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 if (strongSide == BLACK)
88 /// Mate with KX vs K. This function is used to evaluate positions with
89 /// king and plenty of material vs a lone king. It simply gives the
90 /// attacking side a bonus for driving the defending king towards the edge
91 /// of the board, and for keeping the distance between the two kings small.
93 Value Endgame<KXK>::operator()(const Position& pos) const {
95 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
96 assert(!pos.checkers()); // Eval is never called when in check
98 // Stalemate detection with lone king
99 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
102 Square winnerKSq = pos.square<KING>(strongSide);
103 Square loserKSq = pos.square<KING>(weakSide);
105 Value result = pos.non_pawn_material(strongSide)
106 + pos.count<PAWN>(strongSide) * PawnValueEg
107 + PushToEdges[loserKSq]
108 + PushClose[distance(winnerKSq, loserKSq)];
110 if ( pos.count<QUEEN>(strongSide)
111 || pos.count<ROOK>(strongSide)
112 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
113 || ( (pos.pieces(strongSide, BISHOP) & ~DarkSquares)
114 && (pos.pieces(strongSide, BISHOP) & DarkSquares)))
115 result = std::min(result + VALUE_KNOWN_WIN, VALUE_MATE_IN_MAX_PLY - 1);
117 return strongSide == pos.side_to_move() ? result : -result;
121 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
122 /// defending king towards a corner square that our bishop attacks.
124 Value Endgame<KBNK>::operator()(const Position& pos) const {
126 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
127 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
129 Square winnerKSq = pos.square<KING>(strongSide);
130 Square loserKSq = pos.square<KING>(weakSide);
131 Square bishopSq = pos.square<BISHOP>(strongSide);
133 // If our Bishop does not attack A1/H8, we flip the enemy king square
134 // to drive to opposite corners (A8/H1).
136 Value result = VALUE_KNOWN_WIN
137 + PushClose[distance(winnerKSq, loserKSq)]
138 + PushToCorners[opposite_colors(bishopSq, SQ_A1) ? ~loserKSq : loserKSq];
140 assert(abs(result) < VALUE_MATE_IN_MAX_PLY);
141 return strongSide == pos.side_to_move() ? result : -result;
145 /// KP vs K. This endgame is evaluated with the help of a bitbase.
147 Value Endgame<KPK>::operator()(const Position& pos) const {
149 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
150 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
152 // Assume strongSide is white and the pawn is on files A-D
153 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
154 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
155 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
157 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
159 if (!Bitbases::probe(wksq, psq, bksq, us))
162 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
164 return strongSide == pos.side_to_move() ? result : -result;
168 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
169 /// a bitbase. The function below returns drawish scores when the pawn is
170 /// far advanced with support of the king, while the attacking king is far
173 Value Endgame<KRKP>::operator()(const Position& pos) const {
175 assert(verify_material(pos, strongSide, RookValueMg, 0));
176 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
178 Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
179 Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
180 Square rsq = relative_square(strongSide, pos.square<ROOK>(strongSide));
181 Square psq = relative_square(strongSide, pos.square<PAWN>(weakSide));
183 Square queeningSq = make_square(file_of(psq), RANK_1);
186 // If the stronger side's king is in front of the pawn, it's a win
187 if (forward_file_bb(WHITE, wksq) & psq)
188 result = RookValueEg - distance(wksq, psq);
190 // If the weaker side's king is too far from the pawn and the rook,
192 else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
193 && distance(bksq, rsq) >= 3)
194 result = RookValueEg - distance(wksq, psq);
196 // If the pawn is far advanced and supported by the defending king,
197 // the position is drawish
198 else if ( rank_of(bksq) <= RANK_3
199 && distance(bksq, psq) == 1
200 && rank_of(wksq) >= RANK_4
201 && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
202 result = Value(80) - 8 * distance(wksq, psq);
205 result = Value(200) - 8 * ( distance(wksq, psq + SOUTH)
206 - distance(bksq, psq + SOUTH)
207 - distance(psq, queeningSq));
209 return strongSide == pos.side_to_move() ? result : -result;
213 /// KR vs KB. This is very simple, and always returns drawish scores. The
214 /// score is slightly bigger when the defending king is close to the edge.
