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/>.
32 // Table used to drive the king towards the edge of the board
33 // in KX vs K and KQ vs KR endgames.
34 constexpr int PushToEdges[SQUARE_NB] = {
35 100, 90, 80, 70, 70, 80, 90, 100,
36 90, 70, 60, 50, 50, 60, 70, 90,
37 80, 60, 40, 30, 30, 40, 60, 80,
38 70, 50, 30, 20, 20, 30, 50, 70,
39 70, 50, 30, 20, 20, 30, 50, 70,
40 80, 60, 40, 30, 30, 40, 60, 80,
41 90, 70, 60, 50, 50, 60, 70, 90,
42 100, 90, 80, 70, 70, 80, 90, 100
45 // Table used to drive the king towards a corner square of the
46 // right color in KBN vs K endgames.
47 constexpr int PushToCorners[SQUARE_NB] = {
48 6400, 6080, 5760, 5440, 5120, 4800, 4480, 4160,
49 6080, 5760, 5440, 5120, 4800, 4480, 4160, 4480,
50 5760, 5440, 4960, 4480, 4480, 4000, 4480, 4800,
51 5440, 5120, 4480, 3840, 3520, 4480, 4800, 5120,
52 5120, 4800, 4480, 3520, 3840, 4480, 5120, 5440,
53 4800, 4480, 4000, 4480, 4480, 4960, 5440, 5760,
54 4480, 4160, 4480, 4800, 5120, 5440, 5760, 6080,
55 4160, 4480, 4800, 5120, 5440, 5760, 6080, 6400
58 // Tables used to drive a piece towards or away from another piece
59 constexpr int PushClose[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
60 constexpr int PushAway [8] = { 0, 5, 20, 40, 60, 80, 90, 100 };
62 // Pawn Rank based scaling factors used in KRPPKRP endgame
63 constexpr int KRPPKRPScaleFactors[RANK_NB] = { 0, 9, 10, 14, 21, 44, 0, 0 };
66 bool verify_material(const Position& pos, Color c, Value npm, int pawnsCnt) {
67 return pos.non_pawn_material(c) == npm && pos.count<PAWN>(c) == pawnsCnt;
71 // Map the square as if strongSide is white and strongSide's only pawn
72 // is on the left half of the board.
73 Square normalize(const Position& pos, Color strongSide, Square sq) {
75 assert(pos.count<PAWN>(strongSide) == 1);
77 if (file_of(pos.square<PAWN>(strongSide)) >= FILE_E)
78 sq = Square(sq ^ 7); // Mirror SQ_H1 -> SQ_A1
80 if (strongSide == BLACK)
89 /// Mate with KX vs K. This function is used to evaluate positions with
90 /// king and plenty of material vs a lone king. It simply gives the
91 /// attacking side a bonus for driving the defending king towards the edge
92 /// of the board, and for keeping the distance between the two kings small.
94 Value Endgame<KXK>::operator()(const Position& pos) const {
96 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
97 assert(!pos.checkers()); // Eval is never called when in check
99 // Stalemate detection with lone king
100 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
103 Square winnerKSq = pos.square<KING>(strongSide);
104 Square loserKSq = pos.square<KING>(weakSide);
106 Value result = pos.non_pawn_material(strongSide)
107 + pos.count<PAWN>(strongSide) * PawnValueEg
108 + PushToEdges[loserKSq]
109 + PushClose[distance(winnerKSq, loserKSq)];
111 if ( pos.count<QUEEN>(strongSide)
112 || pos.count<ROOK>(strongSide)
113 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
114 || ( (pos.pieces(strongSide, BISHOP) & ~DarkSquares)
115 && (pos.pieces(strongSide, BISHOP) & DarkSquares)))
116 result = std::min(result + VALUE_KNOWN_WIN, VALUE_MATE_IN_MAX_PLY - 1);
118 return strongSide == pos.side_to_move() ? result : -result;
122 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
123 /// defending king towards a corner square that our bishop attacks.
