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) 2015-2019 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 // Tables used to drive a piece towards or away from another piece
58 constexpr int PushClose[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
59 constexpr int PushAway [8] = { 0, 5, 20, 40, 60, 80, 90, 100 };
61 // Pawn Rank based scaling factors used in KRPPKRP endgame
62 constexpr int KRPPKRPScaleFactors[RANK_NB] = { 0, 9, 10, 14, 21, 44, 0, 0 };
65 bool verify_material(const Position& pos, Color c, Value npm, int pawnsCnt) {
66 return pos.non_pawn_material(c) == npm && pos.count<PAWN>(c) == pawnsCnt;
70 // Map the square as if strongSide is white and strongSide's only pawn
71 // is on the left half of the board.
72 Square normalize(const Position& pos, Color strongSide, Square sq) {
74 assert(pos.count<PAWN>(strongSide) == 1);
76 if (file_of(pos.square<PAWN>(strongSide)) >= FILE_E)
77 sq = Square(sq ^ 7); // Mirror SQ_H1 -> SQ_A1
79 return strongSide == WHITE ? sq : ~sq;
85 /// Mate with KX vs K. This function is used to evaluate positions with
86 /// king and plenty of material vs a lone king. It simply gives the
87 /// attacking side a bonus for driving the defending king towards the edge
88 /// of the board, and for keeping the distance between the two kings small.
90 Value Endgame<KXK>::operator()(const Position& pos) const {
92 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
93 assert(!pos.checkers()); // Eval is never called when in check
95 // Stalemate detection with lone king
96 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
99 Square winnerKSq = pos.square<KING>(strongSide);
100 Square loserKSq = pos.square<KING>(weakSide);
102 Value result = pos.non_pawn_material(strongSide)
103 + pos.count<PAWN>(strongSide) * PawnValueEg
104 + PushToEdges[loserKSq]
105 + PushClose[distance(winnerKSq, loserKSq)];
107 if ( pos.count<QUEEN>(strongSide)
108 || pos.count<ROOK>(strongSide)
109 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
110 || ( (pos.pieces(strongSide, BISHOP) & ~DarkSquares)
111 && (pos.pieces(strongSide, BISHOP) & DarkSquares)))
112 result = std::min(result + VALUE_KNOWN_WIN, VALUE_MATE_IN_MAX_PLY - 1);
114 return strongSide == pos.side_to_move() ? result : -result;
118 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
119 /// defending king towards a corner square that our bishop attacks.
121 Value Endgame<KBNK>::operator()(const Position& pos) const {
123 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
124 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
126 Square winnerKSq = pos.square<KING>(strongSide);
127 Square loserKSq = pos.square<KING>(weakSide);
128 Square bishopSq = pos.square<BISHOP>(strongSide);
130 // If our Bishop does not attack A1/H8, we flip the enemy king square
131 // to drive to opposite corners (A8/H1).
133 Value result = VALUE_KNOWN_WIN
134 + PushClose[distance(winnerKSq, loserKSq)]
135 + PushToCorners[opposite_colors(bishopSq, SQ_A1) ? ~loserKSq : loserKSq];
137 assert(abs(result) < VALUE_MATE_IN_MAX_PLY);
138 return strongSide == pos.side_to_move() ? result : -result;
142 /// KP vs K. This endgame is evaluated with the help of a bitbase.
144 Value Endgame<KPK>::operator()(const Position& pos) const {
146 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
147 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
149 // Assume strongSide is white and the pawn is on files A-D
150 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
151 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
152 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
154 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
156 if (!Bitbases::probe(wksq, psq, bksq, us))
159 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
161 return strongSide == pos.side_to_move() ? result : -result;
165 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
166 /// a bitbase. The function below returns drawish scores when the pawn is
167 /// far advanced with support of the king, while the attacking king is far
170 Value Endgame<KRKP>::operator()(const Position& pos) const {
172 assert(verify_material(pos, strongSide, RookValueMg, 0));
173 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
175 Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
176 Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
177 Square rsq = relative_square(strongSide, pos.square<ROOK>(strongSide));
178 Square psq = relative_square(strongSide, pos.square<PAWN>(weakSide));
180 Square queeningSq = make_square(file_of(psq), RANK_1);
183 // If the stronger side's king is in front of the pawn, it's a win
184 if (forward_file_bb(WHITE, wksq) & psq)
185 result = RookValueEg - distance(wksq, psq);
187 // If the weaker side's king is too far from the pawn and the rook,
189 else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
190 && distance(bksq, rsq) >= 3)
191 result = RookValueEg - distance(wksq, psq);
193 // If the pawn is far advanced and supported by the defending king,
194 // the position is drawish
195 else if ( rank_of(bksq) <= RANK_3
196 && distance(bksq, psq) == 1
197 && rank_of(wksq) >= RANK_4
198 && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
199 result = Value(80) - 8 * distance(wksq, psq);
202 result = Value(200) - 8 * ( distance(wksq, psq + SOUTH)
203 - distance(bksq, psq + SOUTH)
204 - distance(psq, queeningSq));
206 return strongSide == pos.side_to_move() ? result : -result;
210 /// KR vs KB. This is very simple, and always returns drawish scores. The
211 /// score is slightly bigger when the defending king is close to the edge.
