2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
4 Copyright (C) 2008-2013 Marco Costalba, Joona Kiiski, Tord Romstad
6 Stockfish is free software: you can redistribute it and/or modify
7 it under the terms of the GNU General Public License as published by
8 the Free Software Foundation, either version 3 of the License, or
9 (at your option) any later version.
11 Stockfish is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 GNU General Public License for more details.
16 You should have received a copy of the GNU General Public License
17 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 const 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 const int PushToCorners[SQUARE_NB] = {
48 200, 190, 180, 170, 160, 150, 140, 130,
49 190, 180, 170, 160, 150, 140, 130, 140,
50 180, 170, 155, 140, 140, 125, 140, 150,
51 170, 160, 140, 120, 110, 140, 150, 160,
52 160, 150, 140, 110, 120, 140, 160, 170,
53 150, 140, 125, 140, 140, 155, 170, 180,
54 140, 130, 140, 150, 160, 170, 180, 190,
55 130, 140, 150, 160, 170, 180, 190, 200
58 // Tables used to drive a piece towards or away from another piece
59 const int PushClose[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
60 const int PushAway [8] = { 0, 5, 20, 40, 60, 80, 90, 100 };
63 bool verify_material(const Position& pos, Color c, Value npm, int num_pawns) {
64 return pos.non_pawn_material(c) == npm && pos.count<PAWN>(c) == num_pawns;
68 // Get the material key of a Position out of the given endgame key code
69 // like "KBPKN". The trick here is to first forge an ad-hoc fen string
70 // and then let a Position object to do the work for us. Note that the
71 // fen string could correspond to an illegal position.
72 Key key(const string& code, Color c) {
74 assert(code.length() > 0 && code.length() < 8);
75 assert(code[0] == 'K');
77 string sides[] = { code.substr(code.find('K', 1)), // Weak
78 code.substr(0, code.find('K', 1)) }; // Strong
80 std::transform(sides[c].begin(), sides[c].end(), sides[c].begin(), tolower);
82 string fen = sides[0] + char('0' + int(8 - code.length()))
83 + sides[1] + "/8/8/8/8/8/8/8 w - - 0 10";
85 return Position(fen, false, NULL).material_key();
89 void delete_endgame(const typename M::value_type& p) { delete p.second; }
94 /// Endgames members definitions
96 Endgames::Endgames() {
114 add<KBPPKB>("KBPPKB");
115 add<KRPPKRP>("KRPPKRP");
118 Endgames::~Endgames() {
120 for_each(m1.begin(), m1.end(), delete_endgame<M1>);
121 for_each(m2.begin(), m2.end(), delete_endgame<M2>);
124 template<EndgameType E>
125 void Endgames::add(const string& code) {
127 map((Endgame<E>*)0)[key(code, WHITE)] = new Endgame<E>(WHITE);
128 map((Endgame<E>*)0)[key(code, BLACK)] = new Endgame<E>(BLACK);
132 /// Mate with KX vs K. This function is used to evaluate positions with
133 /// King and plenty of material vs a lone king. It simply gives the
134 /// attacking side a bonus for driving the defending king towards the edge
135 /// of the board, and for keeping the distance between the two kings small.
137 Value Endgame<KXK>::operator()(const Position& pos) const {
139 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
140 assert(!pos.checkers()); // Eval is never called when in check
142 // Stalemate detection with lone king
143 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
146 Square winnerKSq = pos.king_square(strongSide);
147 Square loserKSq = pos.king_square(weakSide);
149 Value result = pos.non_pawn_material(strongSide)
150 + pos.count<PAWN>(strongSide) * PawnValueEg
151 + PushToEdges[loserKSq]
152 + PushClose[square_distance(winnerKSq, loserKSq)];
154 if ( pos.count<QUEEN>(strongSide)
155 || pos.count<ROOK>(strongSide)
156 || pos.bishop_pair(strongSide))
157 result += VALUE_KNOWN_WIN;
159 return strongSide == pos.side_to_move() ? result : -result;
163 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
164 /// defending king towards a corner square of the right color.
