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;
87 std::pair<Map<Value>, Map<ScaleFactor>> maps;
107 add<KBPPKB>("KBPPKB");
108 add<KRPPKRP>("KRPPKRP");
112 /// Mate with KX vs K. This function is used to evaluate positions with
113 /// king and plenty of material vs a lone king. It simply gives the
114 /// attacking side a bonus for driving the defending king towards the edge
115 /// of the board, and for keeping the distance between the two kings small.
117 Value Endgame<KXK>::operator()(const Position& pos) const {
119 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
120 assert(!pos.checkers()); // Eval is never called when in check
122 // Stalemate detection with lone king
123 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
126 Square winnerKSq = pos.square<KING>(strongSide);
127 Square loserKSq = pos.square<KING>(weakSide);
129 Value result = pos.non_pawn_material(strongSide)
130 + pos.count<PAWN>(strongSide) * PawnValueEg
131 + PushToEdges[loserKSq]
132 + PushClose[distance(winnerKSq, loserKSq)];
134 if ( pos.count<QUEEN>(strongSide)
135 || pos.count<ROOK>(strongSide)
136 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
137 || ( (pos.pieces(strongSide, BISHOP) & ~DarkSquares)
138 && (pos.pieces(strongSide, BISHOP) & DarkSquares)))
139 result = std::min(result + VALUE_KNOWN_WIN, VALUE_MATE_IN_MAX_PLY - 1);
141 return strongSide == pos.side_to_move() ? result : -result;
145 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
146 /// defending king towards a corner square that our bishop attacks.
148 Value Endgame<KBNK>::operator()(const Position& pos) const {
150 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
151 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
153 Square winnerKSq = pos.square<KING>(strongSide);
154 Square loserKSq = pos.square<KING>(weakSide);
155 Square bishopSq = pos.square<BISHOP>(strongSide);
157 // If our Bishop does not attack A1/H8, we flip the enemy king square
158 // to drive to opposite corners (A8/H1).
160 Value result = VALUE_KNOWN_WIN
161 + PushClose[distance(winnerKSq, loserKSq)]
162 + PushToCorners[opposite_colors(bishopSq, SQ_A1) ? ~loserKSq : loserKSq];
164 assert(abs(result) < VALUE_MATE_IN_MAX_PLY);
165 return strongSide == pos.side_to_move() ? result : -result;
169 /// KP vs K. This endgame is evaluated with the help of a bitbase.
171 Value Endgame<KPK>::operator()(const Position& pos) const {
173 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
174 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
176 // Assume strongSide is white and the pawn is on files A-D
177 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
178 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
179 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
181 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
183 if (!Bitbases::probe(wksq, psq, bksq, us))
186 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
188 return strongSide == pos.side_to_move() ? result : -result;
192 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
193 /// a bitbase. The function below returns drawish scores when the pawn is
194 /// far advanced with support of the king, while the attacking king is far
197 Value Endgame<KRKP>::operator()(const Position& pos) const {
199 assert(verify_material(pos, strongSide, RookValueMg, 0));
200 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
202 Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
203 Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
204 Square rsq = relative_square(strongSide, pos.square<ROOK>(strongSide));
205 Square psq = relative_square(strongSide, pos.square<PAWN>(weakSide));
207 Square queeningSq = make_square(file_of(psq), RANK_1);
210 // If the stronger side's king is in front of the pawn, it's a win
211 if (forward_file_bb(WHITE, wksq) & psq)
212 result = RookValueEg - distance(wksq, psq);
214 // If the weaker side's king is too far from the pawn and the rook,
216 else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
217 && distance(bksq, rsq) >= 3)
218 result = RookValueEg - distance(wksq, psq);
220 // If the pawn is far advanced and supported by the defending king,
221 // the position is drawish
222 else if ( rank_of(bksq) <= RANK_3
223 && distance(bksq, psq) == 1
224 && rank_of(wksq) >= RANK_4
225 && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
226 result = Value(80) - 8 * distance(wksq, psq);
229 result = Value(200) - 8 * ( distance(wksq, psq + SOUTH)
230 - distance(bksq, psq + SOUTH)
231 - distance(psq, queeningSq));
233 return strongSide == pos.side_to_move() ? result : -result;
237 /// KR vs KB. This is very simple, and always returns drawish scores. The
238 /// score is slightly bigger when the defending king is close to the edge.