125 Value Endgame<KBNK>::operator()(const Position& pos) const {
127 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
128 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
130 Square winnerKSq = pos.square<KING>(strongSide);
131 Square loserKSq = pos.square<KING>(weakSide);
132 Square bishopSq = pos.square<BISHOP>(strongSide);
134 // If our Bishop does not attack A1/H8, we flip the enemy king square
135 // to drive to opposite corners (A8/H1).
137 Value result = VALUE_KNOWN_WIN
138 + PushClose[distance(winnerKSq, loserKSq)]
139 + PushToCorners[opposite_colors(bishopSq, SQ_A1) ? ~loserKSq : loserKSq];
141 assert(abs(result) < VALUE_MATE_IN_MAX_PLY);
142 return strongSide == pos.side_to_move() ? result : -result;
146 /// KP vs K. This endgame is evaluated with the help of a bitbase.
148 Value Endgame<KPK>::operator()(const Position& pos) const {
150 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
151 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
153 // Assume strongSide is white and the pawn is on files A-D
154 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
155 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
156 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
158 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
160 if (!Bitbases::probe(wksq, psq, bksq, us))
163 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
165 return strongSide == pos.side_to_move() ? result : -result;
169 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
170 /// a bitbase. The function below returns drawish scores when the pawn is
171 /// far advanced with support of the king, while the attacking king is far
174 Value Endgame<KRKP>::operator()(const Position& pos) const {
176 assert(verify_material(pos, strongSide, RookValueMg, 0));
177 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
179 Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
180 Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
181 Square rsq = relative_square(strongSide, pos.square<ROOK>(strongSide));
182 Square psq = relative_square(strongSide, pos.square<PAWN>(weakSide));
184 Square queeningSq = make_square(file_of(psq), RANK_1);
187 // If the stronger side's king is in front of the pawn, it's a win
188 if (forward_file_bb(WHITE, wksq) & psq)
189 result = RookValueEg - distance(wksq, psq);
191 // If the weaker side's king is too far from the pawn and the rook,
193 else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
194 && distance(bksq, rsq) >= 3)
195 result = RookValueEg - distance(wksq, psq);
197 // If the pawn is far advanced and supported by the defending king,
198 // the position is drawish
199 else if ( rank_of(bksq) <= RANK_3
200 && distance(bksq, psq) == 1
201 && rank_of(wksq) >= RANK_4
202 && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
203 result = Value(80) - 8 * distance(wksq, psq);
206 result = Value(200) - 8 * ( distance(wksq, psq + SOUTH)
207 - distance(bksq, psq + SOUTH)
208 - distance(psq, queeningSq));
210 return strongSide == pos.side_to_move() ? result : -result;
214 /// KR vs KB. This is very simple, and always returns drawish scores. The
215 /// score is slightly bigger when the defending king is close to the edge.
217 Value Endgame<KRKB>::operator()(const Position& pos) const {
219 assert(verify_material(pos, strongSide, RookValueMg, 0));
220 assert(verify_material(pos, weakSide, BishopValueMg, 0));
222 Value result = Value(PushToEdges[pos.square<KING>(weakSide)]);
223 return strongSide == pos.side_to_move() ? result : -result;
227 /// KR vs KN. The attacking side has slightly better winning chances than
228 /// in KR vs KB, particularly if the king and the knight are far apart.
230 Value Endgame<KRKN>::operator()(const Position& pos) const {
232 assert(verify_material(pos, strongSide, RookValueMg, 0));
233 assert(verify_material(pos, weakSide, KnightValueMg, 0));
235 Square bksq = pos.square<KING>(weakSide);
236 Square bnsq = pos.square<KNIGHT>(weakSide);
237 Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
238 return strongSide == pos.side_to_move() ? result : -result;
242 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
243 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
244 /// with a king positioned next to it can be a draw, so in that case, we only
245 /// use the distance between the kings.