166 Value Endgame<KBNK>::operator()(const Position& pos) const {
168 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
169 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
171 Square winnerKSq = pos.king_square(strongSide);
172 Square loserKSq = pos.king_square(weakSide);
173 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
175 // kbnk_mate_table() tries to drive toward corners A1 or H8,
176 // if we have a bishop that cannot reach the above squares we
177 // mirror the kings so to drive enemy toward corners A8 or H1.
178 if (opposite_colors(bishopSq, SQ_A1))
180 winnerKSq = mirror(winnerKSq);
181 loserKSq = mirror(loserKSq);
184 Value result = VALUE_KNOWN_WIN
185 + PushClose[square_distance(winnerKSq, loserKSq)]
186 + PushToCorners[loserKSq];
188 return strongSide == pos.side_to_move() ? result : -result;
192 /// KP vs K. This endgame is evaluated with the help of a bitbase.
194 Value Endgame<KPK>::operator()(const Position& pos) const {
196 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
197 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
199 Square wksq = pos.king_square(strongSide);
200 Square bksq = pos.king_square(weakSide);
201 Square psq = pos.list<PAWN>(strongSide)[0];
202 Color us = pos.side_to_move();
204 if (strongSide == BLACK)
212 if (file_of(psq) >= FILE_E)
219 if (!Bitbases::probe_kpk(wksq, psq, bksq, us))
222 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
224 return strongSide == pos.side_to_move() ? result : -result;
228 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
229 /// a bitbase. The function below returns drawish scores when the pawn is
230 /// far advanced with support of the king, while the attacking king is far
233 Value Endgame<KRKP>::operator()(const Position& pos) const {
235 assert(verify_material(pos, strongSide, RookValueMg, 0));
236 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
238 Square wksq = pos.king_square(strongSide);
239 Square bksq = pos.king_square(weakSide);
240 Square rsq = pos.list<ROOK>(strongSide)[0];
241 Square psq = pos.list<PAWN>(weakSide)[0];
243 if (strongSide == BLACK)
251 Square queeningSq = file_of(psq) | RANK_1;
254 // If the stronger side's king is in front of the pawn, it's a win
255 if (wksq < psq && file_of(wksq) == file_of(psq))
256 result = RookValueEg - Value(square_distance(wksq, psq));
258 // If the weaker side's king is too far from the pawn and the rook,
260 else if ( square_distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
261 && square_distance(bksq, rsq) >= 3)
262 result = RookValueEg - Value(square_distance(wksq, psq));
264 // If the pawn is far advanced and supported by the defending king,
265 // the position is drawish
266 else if ( rank_of(bksq) <= RANK_3
267 && square_distance(bksq, psq) == 1
268 && rank_of(wksq) >= RANK_4
269 && square_distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
270 result = Value(80 - square_distance(wksq, psq) * 8);
274 - Value(square_distance(wksq, psq + DELTA_S) * 8)
275 + Value(square_distance(bksq, psq + DELTA_S) * 8)
276 + Value(square_distance(psq, queeningSq) * 8);
278 return strongSide == pos.side_to_move() ? result : -result;
282 /// KR vs KB. This is very simple, and always returns drawish scores. The
283 /// score is slightly bigger when the defending king is close to the edge.
285 Value Endgame<KRKB>::operator()(const Position& pos) const {
287 assert(verify_material(pos, strongSide, RookValueMg, 0));
288 assert(verify_material(pos, weakSide, BishopValueMg, 0));
290 Value result = Value(PushToEdges[pos.king_square(weakSide)]);
291 return strongSide == pos.side_to_move() ? result : -result;
295 /// KR vs KN. The attacking side has slightly better winning chances than
296 /// in KR vs KB, particularly if the king and the knight are far apart.
298 Value Endgame<KRKN>::operator()(const Position& pos) const {
300 assert(verify_material(pos, strongSide, RookValueMg, 0));
301 assert(verify_material(pos, weakSide, KnightValueMg, 0));
303 Square bksq = pos.king_square(weakSide);
304 Square bnsq = pos.list<KNIGHT>(weakSide)[0];
305 Value result = Value(PushToEdges[bksq] + PushAway[square_distance(bksq, bnsq)]);
306 return strongSide == pos.side_to_move() ? result : -result;
310 /// KQ vs KP. In general, a win for the stronger side, however, there are a few
311 /// important exceptions. Pawn on 7th rank, A,C,F or H file, with king next can
312 /// be a draw, so we scale down to distance between kings only.