240 Value Endgame<KRKB>::operator()(const Position& pos) const {
242 assert(verify_material(pos, strongSide, RookValueMg, 0));
243 assert(verify_material(pos, weakSide, BishopValueMg, 0));
245 Value result = Value(PushToEdges[pos.square<KING>(weakSide)]);
246 return strongSide == pos.side_to_move() ? result : -result;
250 /// KR vs KN. The attacking side has slightly better winning chances than
251 /// in KR vs KB, particularly if the king and the knight are far apart.
253 Value Endgame<KRKN>::operator()(const Position& pos) const {
255 assert(verify_material(pos, strongSide, RookValueMg, 0));
256 assert(verify_material(pos, weakSide, KnightValueMg, 0));
258 Square bksq = pos.square<KING>(weakSide);
259 Square bnsq = pos.square<KNIGHT>(weakSide);
260 Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
261 return strongSide == pos.side_to_move() ? result : -result;
265 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
266 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
267 /// with a king positioned next to it can be a draw, so in that case, we only
268 /// use the distance between the kings.
270 Value Endgame<KQKP>::operator()(const Position& pos) const {
272 assert(verify_material(pos, strongSide, QueenValueMg, 0));
273 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
275 Square winnerKSq = pos.square<KING>(strongSide);
276 Square loserKSq = pos.square<KING>(weakSide);
277 Square pawnSq = pos.square<PAWN>(weakSide);
279 Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
281 if ( relative_rank(weakSide, pawnSq) != RANK_7
282 || distance(loserKSq, pawnSq) != 1
283 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
284 result += QueenValueEg - PawnValueEg;
286 return strongSide == pos.side_to_move() ? result : -result;
290 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
291 /// king a bonus for having the kings close together, and for forcing the
292 /// defending king towards the edge. If we also take care to avoid null move for
293 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
295 Value Endgame<KQKR>::operator()(const Position& pos) const {
297 assert(verify_material(pos, strongSide, QueenValueMg, 0));
298 assert(verify_material(pos, weakSide, RookValueMg, 0));
300 Square winnerKSq = pos.square<KING>(strongSide);
301 Square loserKSq = pos.square<KING>(weakSide);
303 Value result = QueenValueEg
305 + PushToEdges[loserKSq]
306 + PushClose[distance(winnerKSq, loserKSq)];
308 return strongSide == pos.side_to_move() ? result : -result;
312 /// KNN vs KP. Simply push the opposing king to the corner
314 Value Endgame<KNNKP>::operator()(const Position& pos) const {
316 assert(verify_material(pos, strongSide, 2 * KnightValueMg, 0));
317 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
319 Value result = 2 * KnightValueEg
321 + PushToEdges[pos.square<KING>(weakSide)];
323 return strongSide == pos.side_to_move() ? result : -result;
327 /// Some cases of trivial draws
328 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
331 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
332 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
333 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
336 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
338 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
339 assert(pos.count<PAWN>(strongSide) >= 1);
341 // No assertions about the material of weakSide, because we want draws to
342 // be detected even when the weaker side has some pawns.
344 Bitboard pawns = pos.pieces(strongSide, PAWN);
345 File pawnsFile = file_of(lsb(pawns));
347 // All pawns are on a single rook file?
348 if ( (pawnsFile == FILE_A || pawnsFile == FILE_H)
349 && !(pawns & ~file_bb(pawnsFile)))
351 Square bishopSq = pos.square<BISHOP>(strongSide);
352 Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
353 Square kingSq = pos.square<KING>(weakSide);
355 if ( opposite_colors(queeningSq, bishopSq)
356 && distance(queeningSq, kingSq) <= 1)
357 return SCALE_FACTOR_DRAW;
360 // If all the pawns are on the same B or G file, then it's potentially a draw
361 if ( (pawnsFile == FILE_B || pawnsFile == FILE_G)
362 && !(pos.pieces(PAWN) & ~file_bb(pawnsFile))
363 && pos.non_pawn_material(weakSide) == 0
364 && pos.count<PAWN>(weakSide) >= 1)
366 // Get weakSide pawn that is closest to the home rank
367 Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
369 Square strongKingSq = pos.square<KING>(strongSide);
370 Square weakKingSq = pos.square<KING>(weakSide);
371 Square bishopSq = pos.square<BISHOP>(strongSide);
373 // There's potential for a draw if our pawn is blocked on the 7th rank,
374 // the bishop cannot attack it or they only have one pawn left
375 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
376 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
377 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
379 int strongKingDist = distance(weakPawnSq, strongKingSq);
380 int weakKingDist = distance(weakPawnSq, weakKingSq);
382 // It's a draw if the weak king is on its back two ranks, within 2
383 // squares of the blocking pawn and the strong king is not
384 // closer. (I think this rule only fails in practically
385 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
386 // and positions where qsearch will immediately correct the
387 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
388 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
390 && weakKingDist <= strongKingDist)
391 return SCALE_FACTOR_DRAW;
395 return SCALE_FACTOR_NONE;
399 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
400 /// the third rank defended by a pawn.
