2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
4 Copyright (C) 2008-2012 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/>.
28 extern uint32_t probe_kpk_bitbase(Square wksq, Square wpsq, Square bksq, Color stm);
32 // Table used to drive the defending king towards the edge of the board
33 // in KX vs K and KQ vs KR endgames.
34 const int MateTable[64] = {
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 defending king towards a corner square of the
46 // right color in KBN vs K endgames.
47 const int KBNKMateTable[64] = {
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 // The attacking side is given a descending bonus based on distance between
59 // the two kings in basic endgames.
60 const int DistanceBonus[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
62 // Get the material key of a Position out of the given endgame key code
63 // like "KBPKN". The trick here is to first forge an ad-hoc fen string
64 // and then let a Position object to do the work for us. Note that the
65 // fen string could correspond to an illegal position.
66 Key key(const string& code, Color c) {
68 assert(code.length() > 0 && code.length() < 8);
69 assert(code[0] == 'K');
71 string sides[] = { code.substr(code.find('K', 1)), // Weaker
72 code.substr(0, code.find('K', 1)) }; // Stronger
74 transform(sides[c].begin(), sides[c].end(), sides[c].begin(), tolower);
76 string fen = sides[0] + char('0' + int(8 - code.length()))
77 + sides[1] + "/8/8/8/8/8/8/8 w - - 0 10";
79 return Position(fen, false, 0).material_key();
83 void delete_endgame(const typename M::value_type& p) { delete p.second; }
85 // Fast stalemate detection with lone king
86 bool is_kxk_stalemate(const Position &pos, const Color c) {
87 if ( pos.side_to_move() == c &&
89 const Square from = pos.king_square(c);
90 Bitboard b = pos.attacks_from<KING>(from);
92 // Assume there are no pinned pieces, as it is a lone king
93 if (pos.pl_move_is_legal(make_move(from, pop_1st_bit(&b)), 0))
103 /// Endgames members definitions
105 Endgames::Endgames() {
120 add<KBPPKB>("KBPPKB");
121 add<KRPPKRP>("KRPPKRP");
124 Endgames::~Endgames() {
126 for_each(m1.begin(), m1.end(), delete_endgame<M1>);
127 for_each(m2.begin(), m2.end(), delete_endgame<M2>);
130 template<EndgameType E>
131 void Endgames::add(const string& code) {
133 typedef typename eg_family<E>::type T;
135 map((T*)0)[key(code, WHITE)] = new Endgame<E>(WHITE);
136 map((T*)0)[key(code, BLACK)] = new Endgame<E>(BLACK);
140 /// Mate with KX vs K. This function is used to evaluate positions with
141 /// King and plenty of material vs a lone king. It simply gives the
142 /// attacking side a bonus for driving the defending king towards the edge
143 /// of the board, and for keeping the distance between the two kings small.
145 Value Endgame<KXK>::operator()(const Position& pos) const {
147 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
148 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
150 if (is_kxk_stalemate(pos, weakerSide)) {
154 Square winnerKSq = pos.king_square(strongerSide);
155 Square loserKSq = pos.king_square(weakerSide);
157 Value result = pos.non_pawn_material(strongerSide)
158 + pos.piece_count(strongerSide, PAWN) * PawnValueEndgame
159 + MateTable[loserKSq]
160 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
162 if ( pos.piece_count(strongerSide, QUEEN)
163 || pos.piece_count(strongerSide, ROOK)
164 || pos.both_color_bishops(strongerSide)) {
165 result += VALUE_KNOWN_WIN;
168 return strongerSide == pos.side_to_move() ? result : -result;
172 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
173 /// defending king towards a corner square of the right color.