216 Value Endgame<KRKB>::operator()(const Position& pos) const {
218 assert(verify_material(pos, strongSide, RookValueMg, 0));
219 assert(verify_material(pos, weakSide, BishopValueMg, 0));
221 Value result = Value(PushToEdges[pos.square<KING>(weakSide)]);
222 return strongSide == pos.side_to_move() ? result : -result;
226 /// KR vs KN. The attacking side has slightly better winning chances than
227 /// in KR vs KB, particularly if the king and the knight are far apart.
229 Value Endgame<KRKN>::operator()(const Position& pos) const {
231 assert(verify_material(pos, strongSide, RookValueMg, 0));
232 assert(verify_material(pos, weakSide, KnightValueMg, 0));
234 Square bksq = pos.square<KING>(weakSide);
235 Square bnsq = pos.square<KNIGHT>(weakSide);
236 Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
237 return strongSide == pos.side_to_move() ? result : -result;
241 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
242 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
243 /// with a king positioned next to it can be a draw, so in that case, we only
244 /// use the distance between the kings.
246 Value Endgame<KQKP>::operator()(const Position& pos) const {
248 assert(verify_material(pos, strongSide, QueenValueMg, 0));
249 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
251 Square winnerKSq = pos.square<KING>(strongSide);
252 Square loserKSq = pos.square<KING>(weakSide);
253 Square pawnSq = pos.square<PAWN>(weakSide);
255 Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
257 if ( relative_rank(weakSide, pawnSq) != RANK_7
258 || distance(loserKSq, pawnSq) != 1
259 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
260 result += QueenValueEg - PawnValueEg;
262 return strongSide == pos.side_to_move() ? result : -result;
266 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
267 /// king a bonus for having the kings close together, and for forcing the
268 /// defending king towards the edge. If we also take care to avoid null move for
269 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
271 Value Endgame<KQKR>::operator()(const Position& pos) const {
273 assert(verify_material(pos, strongSide, QueenValueMg, 0));
274 assert(verify_material(pos, weakSide, RookValueMg, 0));
276 Square winnerKSq = pos.square<KING>(strongSide);
277 Square loserKSq = pos.square<KING>(weakSide);
279 Value result = QueenValueEg
281 + PushToEdges[loserKSq]
282 + PushClose[distance(winnerKSq, loserKSq)];
284 return strongSide == pos.side_to_move() ? result : -result;
288 /// KNN vs KP. Simply push the opposing king to the corner.
290 Value Endgame<KNNKP>::operator()(const Position& pos) const {
292 assert(verify_material(pos, strongSide, 2 * KnightValueMg, 0));
293 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
295 Value result = 2 * KnightValueEg
297 + PushToEdges[pos.square<KING>(weakSide)];
299 return strongSide == pos.side_to_move() ? result : -result;
303 /// Some cases of trivial draws
304 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
307 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
308 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
309 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
312 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
314 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
315 assert(pos.count<PAWN>(strongSide) >= 1);
317 // No assertions about the material of weakSide, because we want draws to
318 // be detected even when the weaker side has some pawns.
320 Bitboard pawns = pos.pieces(strongSide, PAWN);
321 File pawnsFile = file_of(lsb(pawns));
323 // All pawns are on a single rook file?
324 if ( (pawnsFile == FILE_A || pawnsFile == FILE_H)
325 && !(pawns & ~file_bb(pawnsFile)))
327 Square bishopSq = pos.square<BISHOP>(strongSide);
328 Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
329 Square kingSq = pos.square<KING>(weakSide);
331 if ( opposite_colors(queeningSq, bishopSq)
332 && distance(queeningSq, kingSq) <= 1)
333 return SCALE_FACTOR_DRAW;
336 // If all the pawns are on the same B or G file, then it's potentially a draw
337 if ( (pawnsFile == FILE_B || pawnsFile == FILE_G)
338 && !(pos.pieces(PAWN) & ~file_bb(pawnsFile))
339 && pos.non_pawn_material(weakSide) == 0
340 && pos.count<PAWN>(weakSide) >= 1)
342 // Get weakSide pawn that is closest to the home rank
343 Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
345 Square strongKingSq = pos.square<KING>(strongSide);
346 Square weakKingSq = pos.square<KING>(weakSide);
347 Square bishopSq = pos.square<BISHOP>(strongSide);
349 // There's potential for a draw if our pawn is blocked on the 7th rank,
350 // the bishop cannot attack it or they only have one pawn left
351 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
352 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
353 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
355 int strongKingDist = distance(weakPawnSq, strongKingSq);
356 int weakKingDist = distance(weakPawnSq, weakKingSq);
358 // It's a draw if the weak king is on its back two ranks, within 2
359 // squares of the blocking pawn and the strong king is not
360 // closer. (I think this rule only fails in practically
361 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
362 // and positions where qsearch will immediately correct the
363 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
364 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
366 && weakKingDist <= strongKingDist)
367 return SCALE_FACTOR_DRAW;
371 return SCALE_FACTOR_NONE;
375 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
376 /// the third rank defended by a pawn.