402 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
404 assert(verify_material(pos, strongSide, QueenValueMg, 0));
405 assert(pos.count<ROOK>(weakSide) == 1);
406 assert(pos.count<PAWN>(weakSide) >= 1);
408 Square kingSq = pos.square<KING>(weakSide);
409 Square rsq = pos.square<ROOK>(weakSide);
411 if ( relative_rank(weakSide, kingSq) <= RANK_2
412 && relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
413 && relative_rank(weakSide, rsq) == RANK_3
414 && ( pos.pieces(weakSide, PAWN)
415 & pos.attacks_from<KING>(kingSq)
416 & pos.attacks_from<PAWN>(rsq, strongSide)))
417 return SCALE_FACTOR_DRAW;
419 return SCALE_FACTOR_NONE;
423 /// KRP vs KR. This function knows a handful of the most important classes of
424 /// drawn positions, but is far from perfect. It would probably be a good idea
425 /// to add more knowledge in the future.
427 /// It would also be nice to rewrite the actual code for this function,
428 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
430 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
432 assert(verify_material(pos, strongSide, RookValueMg, 1));
433 assert(verify_material(pos, weakSide, RookValueMg, 0));
435 // Assume strongSide is white and the pawn is on files A-D
436 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
437 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
438 Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
439 Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
440 Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
442 File f = file_of(wpsq);
443 Rank r = rank_of(wpsq);
444 Square queeningSq = make_square(f, RANK_8);
445 int tempo = (pos.side_to_move() == strongSide);
447 // If the pawn is not too far advanced and the defending king defends the
448 // queening square, use the third-rank defence.
450 && distance(bksq, queeningSq) <= 1
452 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
453 return SCALE_FACTOR_DRAW;
455 // The defending side saves a draw by checking from behind in case the pawn
456 // has advanced to the 6th rank with the king behind.
458 && distance(bksq, queeningSq) <= 1
459 && rank_of(wksq) + tempo <= RANK_6
460 && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
461 return SCALE_FACTOR_DRAW;
464 && bksq == queeningSq
465 && rank_of(brsq) == RANK_1
466 && (!tempo || distance(wksq, wpsq) >= 2))
467 return SCALE_FACTOR_DRAW;
469 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
470 // and the black rook is behind the pawn.
473 && (bksq == SQ_H7 || bksq == SQ_G7)
474 && file_of(brsq) == FILE_A
475 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
476 return SCALE_FACTOR_DRAW;
478 // If the defending king blocks the pawn and the attacking king is too far
479 // away, it's a draw.
481 && bksq == wpsq + NORTH
482 && distance(wksq, wpsq) - tempo >= 2
483 && distance(wksq, brsq) - tempo >= 2)
484 return SCALE_FACTOR_DRAW;
486 // Pawn on the 7th rank supported by the rook from behind usually wins if the
487 // attacking king is closer to the queening square than the defending king,
488 // and the defending king cannot gain tempi by threatening the attacking rook.
491 && file_of(wrsq) == f
492 && wrsq != queeningSq
493 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
494 && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
495 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
497 // Similar to the above, but with the pawn further back
499 && file_of(wrsq) == f
501 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
502 && (distance(wksq, wpsq + NORTH) < distance(bksq, wpsq + NORTH) - 2 + tempo)
503 && ( distance(bksq, wrsq) + tempo >= 3
504 || ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
505 && (distance(wksq, wpsq + NORTH) < distance(bksq, wrsq) + tempo))))
506 return ScaleFactor( SCALE_FACTOR_MAX
507 - 8 * distance(wpsq, queeningSq)
508 - 2 * distance(wksq, queeningSq));
510 // If the pawn is not far advanced and the defending king is somewhere in
511 // the pawn's path, it's probably a draw.
