2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
4 Copyright (C) 2008-2015 Marco Costalba, Joona Kiiski, Tord Romstad
5 Copyright (C) 2015-2020 Marco Costalba, Joona Kiiski, Gary Linscott, Tord Romstad
7 Stockfish is free software: you can redistribute it and/or modify
8 it under the terms of the GNU General Public License as published by
9 the Free Software Foundation, either version 3 of the License, or
10 (at your option) any later version.
12 Stockfish is distributed in the hope that it will be useful,
13 but WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 GNU General Public License for more details.
17 You should have received a copy of the GNU General Public License
18 along with this program. If not, see <http://www.gnu.org/licenses/>.
31 // Table used to drive the king towards the edge of the board
32 // in KX vs K and KQ vs KR endgames.
33 constexpr int PushToEdges[SQUARE_NB] = {
34 100, 90, 80, 70, 70, 80, 90, 100,
35 90, 70, 60, 50, 50, 60, 70, 90,
36 80, 60, 40, 30, 30, 40, 60, 80,
37 70, 50, 30, 20, 20, 30, 50, 70,
38 70, 50, 30, 20, 20, 30, 50, 70,
39 80, 60, 40, 30, 30, 40, 60, 80,
40 90, 70, 60, 50, 50, 60, 70, 90,
41 100, 90, 80, 70, 70, 80, 90, 100
44 // Table used to drive the king towards a corner square of the
45 // right color in KBN vs K endgames.
46 constexpr int PushToCorners[SQUARE_NB] = {
47 6400, 6080, 5760, 5440, 5120, 4800, 4480, 4160,
48 6080, 5760, 5440, 5120, 4800, 4480, 4160, 4480,
49 5760, 5440, 4960, 4480, 4480, 4000, 4480, 4800,
50 5440, 5120, 4480, 3840, 3520, 4480, 4800, 5120,
51 5120, 4800, 4480, 3520, 3840, 4480, 5120, 5440,
52 4800, 4480, 4000, 4480, 4480, 4960, 5440, 5760,
53 4480, 4160, 4480, 4800, 5120, 5440, 5760, 6080,
54 4160, 4480, 4800, 5120, 5440, 5760, 6080, 6400
57 // 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)
79 return strongSide == WHITE ? sq : flip_rank(sq);
87 std::pair<Map<Value>, Map<ScaleFactor>> maps;
107 add<KBPPKB>("KBPPKB");
108 add<KRPPKRP>("KRPPKRP");
113 /// Mate with KX vs K. This function is used to evaluate positions with
114 /// king and plenty of material vs a lone king. It simply gives the
115 /// attacking side a bonus for driving the defending king towards the edge
116 /// of the board, and for keeping the distance between the two kings small.
118 Value Endgame<KXK>::operator()(const Position& pos) const {
120 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
121 assert(!pos.checkers()); // Eval is never called when in check
123 // Stalemate detection with lone king
124 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
127 Square winnerKSq = pos.square<KING>(strongSide);
128 Square loserKSq = pos.square<KING>(weakSide);
130 Value result = pos.non_pawn_material(strongSide)
131 + pos.count<PAWN>(strongSide) * PawnValueEg
132 + PushToEdges[loserKSq]
133 + PushClose[distance(winnerKSq, loserKSq)];
135 if ( pos.count<QUEEN>(strongSide)
136 || pos.count<ROOK>(strongSide)
137 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
138 || ( (pos.pieces(strongSide, BISHOP) & ~DarkSquares)
139 && (pos.pieces(strongSide, BISHOP) & DarkSquares)))
140 result = std::min(result + VALUE_KNOWN_WIN, VALUE_TB_WIN_IN_MAX_PLY - 1);
142 return strongSide == pos.side_to_move() ? result : -result;
146 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
147 /// defending king towards a corner square that our bishop attacks.
149 Value Endgame<KBNK>::operator()(const Position& pos) const {
151 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
152 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
154 Square winnerKSq = pos.square<KING>(strongSide);
155 Square loserKSq = pos.square<KING>(weakSide);
156 Square bishopSq = pos.square<BISHOP>(strongSide);
158 // If our bishop does not attack A1/H8, we flip the enemy king square
159 // to drive to opposite corners (A8/H1).