247 Value Endgame<KQKP>::operator()(const Position& pos) const {
249 assert(verify_material(pos, strongSide, QueenValueMg, 0));
250 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
252 Square winnerKSq = pos.square<KING>(strongSide);
253 Square loserKSq = pos.square<KING>(weakSide);
254 Square pawnSq = pos.square<PAWN>(weakSide);
256 Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
258 if ( relative_rank(weakSide, pawnSq) != RANK_7
259 || distance(loserKSq, pawnSq) != 1
260 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
261 result += QueenValueEg - PawnValueEg;
263 return strongSide == pos.side_to_move() ? result : -result;
267 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
268 /// king a bonus for having the kings close together, and for forcing the
269 /// defending king towards the edge. If we also take care to avoid null move for
270 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
272 Value Endgame<KQKR>::operator()(const Position& pos) const {
274 assert(verify_material(pos, strongSide, QueenValueMg, 0));
275 assert(verify_material(pos, weakSide, RookValueMg, 0));
277 Square winnerKSq = pos.square<KING>(strongSide);
278 Square loserKSq = pos.square<KING>(weakSide);
280 Value result = QueenValueEg
282 + PushToEdges[loserKSq]
283 + PushClose[distance(winnerKSq, loserKSq)];
285 return strongSide == pos.side_to_move() ? result : -result;
289 /// KNN vs KP. Simply push the opposing king to the corner.
291 Value Endgame<KNNKP>::operator()(const Position& pos) const {
293 assert(verify_material(pos, strongSide, 2 * KnightValueMg, 0));
294 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
296 Value result = 2 * KnightValueEg
298 + PushToEdges[pos.square<KING>(weakSide)];
300 return strongSide == pos.side_to_move() ? result : -result;
304 /// Some cases of trivial draws
305 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
308 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
309 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
310 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
313 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
315 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
316 assert(pos.count<PAWN>(strongSide) >= 1);
318 // No assertions about the material of weakSide, because we want draws to
319 // be detected even when the weaker side has some pawns.
321 Bitboard pawns = pos.pieces(strongSide, PAWN);
322 File pawnsFile = file_of(lsb(pawns));
324 // All pawns are on a single rook file?
325 if ( (pawnsFile == FILE_A || pawnsFile == FILE_H)
326 && !(pawns & ~file_bb(pawnsFile)))
328 Square bishopSq = pos.square<BISHOP>(strongSide);
329 Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
330 Square kingSq = pos.square<KING>(weakSide);
332 if ( opposite_colors(queeningSq, bishopSq)
333 && distance(queeningSq, kingSq) <= 1)
334 return SCALE_FACTOR_DRAW;
337 // If all the pawns are on the same B or G file, then it's potentially a draw
338 if ( (pawnsFile == FILE_B || pawnsFile == FILE_G)
339 && !(pos.pieces(PAWN) & ~file_bb(pawnsFile))
340 && pos.non_pawn_material(weakSide) == 0
341 && pos.count<PAWN>(weakSide) >= 1)
343 // Get weakSide pawn that is closest to the home rank
344 Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
346 Square strongKingSq = pos.square<KING>(strongSide);
347 Square weakKingSq = pos.square<KING>(weakSide);
348 Square bishopSq = pos.square<BISHOP>(strongSide);
350 // There's potential for a draw if our pawn is blocked on the 7th rank,
351 // the bishop cannot attack it or they only have one pawn left
352 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
353 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
354 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
356 int strongKingDist = distance(weakPawnSq, strongKingSq);
357 int weakKingDist = distance(weakPawnSq, weakKingSq);
359 // It's a draw if the weak king is on its back two ranks, within 2
360 // squares of the blocking pawn and the strong king is not
361 // closer. (I think this rule only fails in practically
362 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
363 // and positions where qsearch will immediately correct the
364 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
365 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
367 && weakKingDist <= strongKingDist)
368 return SCALE_FACTOR_DRAW;
372 return SCALE_FACTOR_NONE;
376 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
377 /// the third rank defended by a pawn.