378 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
380 assert(verify_material(pos, strongSide, QueenValueMg, 0));
381 assert(pos.count<ROOK>(weakSide) == 1);
382 assert(pos.count<PAWN>(weakSide) >= 1);
384 Square kingSq = pos.square<KING>(weakSide);
385 Square rsq = pos.square<ROOK>(weakSide);
387 if ( relative_rank(weakSide, kingSq) <= RANK_2
388 && relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
389 && relative_rank(weakSide, rsq) == RANK_3
390 && ( pos.pieces(weakSide, PAWN)
391 & pos.attacks_from<KING>(kingSq)
392 & pos.attacks_from<PAWN>(rsq, strongSide)))
393 return SCALE_FACTOR_DRAW;
395 return SCALE_FACTOR_NONE;
399 /// KRP vs KR. This function knows a handful of the most important classes of
400 /// drawn positions, but is far from perfect. It would probably be a good idea
401 /// to add more knowledge in the future.
403 /// It would also be nice to rewrite the actual code for this function,
404 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
406 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
408 assert(verify_material(pos, strongSide, RookValueMg, 1));
409 assert(verify_material(pos, weakSide, RookValueMg, 0));
411 // Assume strongSide is white and the pawn is on files A-D
412 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
413 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
414 Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
415 Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
416 Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
418 File f = file_of(wpsq);
419 Rank r = rank_of(wpsq);
420 Square queeningSq = make_square(f, RANK_8);
421 int tempo = (pos.side_to_move() == strongSide);
423 // If the pawn is not too far advanced and the defending king defends the
424 // queening square, use the third-rank defence.
426 && distance(bksq, queeningSq) <= 1
428 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
429 return SCALE_FACTOR_DRAW;
431 // The defending side saves a draw by checking from behind in case the pawn
432 // has advanced to the 6th rank with the king behind.
434 && distance(bksq, queeningSq) <= 1
435 && rank_of(wksq) + tempo <= RANK_6
436 && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
437 return SCALE_FACTOR_DRAW;
440 && bksq == queeningSq
441 && rank_of(brsq) == RANK_1
442 && (!tempo || distance(wksq, wpsq) >= 2))
443 return SCALE_FACTOR_DRAW;
445 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
446 // and the black rook is behind the pawn.
449 && (bksq == SQ_H7 || bksq == SQ_G7)
450 && file_of(brsq) == FILE_A
451 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
452 return SCALE_FACTOR_DRAW;
454 // If the defending king blocks the pawn and the attacking king is too far
455 // away, it's a draw.
457 && bksq == wpsq + NORTH
458 && distance(wksq, wpsq) - tempo >= 2
459 && distance(wksq, brsq) - tempo >= 2)
460 return SCALE_FACTOR_DRAW;
462 // Pawn on the 7th rank supported by the rook from behind usually wins if the
463 // attacking king is closer to the queening square than the defending king,
464 // and the defending king cannot gain tempi by threatening the attacking rook.
467 && file_of(wrsq) == f
468 && wrsq != queeningSq
469 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
470 && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
471 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
473 // Similar to the above, but with the pawn further back
475 && file_of(wrsq) == f
477 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
478 && (distance(wksq, wpsq + NORTH) < distance(bksq, wpsq + NORTH) - 2 + tempo)
479 && ( distance(bksq, wrsq) + tempo >= 3
480 || ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
481 && (distance(wksq, wpsq + NORTH) < distance(bksq, wrsq) + tempo))))
482 return ScaleFactor( SCALE_FACTOR_MAX
483 - 8 * distance(wpsq, queeningSq)
484 - 2 * distance(wksq, queeningSq));
486 // If the pawn is not far advanced and the defending king is somewhere in
487 // the pawn's path, it's probably a draw.