314 Value Endgame<KQKP>::operator()(const Position& pos) const {
316 assert(verify_material(pos, strongSide, QueenValueMg, 0));
317 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
319 Square winnerKSq = pos.king_square(strongSide);
320 Square loserKSq = pos.king_square(weakSide);
321 Square pawnSq = pos.list<PAWN>(weakSide)[0];
323 Value result = Value(PushClose[square_distance(winnerKSq, loserKSq)]);
325 if ( relative_rank(weakSide, pawnSq) != RANK_7
326 || square_distance(loserKSq, pawnSq) != 1
327 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
328 result += QueenValueEg - PawnValueEg;
330 return strongSide == pos.side_to_move() ? result : -result;
334 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
335 /// king a bonus for having the kings close together, and for forcing the
336 /// defending king towards the edge. If we also take care to avoid null move
337 /// for the defending side in the search, this is usually sufficient to be
338 /// able to win KQ vs KR.
340 Value Endgame<KQKR>::operator()(const Position& pos) const {
342 assert(verify_material(pos, strongSide, QueenValueMg, 0));
343 assert(verify_material(pos, weakSide, RookValueMg, 0));
345 Square winnerKSq = pos.king_square(strongSide);
346 Square loserKSq = pos.king_square(weakSide);
348 Value result = QueenValueEg
350 + PushToEdges[loserKSq]
351 + PushClose[square_distance(winnerKSq, loserKSq)];
353 return strongSide == pos.side_to_move() ? result : -result;
357 /// KBB vs KN. This is almost always a win. We try to push enemy king to a corner
358 /// and away from his knight. For a reference of this difficult endgame see:
359 /// en.wikipedia.org/wiki/Chess_endgame#Effect_of_tablebases_on_endgame_theory
362 Value Endgame<KBBKN>::operator()(const Position& pos) const {
364 assert(verify_material(pos, strongSide, 2 * BishopValueMg, 0));
365 assert(verify_material(pos, weakSide, KnightValueMg, 0));
367 Square winnerKSq = pos.king_square(strongSide);
368 Square loserKSq = pos.king_square(weakSide);
369 Square knightSq = pos.list<KNIGHT>(weakSide)[0];
371 Value result = VALUE_KNOWN_WIN
372 + PushToCorners[loserKSq]
373 + PushClose[square_distance(winnerKSq, loserKSq)]
374 + PushAway[square_distance(loserKSq, knightSq)];
376 return strongSide == pos.side_to_move() ? result : -result;
380 /// Some cases of trivial draws
381 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
382 template<> Value Endgame<KmmKm>::operator()(const Position&) const { return VALUE_DRAW; }
385 /// K, bishop and one or more pawns vs K. It checks for draws with rook pawns and
386 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
387 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
390 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
392 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
393 assert(pos.count<PAWN>(strongSide) >= 1);
395 // No assertions about the material of weakSide, because we want draws to
396 // be detected even when the weaker side has some pawns.
398 Bitboard pawns = pos.pieces(strongSide, PAWN);
399 File pawnFile = file_of(pos.list<PAWN>(strongSide)[0]);
401 // All pawns are on a single rook file ?