379 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
381 assert(verify_material(pos, strongSide, QueenValueMg, 0));
382 assert(pos.count<ROOK>(weakSide) == 1);
383 assert(pos.count<PAWN>(weakSide) >= 1);
385 Square kingSq = pos.square<KING>(weakSide);
386 Square rsq = pos.square<ROOK>(weakSide);
388 if ( relative_rank(weakSide, kingSq) <= RANK_2
389 && relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
390 && relative_rank(weakSide, rsq) == RANK_3
391 && ( pos.pieces(weakSide, PAWN)
392 & pos.attacks_from<KING>(kingSq)
393 & pos.attacks_from<PAWN>(rsq, strongSide)))
394 return SCALE_FACTOR_DRAW;
396 return SCALE_FACTOR_NONE;
400 /// KRP vs KR. This function knows a handful of the most important classes of
401 /// drawn positions, but is far from perfect. It would probably be a good idea
402 /// to add more knowledge in the future.
404 /// It would also be nice to rewrite the actual code for this function,
405 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
407 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
409 assert(verify_material(pos, strongSide, RookValueMg, 1));
410 assert(verify_material(pos, weakSide, RookValueMg, 0));
412 // Assume strongSide is white and the pawn is on files A-D
413 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
414 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
415 Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
416 Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
417 Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
419 File f = file_of(wpsq);
420 Rank r = rank_of(wpsq);
421 Square queeningSq = make_square(f, RANK_8);
422 int tempo = (pos.side_to_move() == strongSide);
424 // If the pawn is not too far advanced and the defending king defends the
425 // queening square, use the third-rank defence.
427 && distance(bksq, queeningSq) <= 1
429 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
430 return SCALE_FACTOR_DRAW;
432 // The defending side saves a draw by checking from behind in case the pawn
433 // has advanced to the 6th rank with the king behind.
435 && distance(bksq, queeningSq) <= 1
436 && rank_of(wksq) + tempo <= RANK_6
437 && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
438 return SCALE_FACTOR_DRAW;
441 && bksq == queeningSq
442 && rank_of(brsq) == RANK_1
443 && (!tempo || distance(wksq, wpsq) >= 2))
444 return SCALE_FACTOR_DRAW;
446 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
447 // and the black rook is behind the pawn.
450 && (bksq == SQ_H7 || bksq == SQ_G7)
451 && file_of(brsq) == FILE_A
452 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
453 return SCALE_FACTOR_DRAW;
455 // If the defending king blocks the pawn and the attacking king is too far
456 // away, it's a draw.
458 && bksq == wpsq + NORTH
459 && distance(wksq, wpsq) - tempo >= 2
460 && distance(wksq, brsq) - tempo >= 2)
461 return SCALE_FACTOR_DRAW;
463 // Pawn on the 7th rank supported by the rook from behind usually wins if the
464 // attacking king is closer to the queening square than the defending king,
465 // and the defending king cannot gain tempi by threatening the attacking rook.
468 && file_of(wrsq) == f
469 && wrsq != queeningSq
470 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
471 && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
472 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
474 // Similar to the above, but with the pawn further back
476 && file_of(wrsq) == f
478 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
479 && (distance(wksq, wpsq + NORTH) < distance(bksq, wpsq + NORTH) - 2 + tempo)
480 && ( distance(bksq, wrsq) + tempo >= 3
481 || ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
482 && (distance(wksq, wpsq + NORTH) < distance(bksq, wrsq) + tempo))))
483 return ScaleFactor( SCALE_FACTOR_MAX
484 - 8 * distance(wpsq, queeningSq)
485 - 2 * distance(wksq, queeningSq));
487 // If the pawn is not far advanced and the defending king is somewhere in
488 // the pawn's path, it's probably a draw.