175 Value Endgame<KBNK>::operator()(const Position& pos) const {
177 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
178 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
179 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame + BishopValueMidgame);
180 assert(pos.piece_count(strongerSide, BISHOP) == 1);
181 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
182 assert(pos.piece_count(strongerSide, PAWN) == 0);
184 Square winnerKSq = pos.king_square(strongerSide);
185 Square loserKSq = pos.king_square(weakerSide);
186 Square bishopSquare = pos.piece_list(strongerSide, BISHOP)[0];
188 // kbnk_mate_table() tries to drive toward corners A1 or H8,
189 // if we have a bishop that cannot reach the above squares we
190 // mirror the kings so to drive enemy toward corners A8 or H1.
191 if (opposite_colors(bishopSquare, SQ_A1))
193 winnerKSq = mirror(winnerKSq);
194 loserKSq = mirror(loserKSq);
197 Value result = VALUE_KNOWN_WIN
198 + DistanceBonus[square_distance(winnerKSq, loserKSq)]
199 + KBNKMateTable[loserKSq];
201 return strongerSide == pos.side_to_move() ? result : -result;
205 /// KP vs K. This endgame is evaluated with the help of a bitbase.
207 Value Endgame<KPK>::operator()(const Position& pos) const {
209 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
210 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
211 assert(pos.piece_count(strongerSide, PAWN) == 1);
212 assert(pos.piece_count(weakerSide, PAWN) == 0);
214 Square wksq, bksq, wpsq;
217 if (strongerSide == WHITE)
219 wksq = pos.king_square(WHITE);
220 bksq = pos.king_square(BLACK);
221 wpsq = pos.piece_list(WHITE, PAWN)[0];
222 stm = pos.side_to_move();
226 wksq = ~pos.king_square(BLACK);
227 bksq = ~pos.king_square(WHITE);
228 wpsq = ~pos.piece_list(BLACK, PAWN)[0];
229 stm = ~pos.side_to_move();
232 if (file_of(wpsq) >= FILE_E)
239 if (!probe_kpk_bitbase(wksq, wpsq, bksq, stm))
242 Value result = VALUE_KNOWN_WIN
244 + Value(rank_of(wpsq));
246 return strongerSide == pos.side_to_move() ? result : -result;
250 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
251 /// a bitbase. The function below returns drawish scores when the pawn is
252 /// far advanced with support of the king, while the attacking king is far
255 Value Endgame<KRKP>::operator()(const Position& pos) const {
257 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
258 assert(pos.piece_count(strongerSide, PAWN) == 0);
259 assert(pos.non_pawn_material(weakerSide) == 0);
260 assert(pos.piece_count(weakerSide, PAWN) == 1);
262 Square wksq, wrsq, bksq, bpsq;
263 int tempo = (pos.side_to_move() == strongerSide);
265 wksq = pos.king_square(strongerSide);
266 wrsq = pos.piece_list(strongerSide, ROOK)[0];
267 bksq = pos.king_square(weakerSide);
268 bpsq = pos.piece_list(weakerSide, PAWN)[0];
270 if (strongerSide == BLACK)
278 Square queeningSq = make_square(file_of(bpsq), RANK_1);
281 // If the stronger side's king is in front of the pawn, it's a win
282 if (wksq < bpsq && file_of(wksq) == file_of(bpsq))
283 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
285 // If the weaker side's king is too far from the pawn and the rook,
287 else if ( square_distance(bksq, bpsq) - (tempo ^ 1) >= 3
288 && square_distance(bksq, wrsq) >= 3)
289 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
291 // If the pawn is far advanced and supported by the defending king,
292 // the position is drawish
293 else if ( rank_of(bksq) <= RANK_3
294 && square_distance(bksq, bpsq) == 1
295 && rank_of(wksq) >= RANK_4
296 && square_distance(wksq, bpsq) - tempo > 2)
297 result = Value(80 - square_distance(wksq, bpsq) * 8);
301 - Value(square_distance(wksq, bpsq + DELTA_S) * 8)
302 + Value(square_distance(bksq, bpsq + DELTA_S) * 8)
303 + Value(square_distance(bpsq, queeningSq) * 8);
305 return strongerSide == pos.side_to_move() ? result : -result;
309 /// KR vs KB. This is very simple, and always returns drawish scores. The
310 /// score is slightly bigger when the defending king is close to the edge.