213 Value Endgame<KRKB>::operator()(const Position& pos) const {
215 assert(verify_material(pos, strongSide, RookValueMg, 0));
216 assert(verify_material(pos, weakSide, BishopValueMg, 0));
218 Value result = Value(PushToEdges[pos.square<KING>(weakSide)]);
219 return strongSide == pos.side_to_move() ? result : -result;
223 /// KR vs KN. The attacking side has slightly better winning chances than
224 /// in KR vs KB, particularly if the king and the knight are far apart.
226 Value Endgame<KRKN>::operator()(const Position& pos) const {
228 assert(verify_material(pos, strongSide, RookValueMg, 0));
229 assert(verify_material(pos, weakSide, KnightValueMg, 0));
231 Square bksq = pos.square<KING>(weakSide);
232 Square bnsq = pos.square<KNIGHT>(weakSide);
233 Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
234 return strongSide == pos.side_to_move() ? result : -result;
238 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
239 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
240 /// with a king positioned next to it can be a draw, so in that case, we only
241 /// use the distance between the kings.
243 Value Endgame<KQKP>::operator()(const Position& pos) const {
245 assert(verify_material(pos, strongSide, QueenValueMg, 0));
246 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
248 Square winnerKSq = pos.square<KING>(strongSide);
249 Square loserKSq = pos.square<KING>(weakSide);
250 Square pawnSq = pos.square<PAWN>(weakSide);
252 Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
254 if ( relative_rank(weakSide, pawnSq) != RANK_7
255 || distance(loserKSq, pawnSq) != 1
256 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
257 result += QueenValueEg - PawnValueEg;
259 return strongSide == pos.side_to_move() ? result : -result;
263 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
264 /// king a bonus for having the kings close together, and for forcing the
265 /// defending king towards the edge. If we also take care to avoid null move for
266 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
268 Value Endgame<KQKR>::operator()(const Position& pos) const {
270 assert(verify_material(pos, strongSide, QueenValueMg, 0));
271 assert(verify_material(pos, weakSide, RookValueMg, 0));
273 Square winnerKSq = pos.square<KING>(strongSide);
274 Square loserKSq = pos.square<KING>(weakSide);
276 Value result = QueenValueEg
278 + PushToEdges[loserKSq]
279 + PushClose[distance(winnerKSq, loserKSq)];
281 return strongSide == pos.side_to_move() ? result : -result;
285 /// KNN vs KP. Simply push the opposing king to the corner
287 Value Endgame<KNNKP>::operator()(const Position& pos) const {
289 assert(verify_material(pos, strongSide, 2 * KnightValueMg, 0));
290 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
292 Value result = 2 * KnightValueEg
294 + PushToEdges[pos.square<KING>(weakSide)];
296 return strongSide == pos.side_to_move() ? result : -result;
300 /// Some cases of trivial draws
301 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
304 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
305 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
306 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
309 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
311 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
312 assert(pos.count<PAWN>(strongSide) >= 1);
314 // No assertions about the material of weakSide, because we want draws to
315 // be detected even when the weaker side has some pawns.
317 Bitboard pawns = pos.pieces(strongSide, PAWN);
318 File pawnsFile = file_of(lsb(pawns));
320 // All pawns are on a single rook file?