489 if (r <= RANK_4 && bksq > wpsq)
491 if (file_of(bksq) == file_of(wpsq))
492 return ScaleFactor(10);
493 if ( distance<File>(bksq, wpsq) == 1
494 && distance(wksq, bksq) > 2)
495 return ScaleFactor(24 - 2 * distance(wksq, bksq));
497 return SCALE_FACTOR_NONE;
501 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
503 assert(verify_material(pos, strongSide, RookValueMg, 1));
504 assert(verify_material(pos, weakSide, BishopValueMg, 0));
506 // Test for a rook pawn
507 if (pos.pieces(PAWN) & (FileABB | FileHBB))
509 Square ksq = pos.square<KING>(weakSide);
510 Square bsq = pos.square<BISHOP>(weakSide);
511 Square psq = pos.square<PAWN>(strongSide);
512 Rank rk = relative_rank(strongSide, psq);
513 Direction push = pawn_push(strongSide);
515 // If the pawn is on the 5th rank and the pawn (currently) is on
516 // the same color square as the bishop then there is a chance of
517 // a fortress. Depending on the king position give a moderate
518 // reduction or a stronger one if the defending king is near the
519 // corner but not trapped there.
520 if (rk == RANK_5 && !opposite_colors(bsq, psq))
522 int d = distance(psq + 3 * push, ksq);
524 if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
525 return ScaleFactor(24);
527 return ScaleFactor(48);
530 // When the pawn has moved to the 6th rank we can be fairly sure
531 // it's drawn if the bishop attacks the square in front of the
532 // pawn from a reasonable distance and the defending king is near
535 && distance(psq + 2 * push, ksq) <= 1
536 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
537 && distance<File>(bsq, psq) >= 2)
538 return ScaleFactor(8);
541 return SCALE_FACTOR_NONE;
544 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
545 /// pawns and the defending king is actively placed, the position is drawish.
547 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
549 assert(verify_material(pos, strongSide, RookValueMg, 2));
550 assert(verify_material(pos, weakSide, RookValueMg, 1));
552 Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
553 Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
554 Square bksq = pos.square<KING>(weakSide);
556 // Does the stronger side have a passed pawn?
557 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
558 return SCALE_FACTOR_NONE;
560 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
562 if ( distance<File>(bksq, wpsq1) <= 1
563 && distance<File>(bksq, wpsq2) <= 1
564 && relative_rank(strongSide, bksq) > r)
566 assert(r > RANK_1 && r < RANK_7);
567 return ScaleFactor(KRPPKRPScaleFactors[r]);
569 return SCALE_FACTOR_NONE;
573 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
574 /// are on the same rook file and are blocked by the defending king, it's a draw.
576 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
578 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
579 assert(pos.count<PAWN>(strongSide) >= 2);
580 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
582 Square ksq = pos.square<KING>(weakSide);
583 Bitboard pawns = pos.pieces(strongSide, PAWN);
585 // If all pawns are ahead of the king, on a single rook file and
586 // the king is within one file of the pawns, it's a draw.
587 if ( !(pawns & ~forward_ranks_bb(weakSide, ksq))
588 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
589 && distance<File>(ksq, lsb(pawns)) <= 1)
590 return SCALE_FACTOR_DRAW;
592 return SCALE_FACTOR_NONE;
596 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
597 /// path of the pawn, and the square of the king is not of the same color as the
598 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
599 /// it's almost always a draw.
601 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
603 assert(verify_material(pos, strongSide, BishopValueMg, 1));
604 assert(verify_material(pos, weakSide, BishopValueMg, 0));
606 Square pawnSq = pos.square<PAWN>(strongSide);
607 Square strongBishopSq = pos.square<BISHOP>(strongSide);
608 Square weakBishopSq = pos.square<BISHOP>(weakSide);
609 Square weakKingSq = pos.square<KING>(weakSide);
611 // Case 1: Defending king blocks the pawn, and cannot be driven away
612 if ( file_of(weakKingSq) == file_of(pawnSq)
613 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, 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 Rank r1 = rank_of(psq1);
643 Rank r2 = rank_of(psq2);
644 Square blockSq1, blockSq2;
646 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
648 blockSq1 = psq1 + pawn_push(strongSide);
649 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
653 blockSq1 = psq2 + pawn_push(strongSide);
654 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
657 switch (distance<File>(psq1, psq2))
660 // Both pawns are on the same file. It's an easy draw if the defender firmly
661 // controls some square in the frontmost pawn's path.