161 Value result = VALUE_KNOWN_WIN
162 + PushClose[distance(winnerKSq, loserKSq)]
163 + PushToCorners[opposite_colors(bishopSq, SQ_A1) ? ~loserKSq : loserKSq];
165 assert(abs(result) < VALUE_TB_WIN_IN_MAX_PLY);
166 return strongSide == pos.side_to_move() ? result : -result;
170 /// KP vs K. This endgame is evaluated with the help of a bitbase
172 Value Endgame<KPK>::operator()(const Position& pos) const {
174 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
175 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
177 // Assume strongSide is white and the pawn is on files A-D
178 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
179 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
180 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
182 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
184 if (!Bitbases::probe(wksq, psq, bksq, us))
187 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
189 return strongSide == pos.side_to_move() ? result : -result;
193 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
194 /// a bitbase. The function below returns drawish scores when the pawn is
195 /// far advanced with support of the king, while the attacking king is far
198 Value Endgame<KRKP>::operator()(const Position& pos) const {
200 assert(verify_material(pos, strongSide, RookValueMg, 0));
201 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
203 Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
204 Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
205 Square rsq = relative_square(strongSide, pos.square<ROOK>(strongSide));
206 Square psq = relative_square(strongSide, pos.square<PAWN>(weakSide));
208 Square queeningSq = make_square(file_of(psq), RANK_1);
211 // If the stronger side's king is in front of the pawn, it's a win
212 if (forward_file_bb(WHITE, wksq) & psq)
213 result = RookValueEg - distance(wksq, psq);
215 // If the weaker side's king is too far from the pawn and the rook,
217 else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
218 && distance(bksq, rsq) >= 3)
219 result = RookValueEg - distance(wksq, psq);
221 // If the pawn is far advanced and supported by the defending king,
222 // the position is drawish
223 else if ( rank_of(bksq) <= RANK_3
224 && distance(bksq, psq) == 1
225 && rank_of(wksq) >= RANK_4
226 && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
227 result = Value(80) - 8 * distance(wksq, psq);
230 result = Value(200) - 8 * ( distance(wksq, psq + SOUTH)
231 - distance(bksq, psq + SOUTH)
232 - distance(psq, queeningSq));
234 return strongSide == pos.side_to_move() ? result : -result;
238 /// KR vs KB. This is very simple, and always returns drawish scores. The
239 /// score is slightly bigger when the defending king is close to the edge.
241 Value Endgame<KRKB>::operator()(const Position& pos) const {
243 assert(verify_material(pos, strongSide, RookValueMg, 0));
244 assert(verify_material(pos, weakSide, BishopValueMg, 0));
246 Value result = Value(PushToEdges[pos.square<KING>(weakSide)]);
247 return strongSide == pos.side_to_move() ? result : -result;
251 /// KR vs KN. The attacking side has slightly better winning chances than
252 /// in KR vs KB, particularly if the king and the knight are far apart.
254 Value Endgame<KRKN>::operator()(const Position& pos) const {
256 assert(verify_material(pos, strongSide, RookValueMg, 0));
257 assert(verify_material(pos, weakSide, KnightValueMg, 0));
259 Square bksq = pos.square<KING>(weakSide);
260 Square bnsq = pos.square<KNIGHT>(weakSide);
261 Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
262 return strongSide == pos.side_to_move() ? result : -result;
266 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
267 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
268 /// with a king positioned next to it can be a draw, so in that case, we only
269 /// use the distance between the kings.