321 if ( (pawnsFile == FILE_A || pawnsFile == FILE_H)
322 && !(pawns & ~file_bb(pawnsFile)))
324 Square bishopSq = pos.square<BISHOP>(strongSide);
325 Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
326 Square kingSq = pos.square<KING>(weakSide);
328 if ( opposite_colors(queeningSq, bishopSq)
329 && distance(queeningSq, kingSq) <= 1)
330 return SCALE_FACTOR_DRAW;
333 // If all the pawns are on the same B or G file, then it's potentially a draw
334 if ( (pawnsFile == FILE_B || pawnsFile == FILE_G)
335 && !(pos.pieces(PAWN) & ~file_bb(pawnsFile))
336 && pos.non_pawn_material(weakSide) == 0
337 && pos.count<PAWN>(weakSide) >= 1)
339 // Get weakSide pawn that is closest to the home rank
340 Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
342 Square strongKingSq = pos.square<KING>(strongSide);
343 Square weakKingSq = pos.square<KING>(weakSide);
344 Square bishopSq = pos.square<BISHOP>(strongSide);
346 // There's potential for a draw if our pawn is blocked on the 7th rank,
347 // the bishop cannot attack it or they only have one pawn left
348 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
349 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
350 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
352 int strongKingDist = distance(weakPawnSq, strongKingSq);
353 int weakKingDist = distance(weakPawnSq, weakKingSq);
355 // It's a draw if the weak king is on its back two ranks, within 2
356 // squares of the blocking pawn and the strong king is not
357 // closer. (I think this rule only fails in practically
358 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
359 // and positions where qsearch will immediately correct the
360 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
361 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
363 && weakKingDist <= strongKingDist)
364 return SCALE_FACTOR_DRAW;
368 return SCALE_FACTOR_NONE;
372 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
373 /// the third rank defended by a pawn.
375 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
377 assert(verify_material(pos, strongSide, QueenValueMg, 0));
378 assert(pos.count<ROOK>(weakSide) == 1);
379 assert(pos.count<PAWN>(weakSide) >= 1);
381 Square kingSq = pos.square<KING>(weakSide);
382 Square rsq = pos.square<ROOK>(weakSide);
384 if ( relative_rank(weakSide, kingSq) <= RANK_2
385 && relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
386 && relative_rank(weakSide, rsq) == RANK_3
387 && ( pos.pieces(weakSide, PAWN)
388 & pos.attacks_from<KING>(kingSq)
389 & pos.attacks_from<PAWN>(rsq, strongSide)))
390 return SCALE_FACTOR_DRAW;
392 return SCALE_FACTOR_NONE;
396 /// KRP vs KR. This function knows a handful of the most important classes of
397 /// drawn positions, but is far from perfect. It would probably be a good idea
398 /// to add more knowledge in the future.
400 /// It would also be nice to rewrite the actual code for this function,
401 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
403 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
405 assert(verify_material(pos, strongSide, RookValueMg, 1));
406 assert(verify_material(pos, weakSide, RookValueMg, 0));
408 // Assume strongSide is white and the pawn is on files A-D
409 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
410 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
411 Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
412 Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
413 Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
415 File f = file_of(wpsq);
416 Rank r = rank_of(wpsq);
417 Square queeningSq = make_square(f, RANK_8);
418 int tempo = (pos.side_to_move() == strongSide);
420 // If the pawn is not too far advanced and the defending king defends the
421 // queening square, use the third-rank defence.
423 && distance(bksq, queeningSq) <= 1
425 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
426 return SCALE_FACTOR_DRAW;
428 // The defending side saves a draw by checking from behind in case the pawn
429 // has advanced to the 6th rank with the king behind.
431 && distance(bksq, queeningSq) <= 1
432 && rank_of(wksq) + tempo <= RANK_6
433 && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
434 return SCALE_FACTOR_DRAW;
437 && bksq == queeningSq
438 && rank_of(brsq) == RANK_1
439 && (!tempo || distance(wksq, wpsq) >= 2))
440 return SCALE_FACTOR_DRAW;
442 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
443 // and the black rook is behind the pawn.
446 && (bksq == SQ_H7 || bksq == SQ_G7)
447 && file_of(brsq) == FILE_A
448 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
449 return SCALE_FACTOR_DRAW;
451 // If the defending king blocks the pawn and the attacking king is too far
452 // away, it's a draw.
454 && bksq == wpsq + NORTH
455 && distance(wksq, wpsq) - tempo >= 2
456 && distance(wksq, brsq) - tempo >= 2)
457 return SCALE_FACTOR_DRAW;
459 // Pawn on the 7th rank supported by the rook from behind usually wins if the
460 // attacking king is closer to the queening square than the defending king,
461 // and the defending king cannot gain tempi by threatening the attacking rook.
464 && file_of(wrsq) == f
465 && wrsq != queeningSq
466 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
467 && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
468 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
470 // Similar to the above, but with the pawn further back
472 && file_of(wrsq) == f
474 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
475 && (distance(wksq, wpsq + NORTH) < distance(bksq, wpsq + NORTH) - 2 + tempo)
476 && ( distance(bksq, wrsq) + tempo >= 3
477 || ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
478 && (distance(wksq, wpsq + NORTH) < distance(bksq, wrsq) + tempo))))
479 return ScaleFactor( SCALE_FACTOR_MAX
480 - 8 * distance(wpsq, queeningSq)
481 - 2 * distance(wksq, queeningSq));
483 // If the pawn is not far advanced and the defending king is somewhere in
484 // the pawn's path, it's probably a draw.