402 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
403 && !(pawns & ~file_bb(pawnFile)))
405 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
406 Square queeningSq = relative_square(strongSide, pawnFile | RANK_8);
407 Square kingSq = pos.king_square(weakSide);
409 if ( opposite_colors(queeningSq, bishopSq)
410 && square_distance(queeningSq, kingSq) <= 1)
411 return SCALE_FACTOR_DRAW;
414 // All pawns on same B or G file? Then potential draw
415 if ( (pawnFile == FILE_B || pawnFile == FILE_G)
416 && !(pos.pieces(PAWN) & ~file_bb(pawnFile))
417 && pos.non_pawn_material(weakSide) == 0
418 && pos.count<PAWN>(weakSide) >= 1)
420 // Get weakSide pawn that is closest to home rank
421 Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
423 Square strongKingSq = pos.king_square(strongSide);
424 Square weakKingSq = pos.king_square(weakSide);
425 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
427 // Potential for a draw if our pawn is blocked on the 7th rank
428 // the bishop cannot attack it or they only have one pawn left
429 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
430 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
431 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
433 int strongKingDist = square_distance(weakPawnSq, strongKingSq);
434 int weakKingDist = square_distance(weakPawnSq, weakKingSq);
436 // Draw if the weak king is on it's back two ranks, within 2
437 // squares of the blocking pawn and the strong king is not
438 // closer. (I think this rule only fails in practically
439 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
440 // and positions where qsearch will immediately correct the
441 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
442 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
444 && weakKingDist <= strongKingDist)
445 return SCALE_FACTOR_DRAW;
449 return SCALE_FACTOR_NONE;
453 /// K and queen vs K, rook and one or more pawns. It tests for fortress draws with
454 /// a rook on the third rank defended by a pawn.
456 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
458 assert(verify_material(pos, strongSide, QueenValueMg, 0));
459 assert(pos.count<ROOK>(weakSide) == 1);
460 assert(pos.count<PAWN>(weakSide) >= 1);
462 Square kingSq = pos.king_square(weakSide);
463 Square rsq = pos.list<ROOK>(weakSide)[0];
465 if ( relative_rank(weakSide, kingSq) <= RANK_2
466 && relative_rank(weakSide, pos.king_square(strongSide)) >= RANK_4
467 && relative_rank(weakSide, rsq) == RANK_3
468 && ( pos.pieces(weakSide, PAWN)
469 & pos.attacks_from<KING>(kingSq)
470 & pos.attacks_from<PAWN>(rsq, strongSide)))
471 return SCALE_FACTOR_DRAW;
473 return SCALE_FACTOR_NONE;
477 /// K, rook and one pawn vs K and a rook. This function knows a handful of the
478 /// most important classes of drawn positions, but is far from perfect. It would
479 /// probably be a good idea to add more knowledge in the future.
481 /// It would also be nice to rewrite the actual code for this function,
482 /// which is mostly copied from Glaurung 1.x, and not very pretty.
484 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
486 assert(verify_material(pos, strongSide, RookValueMg, 1));
487 assert(verify_material(pos, weakSide, RookValueMg, 0));
489 Square wksq = pos.king_square(strongSide);
490 Square bksq = pos.king_square(weakSide);
491 Square wrsq = pos.list<ROOK>(strongSide)[0];
492 Square wpsq = pos.list<PAWN>(strongSide)[0];
493 Square brsq = pos.list<ROOK>(weakSide)[0];
495 // Orient the board in such a way that the stronger side is white, and the
496 // pawn is on the left half of the board.
497 if (strongSide == BLACK)
506 if (file_of(wpsq) > FILE_D)
515 File f = file_of(wpsq);
516 Rank r = rank_of(wpsq);
517 Square queeningSq = f | RANK_8;
518 int tempo = (pos.side_to_move() == strongSide);
520 // If the pawn is not too far advanced and the defending king defends the
521 // queening square, use the third-rank defence.
523 && square_distance(bksq, queeningSq) <= 1
525 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
526 return SCALE_FACTOR_DRAW;
528 // The defending side saves a draw by checking from behind in case the pawn
529 // has advanced to the 6th rank with the king behind.
531 && square_distance(bksq, queeningSq) <= 1
532 && rank_of(wksq) + tempo <= RANK_6
533 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
534 return SCALE_FACTOR_DRAW;
537 && bksq == queeningSq
538 && rank_of(brsq) == RANK_1
539 && (!tempo || square_distance(wksq, wpsq) >= 2))
540 return SCALE_FACTOR_DRAW;
542 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
543 // and the black rook is behind the pawn.
546 && (bksq == SQ_H7 || bksq == SQ_G7)
547 && file_of(brsq) == FILE_A
548 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
549 return SCALE_FACTOR_DRAW;
551 // If the defending king blocks the pawn and the attacking king is too far
552 // away, it's a draw.