271 Value Endgame<KQKP>::operator()(const Position& pos) const {
273 assert(verify_material(pos, strongSide, QueenValueMg, 0));
274 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
276 Square winnerKSq = pos.square<KING>(strongSide);
277 Square loserKSq = pos.square<KING>(weakSide);
278 Square pawnSq = pos.square<PAWN>(weakSide);
280 Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
282 if ( relative_rank(weakSide, pawnSq) != RANK_7
283 || distance(loserKSq, pawnSq) != 1
284 || ((FileBBB | FileDBB | FileEBB | FileGBB) & pawnSq))
285 result += QueenValueEg - PawnValueEg;
287 return strongSide == pos.side_to_move() ? result : -result;
291 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
292 /// king a bonus for having the kings close together, and for forcing the
293 /// defending king towards the edge. If we also take care to avoid null move for
294 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
296 Value Endgame<KQKR>::operator()(const Position& pos) const {
298 assert(verify_material(pos, strongSide, QueenValueMg, 0));
299 assert(verify_material(pos, weakSide, RookValueMg, 0));
301 Square winnerKSq = pos.square<KING>(strongSide);
302 Square loserKSq = pos.square<KING>(weakSide);
304 Value result = QueenValueEg
306 + PushToEdges[loserKSq]
307 + PushClose[distance(winnerKSq, loserKSq)];
309 return strongSide == pos.side_to_move() ? result : -result;
313 /// KNN vs KP. Very drawish, but there are some mate opportunities if we can
314 // press the weakSide King to a corner before the pawn advances too much.
316 Value Endgame<KNNKP>::operator()(const Position& pos) const {
318 assert(verify_material(pos, strongSide, 2 * KnightValueMg, 0));
319 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
321 Value result = PawnValueEg
322 + 2 * PushToEdges[pos.square<KING>(weakSide)]
323 - 10 * relative_rank(weakSide, pos.square<PAWN>(weakSide));
325 return strongSide == pos.side_to_move() ? result : -result;
329 /// Some cases of trivial draws
330 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
333 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
334 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
335 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
338 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
340 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
341 assert(pos.count<PAWN>(strongSide) >= 1);
343 // No assertions about the material of weakSide, because we want draws to
344 // be detected even when the weaker side has some pawns.
346 Bitboard pawns = pos.pieces(strongSide, PAWN);
347 File pawnsFile = file_of(lsb(pawns));
349 // All pawns are on a single rook file?
350 if ( (pawnsFile == FILE_A || pawnsFile == FILE_H)
351 && !(pawns & ~file_bb(pawnsFile)))
353 Square bishopSq = pos.square<BISHOP>(strongSide);
354 Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
355 Square kingSq = pos.square<KING>(weakSide);
357 if ( opposite_colors(queeningSq, bishopSq)
358 && distance(queeningSq, kingSq) <= 1)
359 return SCALE_FACTOR_DRAW;
362 // If all the pawns are on the same B or G file, then it's potentially a draw
363 if ( (pawnsFile == FILE_B || pawnsFile == FILE_G)
364 && !(pos.pieces(PAWN) & ~file_bb(pawnsFile))
365 && pos.non_pawn_material(weakSide) == 0
366 && pos.count<PAWN>(weakSide) >= 1)
368 // Get weakSide pawn that is closest to the home rank
369 Square weakPawnSq = frontmost_sq(strongSide, pos.pieces(weakSide, PAWN));
371 Square strongKingSq = pos.square<KING>(strongSide);
372 Square weakKingSq = pos.square<KING>(weakSide);
373 Square bishopSq = pos.square<BISHOP>(strongSide);
375 // There's potential for a draw if our pawn is blocked on the 7th rank,
376 // the bishop cannot attack it or they only have one pawn left
377 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
378 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
379 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
381 int strongKingDist = distance(weakPawnSq, strongKingSq);
382 int weakKingDist = distance(weakPawnSq, weakKingSq);
384 // It's a draw if the weak king is on its back two ranks, within 2
385 // squares of the blocking pawn and the strong king is not
386 // closer. (I think this rule only fails in practically
387 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
388 // and positions where qsearch will immediately correct the
389 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
390 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
392 && weakKingDist <= strongKingDist)
393 return SCALE_FACTOR_DRAW;
397 return SCALE_FACTOR_NONE;
401 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
402 /// the third rank defended by a pawn.