312 Value Endgame<KRKB>::operator()(const Position& pos) const {
314 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
315 assert(pos.piece_count(strongerSide, PAWN) == 0);
316 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
317 assert(pos.piece_count(weakerSide, PAWN) == 0);
318 assert(pos.piece_count(weakerSide, BISHOP) == 1);
320 Value result = Value(MateTable[pos.king_square(weakerSide)]);
321 return strongerSide == pos.side_to_move() ? result : -result;
325 /// KR vs KN. The attacking side has slightly better winning chances than
326 /// in KR vs KB, particularly if the king and the knight are far apart.
328 Value Endgame<KRKN>::operator()(const Position& pos) const {
330 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
331 assert(pos.piece_count(strongerSide, PAWN) == 0);
332 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
333 assert(pos.piece_count(weakerSide, PAWN) == 0);
334 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
336 const int penalty[8] = { 0, 10, 14, 20, 30, 42, 58, 80 };
338 Square bksq = pos.king_square(weakerSide);
339 Square bnsq = pos.piece_list(weakerSide, KNIGHT)[0];
340 Value result = Value(MateTable[bksq] + penalty[square_distance(bksq, bnsq)]);
341 return strongerSide == pos.side_to_move() ? result : -result;
345 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
346 /// king a bonus for having the kings close together, and for forcing the
347 /// defending king towards the edge. If we also take care to avoid null move
348 /// for the defending side in the search, this is usually sufficient to be
349 /// able to win KQ vs KR.
351 Value Endgame<KQKR>::operator()(const Position& pos) const {
353 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
354 assert(pos.piece_count(strongerSide, PAWN) == 0);
355 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
356 assert(pos.piece_count(weakerSide, PAWN) == 0);
358 Square winnerKSq = pos.king_square(strongerSide);
359 Square loserKSq = pos.king_square(weakerSide);
361 Value result = QueenValueEndgame
363 + MateTable[loserKSq]
364 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
366 return strongerSide == pos.side_to_move() ? result : -result;
370 Value Endgame<KBBKN>::operator()(const Position& pos) const {
372 assert(pos.piece_count(strongerSide, BISHOP) == 2);
373 assert(pos.non_pawn_material(strongerSide) == 2*BishopValueMidgame);
374 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
375 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
376 assert(!pos.pieces(PAWN));
378 Value result = BishopValueEndgame;
379 Square wksq = pos.king_square(strongerSide);
380 Square bksq = pos.king_square(weakerSide);
381 Square nsq = pos.piece_list(weakerSide, KNIGHT)[0];
383 // Bonus for attacking king close to defending king
384 result += Value(DistanceBonus[square_distance(wksq, bksq)]);
386 // Bonus for driving the defending king and knight apart
387 result += Value(square_distance(bksq, nsq) * 32);
389 // Bonus for restricting the knight's mobility
390 result += Value((8 - popcount<Max15>(pos.attacks_from<KNIGHT>(nsq))) * 8);
392 return strongerSide == pos.side_to_move() ? result : -result;
396 /// K and two minors vs K and one or two minors or K and two knights against
397 /// king alone are always draw.
399 Value Endgame<KmmKm>::operator()(const Position&) const {
404 Value Endgame<KNNK>::operator()(const Position&) const {
408 /// K, bishop and one or more pawns vs K. It checks for draws with rook pawns and
409 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
410 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
413 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
415 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
416 assert(pos.piece_count(strongerSide, BISHOP) == 1);
417 assert(pos.piece_count(strongerSide, PAWN) >= 1);
419 // No assertions about the material of weakerSide, because we want draws to
420 // be detected even when the weaker side has some pawns.
422 Bitboard pawns = pos.pieces(PAWN, strongerSide);
423 File pawnFile = file_of(pos.piece_list(strongerSide, PAWN)[0]);
425 // All pawns are on a single rook file ?
