); }
46 bool verify_material(const Position& pos, Color c, Value npm, int pawnsCnt) {
47 return pos.non_pawn_material(c) == npm && pos.count<PAWN>(c) == pawnsCnt;
51 // Map the square as if strongSide is white and strongSide's only pawn
52 // is on the left half of the board.
53 Square normalize(const Position& pos, Color strongSide, Square sq) {
55 assert(pos.count<PAWN>(strongSide) == 1);
57 if (file_of(pos.square<PAWN>(strongSide)) >= FILE_E)
60 return strongSide == WHITE ? sq : flip_rank(sq);
68 std::pair<Map<Value>, Map<ScaleFactor>> maps;
87 add<KBPPKB>("KBPPKB");
88 add<KRPPKRP>("KRPPKRP");
93 /// Mate with KX vs K. This function is used to evaluate positions with
94 /// king and plenty of material vs a lone king. It simply gives the
95 /// attacking side a bonus for driving the defending king towards the edge
96 /// of the board, and for keeping the distance between the two kings small.
98 Value Endgame<KXK>::operator()(const Position& pos) const {
100 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
101 assert(!pos.checkers()); // Eval is never called when in check
103 // Stalemate detection with lone king
104 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
107 Square winnerKSq = pos.square<KING>(strongSide);
108 Square loserKSq = pos.square<KING>(weakSide);
110 Value result = pos.non_pawn_material(strongSide)
111 + pos.count<PAWN>(strongSide) * PawnValueEg
112 + push_to_edge(loserKSq)
113 + push_close(winnerKSq, loserKSq);
115 if ( pos.count<QUEEN>(strongSide)
116 || pos.count<ROOK>(strongSide)
117 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
118 || ( (pos.pieces(strongSide, BISHOP) & ~DarkSquares)
119 && (pos.pieces(strongSide, BISHOP) & DarkSquares)))
120 result = std::min(result + VALUE_KNOWN_WIN, VALUE_TB_WIN_IN_MAX_PLY - 1);
122 return strongSide == pos.side_to_move() ? result : -result;
126 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
127 /// defending king towards a corner square that our bishop attacks.
129 Value Endgame<KBNK>::operator()(const Position& pos) const {
131 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
132 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
134 Square winnerKSq = pos.square<KING>(strongSide);
135 Square loserKSq = pos.square<KING>(weakSide);
136 Square bishopSq = pos.square<BISHOP>(strongSide);
138 // If our bishop does not attack A1/H8, we flip the enemy king square
139 // to drive to opposite corners (A8/H1).
141 Value result = (VALUE_KNOWN_WIN + 3520)
142 + push_close(winnerKSq, loserKSq)
143 + 420 * push_to_corner(opposite_colors(bishopSq, SQ_A1) ? flip_file(loserKSq) : loserKSq);
145 assert(abs(result) < VALUE_TB_WIN_IN_MAX_PLY);
146 return strongSide == pos.side_to_move() ? result : -result;
150 /// KP vs K. This endgame is evaluated with the help of a bitbase
152 Value Endgame<KPK>::operator()(const Position& pos) const {
154 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
155 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
157 // Assume strongSide is white and the pawn is on files A-D
158 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
159 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
160 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
162 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
164 if (!Bitbases::probe(wksq, psq, bksq, us))
167 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
169 return strongSide == pos.side_to_move() ? result : -result;
173 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
174 /// a bitbase. The function below returns drawish scores when the pawn is
175 /// far advanced with support of the king, while the attacking king is far
178 Value Endgame<KRKP>::operator()(const Position& pos) const {
180 assert(verify_material(pos, strongSide, RookValueMg, 0));
181 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
183 Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
184 Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
185 Square rsq = relative_square(strongSide, pos.square<ROOK>(strongSide));
186 Square psq = relative_square(strongSide, pos.square<PAWN>(weakSide));
188 Square queeningSq = make_square(file_of(psq), RANK_1);
191 // If the stronger side's king is in front of the pawn, it's a win
192 if (forward_file_bb(WHITE, wksq) & psq)
193 result = RookValueEg - distance(wksq, psq);
195 // If the weaker side's king is too far from the pawn and the rook,