662 if ( file_of(ksq) == file_of(blockSq1)
663 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
664 && opposite_colors(ksq, wbsq))
665 return SCALE_FACTOR_DRAW;
667 return SCALE_FACTOR_NONE;
670 // Pawns on adjacent files. It's a draw if the defender firmly controls the
671 // square in front of the frontmost pawn's path, and the square diagonally
672 // behind this square on the file of the other pawn.
674 && opposite_colors(ksq, wbsq)
675 && ( bbsq == blockSq2
676 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
677 || distance(r1, r2) >= 2))
678 return SCALE_FACTOR_DRAW;
680 else if ( ksq == blockSq2
681 && opposite_colors(ksq, wbsq)
682 && ( bbsq == blockSq1
683 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
684 return SCALE_FACTOR_DRAW;
686 return SCALE_FACTOR_NONE;
689 // The pawns are not on the same file or adjacent files. No scaling.
690 return SCALE_FACTOR_NONE;
695 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
696 /// the path of the pawn, and the square of the king is not of the same color as
697 /// the stronger side's bishop, it's a draw.
699 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
701 assert(verify_material(pos, strongSide, BishopValueMg, 1));
702 assert(verify_material(pos, weakSide, KnightValueMg, 0));
704 Square pawnSq = pos.square<PAWN>(strongSide);
705 Square strongBishopSq = pos.square<BISHOP>(strongSide);
706 Square weakKingSq = pos.square<KING>(weakSide);
708 if ( file_of(weakKingSq) == file_of(pawnSq)
709 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
710 && ( opposite_colors(weakKingSq, strongBishopSq)
711 || relative_rank(strongSide, weakKingSq) <= RANK_6))
712 return SCALE_FACTOR_DRAW;
714 return SCALE_FACTOR_NONE;
718 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
719 /// and the defending king prevents the pawn from advancing, the position is drawn.
721 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
723 assert(verify_material(pos, strongSide, KnightValueMg, 1));
724 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
726 // Assume strongSide is white and the pawn is on files A-D
727 Square pawnSq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
728 Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
730 if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
731 return SCALE_FACTOR_DRAW;
733 return SCALE_FACTOR_NONE;
737 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
738 /// Otherwise the position is drawn.
740 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
742 assert(verify_material(pos, strongSide, KnightValueMg, 1));
743 assert(verify_material(pos, weakSide, BishopValueMg, 0));
745 Square pawnSq = pos.square<PAWN>(strongSide);
746 Square bishopSq = pos.square<BISHOP>(weakSide);
747 Square weakKingSq = pos.square<KING>(weakSide);
749 // King needs to get close to promoting pawn to prevent knight from blocking.
750 // Rules for this are very tricky, so just approximate.
751 if (forward_file_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
752 return ScaleFactor(distance(weakKingSq, pawnSq));
754 return SCALE_FACTOR_NONE;
758 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
759 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
760 /// has at least a draw with the pawn as well. The exception is when the stronger
761 /// side's pawn is far advanced and not on a rook file; in this case it is often
762 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
764 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
766 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
767 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
769 // Assume strongSide is white and the pawn is on files A-D
770 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
771 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
772 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
774 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
776 // If the pawn has advanced to the fifth rank or further, and is not a
777 // rook pawn, it's too dangerous to assume that it's at least a draw.
778 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
779 return SCALE_FACTOR_NONE;
781 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
782 // it's probably at least a draw even with the pawn.
783 return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;