426 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
427 && !(pawns & ~file_bb(pawnFile)))
429 Square bishopSq = pos.piece_list(strongerSide, BISHOP)[0];
430 Square queeningSq = relative_square(strongerSide, make_square(pawnFile, RANK_8));
431 Square kingSq = pos.king_square(weakerSide);
433 if ( opposite_colors(queeningSq, bishopSq)
434 && abs(file_of(kingSq) - pawnFile) <= 1)
436 // The bishop has the wrong color, and the defending king is on the
437 // file of the pawn(s) or the adjacent file. Find the rank of the
440 if (strongerSide == WHITE)
442 for (rank = RANK_7; !(rank_bb(rank) & pawns); rank--) {}
443 assert(rank >= RANK_2 && rank <= RANK_7);
447 for (rank = RANK_2; !(rank_bb(rank) & pawns); rank++) {}
448 rank = Rank(rank ^ 7); // HACK to get the relative rank
449 assert(rank >= RANK_2 && rank <= RANK_7);
451 // If the defending king has distance 1 to the promotion square or
452 // is placed somewhere in front of the pawn, it's a draw.
453 if ( square_distance(kingSq, queeningSq) <= 1
454 || relative_rank(strongerSide, kingSq) >= rank)
455 return SCALE_FACTOR_DRAW;
458 return SCALE_FACTOR_NONE;
462 /// K and queen vs K, rook and one or more pawns. It tests for fortress draws with
463 /// a rook on the third rank defended by a pawn.
465 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
467 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
468 assert(pos.piece_count(strongerSide, QUEEN) == 1);
469 assert(pos.piece_count(strongerSide, PAWN) == 0);
470 assert(pos.piece_count(weakerSide, ROOK) == 1);
471 assert(pos.piece_count(weakerSide, PAWN) >= 1);
473 Square kingSq = pos.king_square(weakerSide);
474 if ( relative_rank(weakerSide, kingSq) <= RANK_2
475 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
476 && (pos.pieces(ROOK, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_3)))
477 && (pos.pieces(PAWN, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_2)))
478 && (pos.attacks_from<KING>(kingSq) & pos.pieces(PAWN, weakerSide)))
480 Square rsq = pos.piece_list(weakerSide, ROOK)[0];
481 if (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(PAWN, weakerSide))
482 return SCALE_FACTOR_DRAW;
484 return SCALE_FACTOR_NONE;
488 /// K, rook and one pawn vs K and a rook. This function knows a handful of the
489 /// most important classes of drawn positions, but is far from perfect. It would
490 /// probably be a good idea to add more knowledge in the future.
492 /// It would also be nice to rewrite the actual code for this function,
493 /// which is mostly copied from Glaurung 1.x, and not very pretty.
495 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
497 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
498 assert(pos.piece_count(strongerSide, PAWN) == 1);
499 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
500 assert(pos.piece_count(weakerSide, PAWN) == 0);
502 Square wksq = pos.king_square(strongerSide);
503 Square wrsq = pos.piece_list(strongerSide, ROOK)[0];
504 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
505 Square bksq = pos.king_square(weakerSide);
506 Square brsq = pos.piece_list(weakerSide, ROOK)[0];
508 // Orient the board in such a way that the stronger side is white, and the
509 // pawn is on the left half of the board.
510 if (strongerSide == BLACK)
518 if (file_of(wpsq) > FILE_D)
527 File f = file_of(wpsq);
528 Rank r = rank_of(wpsq);
529 Square queeningSq = make_square(f, RANK_8);
530 int tempo = (pos.side_to_move() == strongerSide);
532 // If the pawn is not too far advanced and the defending king defends the
533 // queening square, use the third-rank defence.
535 && square_distance(bksq, queeningSq) <= 1
537 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
538 return SCALE_FACTOR_DRAW;
540 // The defending side saves a draw by checking from behind in case the pawn
541 // has advanced to the 6th rank with the king behind.