197 else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
198 && distance(bksq, rsq) >= 3)
199 result = RookValueEg - distance(wksq, psq);
201 // If the pawn is far advanced and supported by the defending king,
202 // the position is drawish
203 else if ( rank_of(bksq) <= RANK_3
204 && distance(bksq, psq) == 1
205 && rank_of(wksq) >= RANK_4
206 && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
207 result = Value(80) - 8 * distance(wksq, psq);
210 result = Value(200) - 8 * ( distance(wksq, psq + SOUTH)
211 - distance(bksq, psq + SOUTH)
212 - distance(psq, queeningSq));
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 bksq = pos.square<KING>(weakSide);
240 Square bnsq = pos.square<KNIGHT>(weakSide);
241 Value result = Value(push_to_edge(bksq) + push_away(bksq, bnsq));
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 winnerKSq = pos.square<KING>(strongSide);
257 Square loserKSq = pos.square<KING>(weakSide);
258 Square pawnSq = pos.square<PAWN>(weakSide);
260 Value result = Value(push_close(winnerKSq, loserKSq));
262 if ( relative_rank(weakSide, pawnSq) != RANK_7
263 || distance(loserKSq, pawnSq) != 1
264 || ((FileBBB | FileDBB | FileEBB | FileGBB) & pawnSq))
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 winnerKSq = pos.square<KING>(strongSide);
282 Square loserKSq = pos.square<KING>(weakSide);
284 Value result = QueenValueEg
286 + push_to_edge(loserKSq)
287 + push_close(winnerKSq, loserKSq);
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 Value result = PawnValueEg
302 + 2 * push_to_edge(pos.square<KING>(weakSide))
303 - 10 * relative_rank(weakSide, pos.square<PAWN>(weakSide));
305 return strongSide == pos.side_to_move() ? result : -result;
309 /// Some cases of trivial draws
310 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
313 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
314 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
315 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
318 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
320 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
321 assert(pos.count<PAWN>(strongSide) >= 1);
323 // No assertions about the material of weakSide, because we want draws to
324 // be detected even when the weaker side has some pawns.
326 Bitboard strongPawns = pos.pieces(strongSide, PAWN);
327 Bitboard allPawns = pos.pieces(PAWN);
329 // All strongSide pawns are on a single rook file?
330 if (!(strongPawns & ~FileABB) || !(strongPawns & ~FileHBB))
332 Square bishopSq = pos.square<BISHOP>(strongSide);
333 Square queeningSq = relative_square(strongSide, make_square(file_of(lsb(strongPawns)), RANK_8));
334 Square weakKingSq = pos.square<KING>(weakSide);
336 if ( opposite_colors(queeningSq, bishopSq)
337 && distance(queeningSq, weakKingSq) <= 1)
338 return SCALE_FACTOR_DRAW;
341 // If all the pawns are on the same B or G file, then it's potentially a draw
342 if ((!(allPawns & ~FileBBB) || !(allPawns & ~FileGBB))
343 && pos.non_pawn_material(weakSide) == 0
344 && pos.count<PAWN>(weakSide) >= 1)
346 // Get the least advanced weakSide pawn
347 Square weakPawnSq = frontmost_sq(strongSide, pos.pieces(weakSide, PAWN));
349 Square strongKingSq = pos.square<KING>(strongSide);
350 Square weakKingSq = pos.square<KING>(weakSide);
351 Square bishopSq = pos.square<BISHOP>(strongSide);
353 // There's potential for a draw if our pawn is blocked on the 7th rank,
354 // the bishop cannot attack it or they only have one pawn left
355 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
356 && (strongPawns & (weakPawnSq + pawn_push(weakSide)))
357 && (opposite_colors(bishopSq, weakPawnSq) || !more_than_one(strongPawns)))
359 int strongKingDist = distance(weakPawnSq, strongKingSq);
360 int weakKingDist = distance(weakPawnSq, weakKingSq);
362 // It's a draw if the weak king is on its back two ranks, within 2
363 // squares of the blocking pawn and the strong king is not
364 // closer. (I think this rule only fails in practically
365 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
366 // and positions where qsearch will immediately correct the
367 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
368 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
370 && weakKingDist <= strongKingDist)
371 return SCALE_FACTOR_DRAW;
375 return SCALE_FACTOR_NONE;
379 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
380 /// the third rank defended by a pawn.