485 if (r <= RANK_4 && bksq > wpsq)
487 if (file_of(bksq) == file_of(wpsq))
488 return ScaleFactor(10);
489 if ( distance<File>(bksq, wpsq) == 1
490 && distance(wksq, bksq) > 2)
491 return ScaleFactor(24 - 2 * distance(wksq, bksq));
493 return SCALE_FACTOR_NONE;
497 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
499 assert(verify_material(pos, strongSide, RookValueMg, 1));
500 assert(verify_material(pos, weakSide, BishopValueMg, 0));
502 // Test for a rook pawn
503 if (pos.pieces(PAWN) & (FileABB | FileHBB))
505 Square ksq = pos.square<KING>(weakSide);
506 Square bsq = pos.square<BISHOP>(weakSide);
507 Square psq = pos.square<PAWN>(strongSide);
508 Rank rk = relative_rank(strongSide, psq);
509 Direction push = pawn_push(strongSide);
511 // If the pawn is on the 5th rank and the pawn (currently) is on
512 // the same color square as the bishop then there is a chance of
513 // a fortress. Depending on the king position give a moderate
514 // reduction or a stronger one if the defending king is near the
515 // corner but not trapped there.
516 if (rk == RANK_5 && !opposite_colors(bsq, psq))
518 int d = distance(psq + 3 * push, ksq);
520 if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
521 return ScaleFactor(24);
523 return ScaleFactor(48);
526 // When the pawn has moved to the 6th rank we can be fairly sure
527 // it's drawn if the bishop attacks the square in front of the
528 // pawn from a reasonable distance and the defending king is near
531 && distance(psq + 2 * push, ksq) <= 1
532 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
533 && distance<File>(bsq, psq) >= 2)
534 return ScaleFactor(8);
537 return SCALE_FACTOR_NONE;
540 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
541 /// pawns and the defending king is actively placed, the position is drawish.
543 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
545 assert(verify_material(pos, strongSide, RookValueMg, 2));
546 assert(verify_material(pos, weakSide, RookValueMg, 1));
548 Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
549 Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
550 Square bksq = pos.square<KING>(weakSide);
552 // Does the stronger side have a passed pawn?
553 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
554 return SCALE_FACTOR_NONE;
556 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
558 if ( distance<File>(bksq, wpsq1) <= 1
559 && distance<File>(bksq, wpsq2) <= 1
560 && relative_rank(strongSide, bksq) > r)
562 assert(r > RANK_1 && r < RANK_7);
563 return ScaleFactor(KRPPKRPScaleFactors[r]);
565 return SCALE_FACTOR_NONE;
569 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
570 /// are on the same rook file and are blocked by the defending king, it's a draw.
572 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
574 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
575 assert(pos.count<PAWN>(strongSide) >= 2);
576 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
578 Square ksq = pos.square<KING>(weakSide);
579 Bitboard pawns = pos.pieces(strongSide, PAWN);
581 // If all pawns are ahead of the king, on a single rook file and
582 // the king is within one file of the pawns, it's a draw.
583 if ( !(pawns & ~forward_ranks_bb(weakSide, ksq))
584 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
585 && distance<File>(ksq, lsb(pawns)) <= 1)
586 return SCALE_FACTOR_DRAW;
588 return SCALE_FACTOR_NONE;
592 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
593 /// path of the pawn, and the square of the king is not of the same color as the
594 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
595 /// it's almost always a draw.