554 && bksq == wpsq + DELTA_N
555 && square_distance(wksq, wpsq) - tempo >= 2
556 && square_distance(wksq, brsq) - tempo >= 2)
557 return SCALE_FACTOR_DRAW;
559 // Pawn on the 7th rank supported by the rook from behind usually wins if the
560 // attacking king is closer to the queening square than the defending king,
561 // and the defending king cannot gain tempi by threatening the attacking rook.
564 && file_of(wrsq) == f
565 && wrsq != queeningSq
566 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
567 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
568 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
570 // Similar to the above, but with the pawn further back
572 && file_of(wrsq) == f
574 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
575 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
576 && ( square_distance(bksq, wrsq) + tempo >= 3
577 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
578 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
579 return ScaleFactor( SCALE_FACTOR_MAX
580 - 8 * square_distance(wpsq, queeningSq)
581 - 2 * square_distance(wksq, queeningSq));
583 // If the pawn is not far advanced, and the defending king is somewhere in
584 // the pawn's path, it's probably a draw.
585 if (r <= RANK_4 && bksq > wpsq)
587 if (file_of(bksq) == file_of(wpsq))
588 return ScaleFactor(10);
589 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
590 && square_distance(wksq, bksq) > 2)
591 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
593 return SCALE_FACTOR_NONE;
597 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
599 assert(verify_material(pos, strongSide, RookValueMg, 1));
600 assert(verify_material(pos, weakSide, BishopValueMg, 0));
602 // Test for a rook pawn
603 if (pos.pieces(PAWN) & (FileABB | FileHBB))
605 Square ksq = pos.king_square(weakSide);
606 Square bsq = pos.list<BISHOP>(weakSide)[0];
607 Square psq = pos.list<PAWN>(strongSide)[0];
608 Rank rk = relative_rank(strongSide, psq);
609 Square push = pawn_push(strongSide);
611 // If the pawn is on the 5th rank and the pawn (currently) is on
612 // the same color square as the bishop then there is a chance of
613 // a fortress. Depending on the king position give a moderate
614 // reduction or a stronger one if the defending king is near the
615 // corner but not trapped there.
616 if (rk == RANK_5 && !opposite_colors(bsq, psq))
618 int d = square_distance(psq + 3 * push, ksq);
620 if (d <= 2 && !(d == 0 && ksq == pos.king_square(strongSide) + 2 * push))
621 return ScaleFactor(24);
623 return ScaleFactor(48);
626 // When the pawn has moved to the 6th rank we can be fairly sure
627 // it's drawn if the bishop attacks the square in front of the
628 // pawn from a reasonable distance and the defending king is near
631 && square_distance(psq + 2 * push, ksq) <= 1
632 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
633 && file_distance(bsq, psq) >= 2)
634 return ScaleFactor(8);
637 return SCALE_FACTOR_NONE;
640 /// K, rook and two pawns vs K, rook and one pawn. There is only a single
641 /// pattern: If the stronger side has no passed pawns and the defending king
642 /// is actively placed, the position is drawish.
644 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
646 assert(verify_material(pos, strongSide, RookValueMg, 2));
647 assert(verify_material(pos, weakSide, RookValueMg, 1));
649 Square wpsq1 = pos.list<PAWN>(strongSide)[0];
650 Square wpsq2 = pos.list<PAWN>(strongSide)[1];
651 Square bksq = pos.king_square(weakSide);
653 // Does the stronger side have a passed pawn?
654 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
655 return SCALE_FACTOR_NONE;
657 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
659 if ( file_distance(bksq, wpsq1) <= 1
660 && file_distance(bksq, wpsq2) <= 1
661 && relative_rank(strongSide, bksq) > r)
664 case RANK_2: return ScaleFactor(10);
665 case RANK_3: return ScaleFactor(10);
666 case RANK_4: return ScaleFactor(15);
667 case RANK_5: return ScaleFactor(20);
668 case RANK_6: return ScaleFactor(40);
669 default: assert(false);
672 return SCALE_FACTOR_NONE;
676 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
677 /// are on the same rook file and are blocked by the defending king, it's a draw.