382 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
384 assert(verify_material(pos, strongSide, QueenValueMg, 0));
385 assert(pos.count<ROOK>(weakSide) == 1);
386 assert(pos.count<PAWN>(weakSide) >= 1);
388 Square kingSq = pos.square<KING>(weakSide);
389 Square rsq = pos.square<ROOK>(weakSide);
391 if ( relative_rank(weakSide, kingSq) <= RANK_2
392 && relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
393 && relative_rank(weakSide, rsq) == RANK_3
394 && ( pos.pieces(weakSide, PAWN)
395 & pos.attacks_from<KING>(kingSq)
396 & pos.attacks_from<PAWN>(rsq, strongSide)))
397 return SCALE_FACTOR_DRAW;
399 return SCALE_FACTOR_NONE;
403 /// KRP vs KR. This function knows a handful of the most important classes of
404 /// drawn positions, but is far from perfect. It would probably be a good idea
405 /// to add more knowledge in the future.
407 /// It would also be nice to rewrite the actual code for this function,
408 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
410 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
412 assert(verify_material(pos, strongSide, RookValueMg, 1));
413 assert(verify_material(pos, weakSide, RookValueMg, 0));
415 // Assume strongSide is white and the pawn is on files A-D
416 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
417 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
418 Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
419 Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
420 Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
422 File f = file_of(wpsq);
423 Rank r = rank_of(wpsq);
424 Square queeningSq = make_square(f, RANK_8);
425 int tempo = (pos.side_to_move() == strongSide);
427 // If the pawn is not too far advanced and the defending king defends the
428 // queening square, use the third-rank defence.
430 && distance(bksq, queeningSq) <= 1
432 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
433 return SCALE_FACTOR_DRAW;
435 // The defending side saves a draw by checking from behind in case the pawn
436 // has advanced to the 6th rank with the king behind.
438 && distance(bksq, queeningSq) <= 1
439 && rank_of(wksq) + tempo <= RANK_6
440 && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
441 return SCALE_FACTOR_DRAW;
444 && bksq == queeningSq
445 && rank_of(brsq) == RANK_1
446 && (!tempo || distance(wksq, wpsq) >= 2))
447 return SCALE_FACTOR_DRAW;
449 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
450 // and the black rook is behind the pawn.
453 && (bksq == SQ_H7 || bksq == SQ_G7)
454 && file_of(brsq) == FILE_A
455 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
456 return SCALE_FACTOR_DRAW;
458 // If the defending king blocks the pawn and the attacking king is too far
459 // away, it's a draw.
461 && bksq == wpsq + NORTH
462 && distance(wksq, wpsq) - tempo >= 2
463 && distance(wksq, brsq) - tempo >= 2)
464 return SCALE_FACTOR_DRAW;
466 // Pawn on the 7th rank supported by the rook from behind usually wins if the
467 // attacking king is closer to the queening square than the defending king,
468 // and the defending king cannot gain tempi by threatening the attacking rook.
471 && file_of(wrsq) == f
472 && wrsq != queeningSq
473 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
474 && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
475 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
477 // Similar to the above, but with the pawn further back
479 && file_of(wrsq) == f
481 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
482 && (distance(wksq, wpsq + NORTH) < distance(bksq, wpsq + NORTH) - 2 + tempo)
483 && ( distance(bksq, wrsq) + tempo >= 3
484 || ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
485 && (distance(wksq, wpsq + NORTH) < distance(bksq, wrsq) + tempo))))
486 return ScaleFactor( SCALE_FACTOR_MAX
487 - 8 * distance(wpsq, queeningSq)
488 - 2 * distance(wksq, queeningSq));
490 // If the pawn is not far advanced and the defending king is somewhere in
491 // the pawn's path, it's probably a draw.