543 && square_distance(bksq, queeningSq) <= 1
544 && rank_of(wksq) + tempo <= RANK_6
545 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
546 return SCALE_FACTOR_DRAW;
549 && bksq == queeningSq
550 && rank_of(brsq) == RANK_1
551 && (!tempo || square_distance(wksq, wpsq) >= 2))
552 return SCALE_FACTOR_DRAW;
554 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
555 // and the black rook is behind the pawn.
558 && (bksq == SQ_H7 || bksq == SQ_G7)
559 && file_of(brsq) == FILE_A
560 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
561 return SCALE_FACTOR_DRAW;
563 // If the defending king blocks the pawn and the attacking king is too far
564 // away, it's a draw.
566 && bksq == wpsq + DELTA_N
567 && square_distance(wksq, wpsq) - tempo >= 2
568 && square_distance(wksq, brsq) - tempo >= 2)
569 return SCALE_FACTOR_DRAW;
571 // Pawn on the 7th rank supported by the rook from behind usually wins if the
572 // attacking king is closer to the queening square than the defending king,
573 // and the defending king cannot gain tempi by threatening the attacking rook.
576 && file_of(wrsq) == f
577 && wrsq != queeningSq
578 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
579 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
580 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
582 // Similar to the above, but with the pawn further back
584 && file_of(wrsq) == f
586 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
587 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
588 && ( square_distance(bksq, wrsq) + tempo >= 3
589 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
590 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
591 return ScaleFactor( SCALE_FACTOR_MAX
592 - 8 * square_distance(wpsq, queeningSq)
593 - 2 * square_distance(wksq, queeningSq));
595 // If the pawn is not far advanced, and the defending king is somewhere in
596 // the pawn's path, it's probably a draw.
597 if (r <= RANK_4 && bksq > wpsq)
599 if (file_of(bksq) == file_of(wpsq))
600 return ScaleFactor(10);
601 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
602 && square_distance(wksq, bksq) > 2)
603 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
605 return SCALE_FACTOR_NONE;
609 /// K, rook and two pawns vs K, rook and one pawn. There is only a single
610 /// pattern: If the stronger side has no passed pawns and the defending king
611 /// is actively placed, the position is drawish.
613 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
615 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
616 assert(pos.piece_count(strongerSide, PAWN) == 2);
617 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
618 assert(pos.piece_count(weakerSide, PAWN) == 1);
620 Square wpsq1 = pos.piece_list(strongerSide, PAWN)[0];
621 Square wpsq2 = pos.piece_list(strongerSide, PAWN)[1];
622 Square bksq = pos.king_square(weakerSide);
624 // Does the stronger side have a passed pawn?
625 if ( pos.pawn_is_passed(strongerSide, wpsq1)
626 || pos.pawn_is_passed(strongerSide, wpsq2))
627 return SCALE_FACTOR_NONE;
629 Rank r = std::max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
631 if ( file_distance(bksq, wpsq1) <= 1
632 && file_distance(bksq, wpsq2) <= 1
633 && relative_rank(strongerSide, bksq) > r)
636 case RANK_2: return ScaleFactor(10);
637 case RANK_3: return ScaleFactor(10);
638 case RANK_4: return ScaleFactor(15);
639 case RANK_5: return ScaleFactor(20);
640 case RANK_6: return ScaleFactor(40);
641 default: assert(false);
644 return SCALE_FACTOR_NONE;
648 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
649 /// are on the same rook file and are blocked by the defending king, it's a draw.
651 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
653 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
654 assert(pos.piece_count(strongerSide, PAWN) >= 2);
655 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
656 assert(pos.piece_count(weakerSide, PAWN) == 0);
658 Square ksq = pos.king_square(weakerSide);
659 Bitboard pawns = pos.pieces(PAWN, strongerSide);
661 // Are all pawns on the 'a' file?
662 if (!(pawns & ~FileABB))
664 // Does the defending king block the pawns?