404 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
406 assert(verify_material(pos, strongSide, QueenValueMg, 0));
407 assert(pos.count<ROOK>(weakSide) == 1);
408 assert(pos.count<PAWN>(weakSide) >= 1);
410 Square kingSq = pos.square<KING>(weakSide);
411 Square rsq = pos.square<ROOK>(weakSide);
413 if ( relative_rank(weakSide, kingSq) <= RANK_2
414 && relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
415 && relative_rank(weakSide, rsq) == RANK_3
416 && ( pos.pieces(weakSide, PAWN)
417 & pos.attacks_from<KING>(kingSq)
418 & pos.attacks_from<PAWN>(rsq, strongSide)))
419 return SCALE_FACTOR_DRAW;
421 return SCALE_FACTOR_NONE;
425 /// KRP vs KR. This function knows a handful of the most important classes of
426 /// drawn positions, but is far from perfect. It would probably be a good idea
427 /// to add more knowledge in the future.
429 /// It would also be nice to rewrite the actual code for this function,
430 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
432 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
434 assert(verify_material(pos, strongSide, RookValueMg, 1));
435 assert(verify_material(pos, weakSide, RookValueMg, 0));
437 // Assume strongSide is white and the pawn is on files A-D
438 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
439 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
440 Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
441 Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
442 Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
444 File f = file_of(wpsq);
445 Rank r = rank_of(wpsq);
446 Square queeningSq = make_square(f, RANK_8);
447 int tempo = (pos.side_to_move() == strongSide);
449 // If the pawn is not too far advanced and the defending king defends the
450 // queening square, use the third-rank defence.
452 && distance(bksq, queeningSq) <= 1
454 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
455 return SCALE_FACTOR_DRAW;
457 // The defending side saves a draw by checking from behind in case the pawn
458 // has advanced to the 6th rank with the king behind.
460 && distance(bksq, queeningSq) <= 1
461 && rank_of(wksq) + tempo <= RANK_6
462 && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
463 return SCALE_FACTOR_DRAW;
466 && bksq == queeningSq
467 && rank_of(brsq) == RANK_1
468 && (!tempo || distance(wksq, wpsq) >= 2))
469 return SCALE_FACTOR_DRAW;
471 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
472 // and the black rook is behind the pawn.
475 && (bksq == SQ_H7 || bksq == SQ_G7)
476 && file_of(brsq) == FILE_A
477 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
478 return SCALE_FACTOR_DRAW;
480 // If the defending king blocks the pawn and the attacking king is too far
481 // away, it's a draw.
483 && bksq == wpsq + NORTH
484 && distance(wksq, wpsq) - tempo >= 2
485 && distance(wksq, brsq) - tempo >= 2)
486 return SCALE_FACTOR_DRAW;
488 // Pawn on the 7th rank supported by the rook from behind usually wins if the
489 // attacking king is closer to the queening square than the defending king,
490 // and the defending king cannot gain tempi by threatening the attacking rook.
493 && file_of(wrsq) == f
494 && wrsq != queeningSq
495 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
496 && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
497 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
499 // Similar to the above, but with the pawn further back
501 && file_of(wrsq) == f
503 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
504 && (distance(wksq, wpsq + NORTH) < distance(bksq, wpsq + NORTH) - 2 + tempo)
505 && ( distance(bksq, wrsq) + tempo >= 3
506 || ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
507 && (distance(wksq, wpsq + NORTH) < distance(bksq, wrsq) + tempo))))
508 return ScaleFactor( SCALE_FACTOR_MAX
509 - 8 * distance(wpsq, queeningSq)
510 - 2 * distance(wksq, queeningSq));
512 // If the pawn is not far advanced and the defending king is somewhere in
513 // the pawn's path, it's probably a draw.
514 if (r <= RANK_4 && bksq > wpsq)
516 if (file_of(bksq) == file_of(wpsq))
517 return ScaleFactor(10);
518 if ( distance<File>(bksq, wpsq) == 1
519 && distance(wksq, bksq) > 2)
520 return ScaleFactor(24 - 2 * distance(wksq, bksq));
522 return SCALE_FACTOR_NONE;
526 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
528 assert(verify_material(pos, strongSide, RookValueMg, 1));
529 assert(verify_material(pos, weakSide, BishopValueMg, 0));
531 // Test for a rook pawn
532 if (pos.pieces(PAWN) & (FileABB | FileHBB))
534 Square ksq = pos.square<KING>(weakSide);
535 Square bsq = pos.square<BISHOP>(weakSide);
536 Square psq = pos.square<PAWN>(strongSide);
537 Rank rk = relative_rank(strongSide, psq);
538 Direction push = pawn_push(strongSide);
540 // If the pawn is on the 5th rank and the pawn (currently) is on
541 // the same color square as the bishop then there is a chance of
542 // a fortress. Depending on the king position give a moderate
543 // reduction or a stronger one if the defending king is near the
544 // corner but not trapped there.