492 if (r <= RANK_4 && bksq > wpsq)
494 if (file_of(bksq) == file_of(wpsq))
495 return ScaleFactor(10);
496 if ( distance<File>(bksq, wpsq) == 1
497 && distance(wksq, bksq) > 2)
498 return ScaleFactor(24 - 2 * distance(wksq, bksq));
500 return SCALE_FACTOR_NONE;
504 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
506 assert(verify_material(pos, strongSide, RookValueMg, 1));
507 assert(verify_material(pos, weakSide, BishopValueMg, 0));
509 // Test for a rook pawn
510 if (pos.pieces(PAWN) & (FileABB | FileHBB))
512 Square ksq = pos.square<KING>(weakSide);
513 Square bsq = pos.square<BISHOP>(weakSide);
514 Square psq = pos.square<PAWN>(strongSide);
515 Rank rk = relative_rank(strongSide, psq);
516 Direction push = pawn_push(strongSide);
518 // If the pawn is on the 5th rank and the pawn (currently) is on
519 // the same color square as the bishop then there is a chance of
520 // a fortress. Depending on the king position give a moderate
521 // reduction or a stronger one if the defending king is near the
522 // corner but not trapped there.
523 if (rk == RANK_5 && !opposite_colors(bsq, psq))
525 int d = distance(psq + 3 * push, ksq);
527 if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
528 return ScaleFactor(24);
530 return ScaleFactor(48);
533 // When the pawn has moved to the 6th rank we can be fairly sure
534 // it's drawn if the bishop attacks the square in front of the
535 // pawn from a reasonable distance and the defending king is near
538 && distance(psq + 2 * push, ksq) <= 1
539 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
540 && distance<File>(bsq, psq) >= 2)
541 return ScaleFactor(8);
544 return SCALE_FACTOR_NONE;
547 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
548 /// pawns and the defending king is actively placed, the position is drawish.
550 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
552 assert(verify_material(pos, strongSide, RookValueMg, 2));
553 assert(verify_material(pos, weakSide, RookValueMg, 1));
555 Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
556 Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
557 Square bksq = pos.square<KING>(weakSide);
559 // Does the stronger side have a passed pawn?
560 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
561 return SCALE_FACTOR_NONE;
563 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
565 if ( distance<File>(bksq, wpsq1) <= 1
566 && distance<File>(bksq, wpsq2) <= 1
567 && relative_rank(strongSide, bksq) > r)
569 assert(r > RANK_1 && r < RANK_7);
570 return ScaleFactor(7 * r);
572 return SCALE_FACTOR_NONE;
576 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
577 /// are on the same rook file and are blocked by the defending king, it's a draw.
579 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
581 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
582 assert(pos.count<PAWN>(strongSide) >= 2);
583 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
585 Square ksq = pos.square<KING>(weakSide);
586 Bitboard pawns = pos.pieces(strongSide, PAWN);
588 // If all pawns are ahead of the king on a single rook file, it's a draw.
589 if (!((pawns & ~FileABB) || (pawns & ~FileHBB)) &&
590 !(pawns & ~passed_pawn_span(weakSide, ksq)))
591 return SCALE_FACTOR_DRAW;
593 return SCALE_FACTOR_NONE;
597 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
598 /// path of the pawn, and the square of the king is not of the same color as the
599 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
600 /// it's almost always a draw.