679 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
681 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
682 assert(pos.count<PAWN>(strongSide) >= 2);
683 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
685 Square ksq = pos.king_square(weakSide);
686 Bitboard pawns = pos.pieces(strongSide, PAWN);
687 Square psq = pos.list<PAWN>(strongSide)[0];
689 // If all pawns are ahead of the king, all pawns are on a single
690 // rook file and the king is within one file of the pawns then draw.
691 if ( !(pawns & ~in_front_bb(weakSide, rank_of(ksq)))
692 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
693 && file_distance(ksq, psq) <= 1)
694 return SCALE_FACTOR_DRAW;
696 return SCALE_FACTOR_NONE;
700 /// K, bishop and a pawn vs K and a bishop. There are two rules: If the defending
701 /// king is somewhere along the path of the pawn, and the square of the king is
702 /// not of the same color as the stronger side's bishop, it's a draw. If the two
703 /// bishops have opposite color, it's almost always a draw.
705 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
707 assert(verify_material(pos, strongSide, BishopValueMg, 1));
708 assert(verify_material(pos, weakSide, BishopValueMg, 0));
710 Square pawnSq = pos.list<PAWN>(strongSide)[0];
711 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
712 Square weakBishopSq = pos.list<BISHOP>(weakSide)[0];
713 Square weakKingSq = pos.king_square(weakSide);
715 // Case 1: Defending king blocks the pawn, and cannot be driven away
716 if ( file_of(weakKingSq) == file_of(pawnSq)
717 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
718 && ( opposite_colors(weakKingSq, strongBishopSq)
719 || relative_rank(strongSide, weakKingSq) <= RANK_6))
720 return SCALE_FACTOR_DRAW;
722 // Case 2: Opposite colored bishops
723 if (opposite_colors(strongBishopSq, weakBishopSq))
725 // We assume that the position is drawn in the following three situations:
727 // a. The pawn is on rank 5 or further back.
728 // b. The defending king is somewhere in the pawn's path.
729 // c. The defending bishop attacks some square along the pawn's path,
730 // and is at least three squares away from the pawn.
732 // These rules are probably not perfect, but in practice they work
735 if (relative_rank(strongSide, pawnSq) <= RANK_5)
736 return SCALE_FACTOR_DRAW;
739 Bitboard path = forward_bb(strongSide, pawnSq);
741 if (path & pos.pieces(weakSide, KING))
742 return SCALE_FACTOR_DRAW;
744 if ( (pos.attacks_from<BISHOP>(weakBishopSq) & path)
745 && square_distance(weakBishopSq, pawnSq) >= 3)
746 return SCALE_FACTOR_DRAW;
749 return SCALE_FACTOR_NONE;
753 /// K, bishop and two pawns vs K and bishop. It detects a few basic draws with
754 /// opposite-colored bishops.
756 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
758 assert(verify_material(pos, strongSide, BishopValueMg, 2));
759 assert(verify_material(pos, weakSide, BishopValueMg, 0));
761 Square wbsq = pos.list<BISHOP>(strongSide)[0];
762 Square bbsq = pos.list<BISHOP>(weakSide)[0];
764 if (!opposite_colors(wbsq, bbsq))
765 return SCALE_FACTOR_NONE;
767 Square ksq = pos.king_square(weakSide);
768 Square psq1 = pos.list<PAWN>(strongSide)[0];
769 Square psq2 = pos.list<PAWN>(strongSide)[1];
770 Rank r1 = rank_of(psq1);
771 Rank r2 = rank_of(psq2);
772 Square blockSq1, blockSq2;
774 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
776 blockSq1 = psq1 + pawn_push(strongSide);
777 blockSq2 = file_of(psq2) | rank_of(psq1);
781 blockSq1 = psq2 + pawn_push(strongSide);
782 blockSq2 = file_of(psq1) | rank_of(psq2);
785 switch (file_distance(psq1, psq2))
788 // Both pawns are on the same file. Easy draw if defender firmly controls
789 // some square in the frontmost pawn's path.
790 if ( file_of(ksq) == file_of(blockSq1)
791 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
792 && opposite_colors(ksq, wbsq))
793 return SCALE_FACTOR_DRAW;
795 return SCALE_FACTOR_NONE;
798 // Pawns on adjacent files. Draw if defender firmly controls the square
799 // in front of the frontmost pawn's path, and the square diagonally behind
800 // this square on the file of the other pawn.