488 if (r <= RANK_4 && bksq > wpsq)
490 if (file_of(bksq) == file_of(wpsq))
491 return ScaleFactor(10);
492 if ( distance<File>(bksq, wpsq) == 1
493 && distance(wksq, bksq) > 2)
494 return ScaleFactor(24 - 2 * distance(wksq, bksq));
496 return SCALE_FACTOR_NONE;
500 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
502 assert(verify_material(pos, strongSide, RookValueMg, 1));
503 assert(verify_material(pos, weakSide, BishopValueMg, 0));
505 // Test for a rook pawn
506 if (pos.pieces(PAWN) & (FileABB | FileHBB))
508 Square ksq = pos.square<KING>(weakSide);
509 Square bsq = pos.square<BISHOP>(weakSide);
510 Square psq = pos.square<PAWN>(strongSide);
511 Rank rk = relative_rank(strongSide, psq);
512 Direction push = pawn_push(strongSide);
514 // If the pawn is on the 5th rank and the pawn (currently) is on
515 // the same color square as the bishop then there is a chance of
516 // a fortress. Depending on the king position give a moderate
517 // reduction or a stronger one if the defending king is near the
518 // corner but not trapped there.
519 if (rk == RANK_5 && !opposite_colors(bsq, psq))
521 int d = distance(psq + 3 * push, ksq);
523 if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
524 return ScaleFactor(24);
526 return ScaleFactor(48);
529 // When the pawn has moved to the 6th rank we can be fairly sure
530 // it's drawn if the bishop attacks the square in front of the
531 // pawn from a reasonable distance and the defending king is near
534 && distance(psq + 2 * push, ksq) <= 1
535 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
536 && distance<File>(bsq, psq) >= 2)
537 return ScaleFactor(8);
540 return SCALE_FACTOR_NONE;
543 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
544 /// pawns and the defending king is actively placed, the position is drawish.
546 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
548 assert(verify_material(pos, strongSide, RookValueMg, 2));
549 assert(verify_material(pos, weakSide, RookValueMg, 1));
551 Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
552 Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
553 Square bksq = pos.square<KING>(weakSide);
555 // Does the stronger side have a passed pawn?
556 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
557 return SCALE_FACTOR_NONE;
559 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
561 if ( distance<File>(bksq, wpsq1) <= 1
562 && distance<File>(bksq, wpsq2) <= 1
563 && relative_rank(strongSide, bksq) > r)
565 assert(r > RANK_1 && r < RANK_7);
566 return ScaleFactor(KRPPKRPScaleFactors[r]);
568 return SCALE_FACTOR_NONE;
572 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
573 /// are on the same rook file and are blocked by the defending king, it's a draw.
575 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
577 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
578 assert(pos.count<PAWN>(strongSide) >= 2);
579 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
581 Square ksq = pos.square<KING>(weakSide);
582 Bitboard pawns = pos.pieces(strongSide, PAWN);
584 // If all pawns are ahead of the king, on a single rook file and
585 // the king is within one file of the pawns, it's a draw.
586 if ( !(pawns & ~forward_ranks_bb(weakSide, ksq))
587 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
588 && distance<File>(ksq, lsb(pawns)) <= 1)
589 return SCALE_FACTOR_DRAW;
591 return SCALE_FACTOR_NONE;
595 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
596 /// path of the pawn, and the square of the king is not of the same color as the
597 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
598 /// it's almost always a draw.
600 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
602 assert(verify_material(pos, strongSide, BishopValueMg, 1));
603 assert(verify_material(pos, weakSide, BishopValueMg, 0));
605 Square pawnSq = pos.square<PAWN>(strongSide);
606 Square strongBishopSq = pos.square<BISHOP>(strongSide);
607 Square weakBishopSq = pos.square<BISHOP>(weakSide);
608 Square weakKingSq = pos.square<KING>(weakSide);
610 // Case 1: Defending king blocks the pawn, and cannot be driven away
611 if ( file_of(weakKingSq) == file_of(pawnSq)
612 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
613 && ( opposite_colors(weakKingSq, strongBishopSq)
614 || relative_rank(strongSide, weakKingSq) <= RANK_6))
615 return SCALE_FACTOR_DRAW;
617 // Case 2: Opposite colored bishops
618 if (opposite_colors(strongBishopSq, weakBishopSq))
619 return SCALE_FACTOR_DRAW;
621 return SCALE_FACTOR_NONE;
625 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
627 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
629 assert(verify_material(pos, strongSide, BishopValueMg, 2));
630 assert(verify_material(pos, weakSide, BishopValueMg, 0));
632 Square wbsq = pos.square<BISHOP>(strongSide);
633 Square bbsq = pos.square<BISHOP>(weakSide);
635 if (!opposite_colors(wbsq, bbsq))
636 return SCALE_FACTOR_NONE;
638 Square ksq = pos.square<KING>(weakSide);
639 Square psq1 = pos.squares<PAWN>(strongSide)[0];
640 Square psq2 = pos.squares<PAWN>(strongSide)[1];
641 Rank r1 = rank_of(psq1);
642 Rank r2 = rank_of(psq2);
643 Square blockSq1, blockSq2;
645 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
647 blockSq1 = psq1 + pawn_push(strongSide);
648 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
652 blockSq1 = psq2 + pawn_push(strongSide);
653 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
656 switch (distance<File>(psq1, psq2))
659 // Both pawns are on the same file. It's an easy draw if the defender firmly
660 // controls some square in the frontmost pawn's path.