597 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
599 assert(verify_material(pos, strongSide, BishopValueMg, 1));
600 assert(verify_material(pos, weakSide, BishopValueMg, 0));
602 Square pawnSq = pos.square<PAWN>(strongSide);
603 Square strongBishopSq = pos.square<BISHOP>(strongSide);
604 Square weakBishopSq = pos.square<BISHOP>(weakSide);
605 Square weakKingSq = pos.square<KING>(weakSide);
607 // Case 1: Defending king blocks the pawn, and cannot be driven away
608 if ( file_of(weakKingSq) == file_of(pawnSq)
609 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
610 && ( opposite_colors(weakKingSq, strongBishopSq)
611 || relative_rank(strongSide, weakKingSq) <= RANK_6))
612 return SCALE_FACTOR_DRAW;
614 // Case 2: Opposite colored bishops
615 if (opposite_colors(strongBishopSq, weakBishopSq))
616 return SCALE_FACTOR_DRAW;
618 return SCALE_FACTOR_NONE;
622 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
624 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
626 assert(verify_material(pos, strongSide, BishopValueMg, 2));
627 assert(verify_material(pos, weakSide, BishopValueMg, 0));
629 Square wbsq = pos.square<BISHOP>(strongSide);
630 Square bbsq = pos.square<BISHOP>(weakSide);
632 if (!opposite_colors(wbsq, bbsq))
633 return SCALE_FACTOR_NONE;
635 Square ksq = pos.square<KING>(weakSide);
636 Square psq1 = pos.squares<PAWN>(strongSide)[0];
637 Square psq2 = pos.squares<PAWN>(strongSide)[1];
638 Square blockSq1, blockSq2;
640 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
642 blockSq1 = psq1 + pawn_push(strongSide);
643 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
647 blockSq1 = psq2 + pawn_push(strongSide);
648 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
651 switch (distance<File>(psq1, psq2))
654 // Both pawns are on the same file. It's an easy draw if the defender firmly
655 // controls some square in the frontmost pawn's path.
656 if ( file_of(ksq) == file_of(blockSq1)
657 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
658 && opposite_colors(ksq, wbsq))
659 return SCALE_FACTOR_DRAW;
661 return SCALE_FACTOR_NONE;
664 // Pawns on adjacent files. It's a draw if the defender firmly controls the
665 // square in front of the frontmost pawn's path, and the square diagonally
666 // behind this square on the file of the other pawn.
668 && opposite_colors(ksq, wbsq)
669 && ( bbsq == blockSq2
670 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
671 || distance<Rank>(psq1, psq2) >= 2))
672 return SCALE_FACTOR_DRAW;
674 else if ( ksq == blockSq2
675 && opposite_colors(ksq, wbsq)
676 && ( bbsq == blockSq1
677 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
678 return SCALE_FACTOR_DRAW;
680 return SCALE_FACTOR_NONE;
683 // The pawns are not on the same file or adjacent files. No scaling.
684 return SCALE_FACTOR_NONE;
689 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
690 /// the path of the pawn, and the square of the king is not of the same color as
691 /// the stronger side's bishop, it's a draw.
693 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
695 assert(verify_material(pos, strongSide, BishopValueMg, 1));
696 assert(verify_material(pos, weakSide, KnightValueMg, 0));
698 Square pawnSq = pos.square<PAWN>(strongSide);
699 Square strongBishopSq = pos.square<BISHOP>(strongSide);
700 Square weakKingSq = pos.square<KING>(weakSide);
702 if ( file_of(weakKingSq) == file_of(pawnSq)
703 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
704 && ( opposite_colors(weakKingSq, strongBishopSq)
705 || relative_rank(strongSide, weakKingSq) <= RANK_6))
706 return SCALE_FACTOR_DRAW;
708 return SCALE_FACTOR_NONE;
712 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
713 /// and the defending king prevents the pawn from advancing, the position is drawn.
715 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
717 assert(verify_material(pos, strongSide, KnightValueMg, 1));
718 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
720 // Assume strongSide is white and the pawn is on files A-D
721 Square pawnSq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
722 Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
724 if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
725 return SCALE_FACTOR_DRAW;
727 return SCALE_FACTOR_NONE;
731 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
732 /// Otherwise the position is drawn.
734 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
736 assert(verify_material(pos, strongSide, KnightValueMg, 1));
737 assert(verify_material(pos, weakSide, BishopValueMg, 0));
739 Square pawnSq = pos.square<PAWN>(strongSide);
740 Square bishopSq = pos.square<BISHOP>(weakSide);
741 Square weakKingSq = pos.square<KING>(weakSide);
743 // King needs to get close to promoting pawn to prevent knight from blocking.
744 // Rules for this are very tricky, so just approximate.
745 if (forward_file_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
746 return ScaleFactor(distance(weakKingSq, pawnSq));
748 return SCALE_FACTOR_NONE;
752 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
753 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
754 /// has at least a draw with the pawn as well. The exception is when the stronger
755 /// side's pawn is far advanced and not on a rook file; in this case it is often
756 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
758 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
760 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
761 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
763 // Assume strongSide is white and the pawn is on files A-D
764 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
765 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
766 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
768 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
770 // If the pawn has advanced to the fifth rank or further, and is not a
771 // rook pawn, it's too dangerous to assume that it's at least a draw.
772 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
773 return SCALE_FACTOR_NONE;
775 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
776 // it's probably at least a draw even with the pawn.
777 return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;