545 if (rk == RANK_5 && !opposite_colors(bsq, psq))
547 int d = distance(psq + 3 * push, ksq);
549 if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
550 return ScaleFactor(24);
552 return ScaleFactor(48);
555 // When the pawn has moved to the 6th rank we can be fairly sure
556 // it's drawn if the bishop attacks the square in front of the
557 // pawn from a reasonable distance and the defending king is near
560 && distance(psq + 2 * push, ksq) <= 1
561 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
562 && distance<File>(bsq, psq) >= 2)
563 return ScaleFactor(8);
566 return SCALE_FACTOR_NONE;
569 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
570 /// pawns and the defending king is actively placed, the position is drawish.
572 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
574 assert(verify_material(pos, strongSide, RookValueMg, 2));
575 assert(verify_material(pos, weakSide, RookValueMg, 1));
577 Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
578 Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
579 Square bksq = pos.square<KING>(weakSide);
581 // Does the stronger side have a passed pawn?
582 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
583 return SCALE_FACTOR_NONE;
585 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
587 if ( distance<File>(bksq, wpsq1) <= 1
588 && distance<File>(bksq, wpsq2) <= 1
589 && relative_rank(strongSide, bksq) > r)
591 assert(r > RANK_1 && r < RANK_7);
592 return ScaleFactor(KRPPKRPScaleFactors[r]);
594 return SCALE_FACTOR_NONE;
598 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
599 /// are on the same rook file and are blocked by the defending king, it's a draw.
601 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
603 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
604 assert(pos.count<PAWN>(strongSide) >= 2);
605 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
607 Square ksq = pos.square<KING>(weakSide);
608 Bitboard pawns = pos.pieces(strongSide, PAWN);
610 // If all pawns are ahead of the king, on a single rook file and
611 // the king is within one file of the pawns, it's a draw.
612 if ( !(pawns & ~forward_ranks_bb(weakSide, ksq))
613 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
614 && distance<File>(ksq, lsb(pawns)) <= 1)
615 return SCALE_FACTOR_DRAW;
617 return SCALE_FACTOR_NONE;
621 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
622 /// path of the pawn, and the square of the king is not of the same color as the
623 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
624 /// it's almost always a draw.
626 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
628 assert(verify_material(pos, strongSide, BishopValueMg, 1));
629 assert(verify_material(pos, weakSide, BishopValueMg, 0));
631 Square pawnSq = pos.square<PAWN>(strongSide);
632 Square strongBishopSq = pos.square<BISHOP>(strongSide);
633 Square weakBishopSq = pos.square<BISHOP>(weakSide);
634 Square weakKingSq = pos.square<KING>(weakSide);
636 // Case 1: Defending king blocks the pawn, and cannot be driven away
637 if ( file_of(weakKingSq) == file_of(pawnSq)
638 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
639 && ( opposite_colors(weakKingSq, strongBishopSq)
640 || relative_rank(strongSide, weakKingSq) <= RANK_6))
641 return SCALE_FACTOR_DRAW;
643 // Case 2: Opposite colored bishops
644 if (opposite_colors(strongBishopSq, weakBishopSq))
645 return SCALE_FACTOR_DRAW;
647 return SCALE_FACTOR_NONE;
651 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
653 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
655 assert(verify_material(pos, strongSide, BishopValueMg, 2));
656 assert(verify_material(pos, weakSide, BishopValueMg, 0));
658 Square wbsq = pos.square<BISHOP>(strongSide);
659 Square bbsq = pos.square<BISHOP>(weakSide);
661 if (!opposite_colors(wbsq, bbsq))
662 return SCALE_FACTOR_NONE;
664 Square ksq = pos.square<KING>(weakSide);
665 Square psq1 = pos.squares<PAWN>(strongSide)[0];
666 Square psq2 = pos.squares<PAWN>(strongSide)[1];
667 Square blockSq1, blockSq2;
669 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
671 blockSq1 = psq1 + pawn_push(strongSide);
672 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
676 blockSq1 = psq2 + pawn_push(strongSide);
677 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
680 switch (distance<File>(psq1, psq2))
683 // Both pawns are on the same file. It's an easy draw if the defender firmly
684 // controls some square in the frontmost pawn's path.