661 if ( file_of(ksq) == file_of(blockSq1)
662 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
663 && opposite_colors(ksq, wbsq))
664 return SCALE_FACTOR_DRAW;
666 return SCALE_FACTOR_NONE;
669 // Pawns on adjacent files. It's a draw if the defender firmly controls the
670 // square in front of the frontmost pawn's path, and the square diagonally
671 // behind this square on the file of the other pawn.
673 && opposite_colors(ksq, wbsq)
674 && ( bbsq == blockSq2
675 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
676 || distance(r1, r2) >= 2))
677 return SCALE_FACTOR_DRAW;
679 else if ( ksq == blockSq2
680 && opposite_colors(ksq, wbsq)
681 && ( bbsq == blockSq1
682 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
683 return SCALE_FACTOR_DRAW;
685 return SCALE_FACTOR_NONE;
688 // The pawns are not on the same file or adjacent files. No scaling.
689 return SCALE_FACTOR_NONE;
694 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
695 /// the path of the pawn, and the square of the king is not of the same color as
696 /// the stronger side's bishop, it's a draw.
698 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
700 assert(verify_material(pos, strongSide, BishopValueMg, 1));
701 assert(verify_material(pos, weakSide, KnightValueMg, 0));
703 Square pawnSq = pos.square<PAWN>(strongSide);
704 Square strongBishopSq = pos.square<BISHOP>(strongSide);
705 Square weakKingSq = pos.square<KING>(weakSide);
707 if ( file_of(weakKingSq) == file_of(pawnSq)
708 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
709 && ( opposite_colors(weakKingSq, strongBishopSq)
710 || relative_rank(strongSide, weakKingSq) <= RANK_6))
711 return SCALE_FACTOR_DRAW;
713 return SCALE_FACTOR_NONE;
717 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
718 /// and the defending king prevents the pawn from advancing, the position is drawn.
720 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
722 assert(verify_material(pos, strongSide, KnightValueMg, 1));
723 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
725 // Assume strongSide is white and the pawn is on files A-D
726 Square pawnSq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
727 Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
729 if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
730 return SCALE_FACTOR_DRAW;
732 return SCALE_FACTOR_NONE;
736 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
737 /// Otherwise the position is drawn.
739 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
741 assert(verify_material(pos, strongSide, KnightValueMg, 1));
742 assert(verify_material(pos, weakSide, BishopValueMg, 0));
744 Square pawnSq = pos.square<PAWN>(strongSide);
745 Square bishopSq = pos.square<BISHOP>(weakSide);
746 Square weakKingSq = pos.square<KING>(weakSide);
748 // King needs to get close to promoting pawn to prevent knight from blocking.
749 // Rules for this are very tricky, so just approximate.
750 if (forward_file_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
751 return ScaleFactor(distance(weakKingSq, pawnSq));
753 return SCALE_FACTOR_NONE;
757 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
758 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
759 /// has at least a draw with the pawn as well. The exception is when the stronger
760 /// side's pawn is far advanced and not on a rook file; in this case it is often
761 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
763 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
765 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
766 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
768 // Assume strongSide is white and the pawn is on files A-D
769 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
770 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
771 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
773 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
775 // If the pawn has advanced to the fifth rank or further, and is not a
776 // rook pawn, it's too dangerous to assume that it's at least a draw.
777 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
778 return SCALE_FACTOR_NONE;
780 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
781 // it's probably at least a draw even with the pawn.
782 return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;