602 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
604 assert(verify_material(pos, strongSide, BishopValueMg, 1));
605 assert(verify_material(pos, weakSide, BishopValueMg, 0));
607 Square pawnSq = pos.square<PAWN>(strongSide);
608 Square strongBishopSq = pos.square<BISHOP>(strongSide);
609 Square weakBishopSq = pos.square<BISHOP>(weakSide);
610 Square weakKingSq = pos.square<KING>(weakSide);
612 // Case 1: Defending king blocks the pawn, and cannot be driven away
613 if ( (forward_file_bb(strongSide, pawnSq) & weakKingSq)
614 && ( opposite_colors(weakKingSq, strongBishopSq)
615 || relative_rank(strongSide, weakKingSq) <= RANK_6))
616 return SCALE_FACTOR_DRAW;
618 // Case 2: Opposite colored bishops
619 if (opposite_colors(strongBishopSq, weakBishopSq))
620 return SCALE_FACTOR_DRAW;
622 return SCALE_FACTOR_NONE;
626 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
628 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
630 assert(verify_material(pos, strongSide, BishopValueMg, 2));
631 assert(verify_material(pos, weakSide, BishopValueMg, 0));
633 Square wbsq = pos.square<BISHOP>(strongSide);
634 Square bbsq = pos.square<BISHOP>(weakSide);
636 if (!opposite_colors(wbsq, bbsq))
637 return SCALE_FACTOR_NONE;
639 Square ksq = pos.square<KING>(weakSide);
640 Square psq1 = pos.squares<PAWN>(strongSide)[0];
641 Square psq2 = pos.squares<PAWN>(strongSide)[1];
642 Square blockSq1, blockSq2;
644 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
646 blockSq1 = psq1 + pawn_push(strongSide);
647 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
651 blockSq1 = psq2 + pawn_push(strongSide);
652 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
655 switch (distance<File>(psq1, psq2))
658 // Both pawns are on the same file. It's an easy draw if the defender firmly
659 // controls some square in the frontmost pawn's path.
660 if ( file_of(ksq) == file_of(blockSq1)
661 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
662 && opposite_colors(ksq, wbsq))
663 return SCALE_FACTOR_DRAW;
665 return SCALE_FACTOR_NONE;
668 // Pawns on adjacent files. It's a draw if the defender firmly controls the
669 // square in front of the frontmost pawn's path, and the square diagonally
670 // behind this square on the file of the other pawn.
672 && opposite_colors(ksq, wbsq)
673 && ( bbsq == blockSq2
674 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
675 || distance<Rank>(psq1, psq2) >= 2))
676 return SCALE_FACTOR_DRAW;
678 else if ( ksq == blockSq2
679 && opposite_colors(ksq, wbsq)
680 && ( bbsq == blockSq1
681 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
682 return SCALE_FACTOR_DRAW;
684 return SCALE_FACTOR_NONE;
687 // The pawns are not on the same file or adjacent files. No scaling.
688 return SCALE_FACTOR_NONE;
693 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
694 /// the path of the pawn, and the square of the king is not of the same color as
695 /// the stronger side's bishop, it's a draw.
697 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
699 assert(verify_material(pos, strongSide, BishopValueMg, 1));
700 assert(verify_material(pos, weakSide, KnightValueMg, 0));
702 Square pawnSq = pos.square<PAWN>(strongSide);
703 Square strongBishopSq = pos.square<BISHOP>(strongSide);
704 Square weakKingSq = pos.square<KING>(weakSide);
706 if ( file_of(weakKingSq) == file_of(pawnSq)
707 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
708 && ( opposite_colors(weakKingSq, strongBishopSq)
709 || relative_rank(strongSide, weakKingSq) <= RANK_6))
710 return SCALE_FACTOR_DRAW;
712 return SCALE_FACTOR_NONE;
716 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
717 /// and the defending king prevents the pawn from advancing, the position is drawn.
719 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
721 assert(verify_material(pos, strongSide, KnightValueMg, 1));
722 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
724 // Assume strongSide is white and the pawn is on files A-D
725 Square pawnSq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
726 Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
728 if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
729 return SCALE_FACTOR_DRAW;
731 return SCALE_FACTOR_NONE;
735 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
736 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
737 /// has at least a draw with the pawn as well. The exception is when the stronger
738 /// side's pawn is far advanced and not on a rook file; in this case it is often
739 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
741 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
743 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
744 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
746 // Assume strongSide is white and the pawn is on files A-D
747 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
748 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
749 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
751 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
753 // If the pawn has advanced to the fifth rank or further, and is not a
754 // rook pawn, it's too dangerous to assume that it's at least a draw.
755 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
756 return SCALE_FACTOR_NONE;
758 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
759 // it's probably at least a draw even with the pawn.
760 return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;