685 if ( file_of(ksq) == file_of(blockSq1)
686 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
687 && opposite_colors(ksq, wbsq))
688 return SCALE_FACTOR_DRAW;
690 return SCALE_FACTOR_NONE;
693 // Pawns on adjacent files. It's a draw if the defender firmly controls the
694 // square in front of the frontmost pawn's path, and the square diagonally
695 // behind this square on the file of the other pawn.
697 && opposite_colors(ksq, wbsq)
698 && ( bbsq == blockSq2
699 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
700 || distance<Rank>(psq1, psq2) >= 2))
701 return SCALE_FACTOR_DRAW;
703 else if ( ksq == blockSq2
704 && opposite_colors(ksq, wbsq)
705 && ( bbsq == blockSq1
706 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
707 return SCALE_FACTOR_DRAW;
709 return SCALE_FACTOR_NONE;
712 // The pawns are not on the same file or adjacent files. No scaling.
713 return SCALE_FACTOR_NONE;
718 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
719 /// the path of the pawn, and the square of the king is not of the same color as
720 /// the stronger side's bishop, it's a draw.
722 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
724 assert(verify_material(pos, strongSide, BishopValueMg, 1));
725 assert(verify_material(pos, weakSide, KnightValueMg, 0));
727 Square pawnSq = pos.square<PAWN>(strongSide);
728 Square strongBishopSq = pos.square<BISHOP>(strongSide);
729 Square weakKingSq = pos.square<KING>(weakSide);
731 if ( file_of(weakKingSq) == file_of(pawnSq)
732 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
733 && ( opposite_colors(weakKingSq, strongBishopSq)
734 || relative_rank(strongSide, weakKingSq) <= RANK_6))
735 return SCALE_FACTOR_DRAW;
737 return SCALE_FACTOR_NONE;
741 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
742 /// and the defending king prevents the pawn from advancing, the position is drawn.
744 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
746 assert(verify_material(pos, strongSide, KnightValueMg, 1));
747 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
749 // Assume strongSide is white and the pawn is on files A-D
750 Square pawnSq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
751 Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
753 if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
754 return SCALE_FACTOR_DRAW;
756 return SCALE_FACTOR_NONE;
760 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
761 /// Otherwise the position is drawn.
763 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
765 assert(verify_material(pos, strongSide, KnightValueMg, 1));
766 assert(verify_material(pos, weakSide, BishopValueMg, 0));
768 Square pawnSq = pos.square<PAWN>(strongSide);
769 Square bishopSq = pos.square<BISHOP>(weakSide);
770 Square weakKingSq = pos.square<KING>(weakSide);
772 // King needs to get close to promoting pawn to prevent knight from blocking.
773 // Rules for this are very tricky, so just approximate.
774 if (forward_file_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
775 return ScaleFactor(distance(weakKingSq, pawnSq));
777 return SCALE_FACTOR_NONE;
781 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
782 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
783 /// has at least a draw with the pawn as well. The exception is when the stronger
784 /// side's pawn is far advanced and not on a rook file; in this case it is often
785 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
787 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
789 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
790 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
792 // Assume strongSide is white and the pawn is on files A-D
793 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
794 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
795 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
797 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
799 // If the pawn has advanced to the fifth rank or further, and is not a
800 // rook pawn, it's too dangerous to assume that it's at least a draw.
801 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
802 return SCALE_FACTOR_NONE;
804 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
805 // it's probably at least a draw even with the pawn.
806 return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;