512 if (r <= RANK_4 && bksq > wpsq)
514 if (file_of(bksq) == file_of(wpsq))
515 return ScaleFactor(10);
516 if ( distance<File>(bksq, wpsq) == 1
517 && distance(wksq, bksq) > 2)
518 return ScaleFactor(24 - 2 * distance(wksq, bksq));
520 return SCALE_FACTOR_NONE;
524 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
526 assert(verify_material(pos, strongSide, RookValueMg, 1));
527 assert(verify_material(pos, weakSide, BishopValueMg, 0));
529 // Test for a rook pawn
530 if (pos.pieces(PAWN) & (FileABB | FileHBB))
532 Square ksq = pos.square<KING>(weakSide);
533 Square bsq = pos.square<BISHOP>(weakSide);
534 Square psq = pos.square<PAWN>(strongSide);
535 Rank rk = relative_rank(strongSide, psq);
536 Direction push = pawn_push(strongSide);
538 // If the pawn is on the 5th rank and the pawn (currently) is on
539 // the same color square as the bishop then there is a chance of
540 // a fortress. Depending on the king position give a moderate
541 // reduction or a stronger one if the defending king is near the
542 // corner but not trapped there.
543 if (rk == RANK_5 && !opposite_colors(bsq, psq))
545 int d = distance(psq + 3 * push, ksq);
547 if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
548 return ScaleFactor(24);
550 return ScaleFactor(48);
553 // When the pawn has moved to the 6th rank we can be fairly sure
554 // it's drawn if the bishop attacks the square in front of the
555 // pawn from a reasonable distance and the defending king is near
558 && distance(psq + 2 * push, ksq) <= 1
559 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
560 && distance<File>(bsq, psq) >= 2)
561 return ScaleFactor(8);
564 return SCALE_FACTOR_NONE;
567 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
568 /// pawns and the defending king is actively placed, the position is drawish.
570 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
572 assert(verify_material(pos, strongSide, RookValueMg, 2));
573 assert(verify_material(pos, weakSide, RookValueMg, 1));
575 Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
576 Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
577 Square bksq = pos.square<KING>(weakSide);
579 // Does the stronger side have a passed pawn?
580 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
581 return SCALE_FACTOR_NONE;
583 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
585 if ( distance<File>(bksq, wpsq1) <= 1
586 && distance<File>(bksq, wpsq2) <= 1
587 && relative_rank(strongSide, bksq) > r)
589 assert(r > RANK_1 && r < RANK_7);
590 return ScaleFactor(KRPPKRPScaleFactors[r]);
592 return SCALE_FACTOR_NONE;
596 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
597 /// are on the same rook file and are blocked by the defending king, it's a draw.
599 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
601 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
602 assert(pos.count<PAWN>(strongSide) >= 2);
603 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
605 Square ksq = pos.square<KING>(weakSide);
606 Bitboard pawns = pos.pieces(strongSide, PAWN);
608 // If all pawns are ahead of the king, on a single rook file and
609 // the king is within one file of the pawns, it's a draw.
610 if ( !(pawns & ~forward_ranks_bb(weakSide, ksq))
611 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
612 && distance<File>(ksq, lsb(pawns)) <= 1)
613 return SCALE_FACTOR_DRAW;
615 return SCALE_FACTOR_NONE;
619 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
620 /// path of the pawn, and the square of the king is not of the same color as the
621 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
622 /// it's almost always a draw.
624 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
626 assert(verify_material(pos, strongSide, BishopValueMg, 1));
627 assert(verify_material(pos, weakSide, BishopValueMg, 0));
629 Square pawnSq = pos.square<PAWN>(strongSide);
630 Square strongBishopSq = pos.square<BISHOP>(strongSide);
631 Square weakBishopSq = pos.square<BISHOP>(weakSide);
632 Square weakKingSq = pos.square<KING>(weakSide);
634 // Case 1: Defending king blocks the pawn, and cannot be driven away
635 if ( file_of(weakKingSq) == file_of(pawnSq)
636 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
637 && ( opposite_colors(weakKingSq, strongBishopSq)
638 || relative_rank(strongSide, weakKingSq) <= RANK_6))
639 return SCALE_FACTOR_DRAW;
641 // Case 2: Opposite colored bishops
642 if (opposite_colors(strongBishopSq, weakBishopSq))
643 return SCALE_FACTOR_DRAW;
645 return SCALE_FACTOR_NONE;
649 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
651 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
653 assert(verify_material(pos, strongSide, BishopValueMg, 2));
654 assert(verify_material(pos, weakSide, BishopValueMg, 0));
656 Square wbsq = pos.square<BISHOP>(strongSide);
657 Square bbsq = pos.square<BISHOP>(weakSide);
659 if (!opposite_colors(wbsq, bbsq))
660 return SCALE_FACTOR_NONE;
662 Square ksq = pos.square<KING>(weakSide);
663 Square psq1 = pos.squares<PAWN>(strongSide)[0];
664 Square psq2 = pos.squares<PAWN>(strongSide)[1];
665 Square blockSq1, blockSq2;
667 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
669 blockSq1 = psq1 + pawn_push(strongSide);
670 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
674 blockSq1 = psq2 + pawn_push(strongSide);
675 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
678 switch (distance<File>(psq1, psq2))
681 // Both pawns are on the same file. It's an easy draw if the defender firmly
682 // controls some square in the frontmost pawn's path.