802 && opposite_colors(ksq, wbsq)
803 && ( bbsq == blockSq2
804 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
805 || abs(r1 - r2) >= 2))
806 return SCALE_FACTOR_DRAW;
808 else if ( ksq == blockSq2
809 && opposite_colors(ksq, wbsq)
810 && ( bbsq == blockSq1
811 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
812 return SCALE_FACTOR_DRAW;
814 return SCALE_FACTOR_NONE;
817 // The pawns are not on the same file or adjacent files. No scaling.
818 return SCALE_FACTOR_NONE;
823 /// K, bisop and a pawn vs K and knight. There is a single rule: If the defending
824 /// king is somewhere along the path of the pawn, and the square of the king is
825 /// not of the same color as the stronger side's bishop, it's a draw.
827 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
829 assert(verify_material(pos, strongSide, BishopValueMg, 1));
830 assert(verify_material(pos, weakSide, KnightValueMg, 0));
832 Square pawnSq = pos.list<PAWN>(strongSide)[0];
833 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
834 Square weakKingSq = pos.king_square(weakSide);
836 if ( file_of(weakKingSq) == file_of(pawnSq)
837 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
838 && ( opposite_colors(weakKingSq, strongBishopSq)
839 || relative_rank(strongSide, weakKingSq) <= RANK_6))
840 return SCALE_FACTOR_DRAW;
842 return SCALE_FACTOR_NONE;
846 /// K, knight and a pawn vs K. There is a single rule: If the pawn is a rook pawn
847 /// on the 7th rank and the defending king prevents the pawn from advancing, the
848 /// position is drawn.
850 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
852 assert(verify_material(pos, strongSide, KnightValueMg, 1));
853 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
855 Square pawnSq = pos.list<PAWN>(strongSide)[0];
856 Square weakKingSq = pos.king_square(weakSide);
858 if ( pawnSq == relative_square(strongSide, SQ_A7)
859 && square_distance(weakKingSq, relative_square(strongSide, SQ_A8)) <= 1)
860 return SCALE_FACTOR_DRAW;
862 if ( pawnSq == relative_square(strongSide, SQ_H7)
863 && square_distance(weakKingSq, relative_square(strongSide, SQ_H8)) <= 1)
864 return SCALE_FACTOR_DRAW;
866 return SCALE_FACTOR_NONE;
870 /// K, knight and a pawn vs K and bishop. If knight can block bishop from taking
871 /// pawn, it's a win. Otherwise, drawn.
873 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
875 Square pawnSq = pos.list<PAWN>(strongSide)[0];
876 Square bishopSq = pos.list<BISHOP>(weakSide)[0];
877 Square weakKingSq = pos.king_square(weakSide);
879 // King needs to get close to promoting pawn to prevent knight from blocking.
880 // Rules for this are very tricky, so just approximate.
881 if (forward_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
882 return ScaleFactor(square_distance(weakKingSq, pawnSq));
884 return SCALE_FACTOR_NONE;
888 /// K and a pawn vs K and a pawn. This is done by removing the weakest side's
889 /// pawn and probing the KP vs K bitbase: If the weakest side has a draw without
890 /// the pawn, she probably has at least a draw with the pawn as well. The exception
891 /// is when the stronger side's pawn is far advanced and not on a rook file; in
892 /// this case it is often possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
894 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
896 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
897 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
899 Square wksq = pos.king_square(strongSide);
900 Square bksq = pos.king_square(weakSide);
901 Square psq = pos.list<PAWN>(strongSide)[0];
902 Color us = pos.side_to_move();
904 if (strongSide == BLACK)
912 if (file_of(psq) >= FILE_E)
919 // If the pawn has advanced to the fifth rank or further, and is not a
920 // rook pawn, it's too dangerous to assume that it's at least a draw.
921 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
922 return SCALE_FACTOR_NONE;
924 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
925 // it's probably at least a draw even with the pawn.
926 return Bitbases::probe_kpk(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;