683 if ( file_of(ksq) == file_of(blockSq1)
684 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
685 && opposite_colors(ksq, wbsq))
686 return SCALE_FACTOR_DRAW;
688 return SCALE_FACTOR_NONE;
691 // Pawns on adjacent files. It's a draw if the defender firmly controls the
692 // square in front of the frontmost pawn's path, and the square diagonally
693 // behind this square on the file of the other pawn.
695 && opposite_colors(ksq, wbsq)
696 && ( bbsq == blockSq2
697 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
698 || distance<Rank>(psq1, psq2) >= 2))
699 return SCALE_FACTOR_DRAW;
701 else if ( ksq == blockSq2
702 && opposite_colors(ksq, wbsq)
703 && ( bbsq == blockSq1
704 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
705 return SCALE_FACTOR_DRAW;
707 return SCALE_FACTOR_NONE;
710 // The pawns are not on the same file or adjacent files. No scaling.
711 return SCALE_FACTOR_NONE;
716 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
717 /// the path of the pawn, and the square of the king is not of the same color as
718 /// the stronger side's bishop, it's a draw.
720 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
722 assert(verify_material(pos, strongSide, BishopValueMg, 1));
723 assert(verify_material(pos, weakSide, KnightValueMg, 0));
725 Square pawnSq = pos.square<PAWN>(strongSide);
726 Square strongBishopSq = pos.square<BISHOP>(strongSide);
727 Square weakKingSq = pos.square<KING>(weakSide);
729 if ( file_of(weakKingSq) == file_of(pawnSq)
730 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
731 && ( opposite_colors(weakKingSq, strongBishopSq)
732 || relative_rank(strongSide, weakKingSq) <= RANK_6))
733 return SCALE_FACTOR_DRAW;
735 return SCALE_FACTOR_NONE;
739 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
740 /// and the defending king prevents the pawn from advancing, the position is drawn.
742 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
744 assert(verify_material(pos, strongSide, KnightValueMg, 1));
745 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
747 // Assume strongSide is white and the pawn is on files A-D
748 Square pawnSq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
749 Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
751 if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
752 return SCALE_FACTOR_DRAW;
754 return SCALE_FACTOR_NONE;
758 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
759 /// Otherwise the position is drawn.
761 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
763 assert(verify_material(pos, strongSide, KnightValueMg, 1));
764 assert(verify_material(pos, weakSide, BishopValueMg, 0));
766 Square pawnSq = pos.square<PAWN>(strongSide);
767 Square bishopSq = pos.square<BISHOP>(weakSide);
768 Square weakKingSq = pos.square<KING>(weakSide);
770 // King needs to get close to promoting pawn to prevent knight from blocking.
771 // Rules for this are very tricky, so just approximate.
772 if (forward_file_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
773 return ScaleFactor(distance(weakKingSq, pawnSq));
775 return SCALE_FACTOR_NONE;
779 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
780 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
781 /// has at least a draw with the pawn as well. The exception is when the stronger
782 /// side's pawn is far advanced and not on a rook file; in this case it is often
783 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
785 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
787 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
788 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
790 // Assume strongSide is white and the pawn is on files A-D
791 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
792 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
793 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
795 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
797 // If the pawn has advanced to the fifth rank or further, and is not a
798 // rook pawn, it's too dangerous to assume that it's at least a draw.
799 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
800 return SCALE_FACTOR_NONE;
802 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
803 // it's probably at least a draw even with the pawn.
804 return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;