665 if ( square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
666 || ( file_of(ksq) == FILE_A
667 && !in_front_bb(strongerSide, ksq) & pawns))
668 return SCALE_FACTOR_DRAW;
670 // Are all pawns on the 'h' file?
671 else if (!(pawns & ~FileHBB))
673 // Does the defending king block the pawns?
674 if ( square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
675 || ( file_of(ksq) == FILE_H
676 && !in_front_bb(strongerSide, ksq) & pawns))
677 return SCALE_FACTOR_DRAW;
679 return SCALE_FACTOR_NONE;
683 /// K, bishop and a pawn vs K and a bishop. There are two rules: If the defending
684 /// king is somewhere along the path of the pawn, and the square of the king is
685 /// not of the same color as the stronger side's bishop, it's a draw. If the two
686 /// bishops have opposite color, it's almost always a draw.
688 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
690 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
691 assert(pos.piece_count(strongerSide, BISHOP) == 1);
692 assert(pos.piece_count(strongerSide, PAWN) == 1);
693 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
694 assert(pos.piece_count(weakerSide, BISHOP) == 1);
695 assert(pos.piece_count(weakerSide, PAWN) == 0);
697 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
698 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
699 Square weakerBishopSq = pos.piece_list(weakerSide, BISHOP)[0];
700 Square weakerKingSq = pos.king_square(weakerSide);
702 // Case 1: Defending king blocks the pawn, and cannot be driven away
703 if ( file_of(weakerKingSq) == file_of(pawnSq)
704 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
705 && ( opposite_colors(weakerKingSq, strongerBishopSq)
706 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
707 return SCALE_FACTOR_DRAW;
709 // Case 2: Opposite colored bishops
710 if (opposite_colors(strongerBishopSq, weakerBishopSq))
712 // We assume that the position is drawn in the following three situations:
714 // a. The pawn is on rank 5 or further back.
715 // b. The defending king is somewhere in the pawn's path.
716 // c. The defending bishop attacks some square along the pawn's path,
717 // and is at least three squares away from the pawn.
719 // These rules are probably not perfect, but in practice they work
722 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
723 return SCALE_FACTOR_DRAW;
726 Bitboard path = squares_in_front_of(strongerSide, pawnSq);
728 if (path & pos.pieces(KING, weakerSide))
729 return SCALE_FACTOR_DRAW;
731 if ( (pos.attacks_from<BISHOP>(weakerBishopSq) & path)
732 && square_distance(weakerBishopSq, pawnSq) >= 3)
733 return SCALE_FACTOR_DRAW;
736 return SCALE_FACTOR_NONE;
740 /// K, bishop and two pawns vs K and bishop. It detects a few basic draws with
741 /// opposite-colored bishops.
743 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
745 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
746 assert(pos.piece_count(strongerSide, BISHOP) == 1);
747 assert(pos.piece_count(strongerSide, PAWN) == 2);
748 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
749 assert(pos.piece_count(weakerSide, BISHOP) == 1);
750 assert(pos.piece_count(weakerSide, PAWN) == 0);
752 Square wbsq = pos.piece_list(strongerSide, BISHOP)[0];
753 Square bbsq = pos.piece_list(weakerSide, BISHOP)[0];
755 if (!opposite_colors(wbsq, bbsq))
756 return SCALE_FACTOR_NONE;
758 Square ksq = pos.king_square(weakerSide);
759 Square psq1 = pos.piece_list(strongerSide, PAWN)[0];
760 Square psq2 = pos.piece_list(strongerSide, PAWN)[1];
761 Rank r1 = rank_of(psq1);
762 Rank r2 = rank_of(psq2);
763 Square blockSq1, blockSq2;
765 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
767 blockSq1 = psq1 + pawn_push(strongerSide);
768 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
772 blockSq1 = psq2 + pawn_push(strongerSide);
773 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
776 switch (file_distance(psq1, psq2))
779 // Both pawns are on the same file. Easy draw if defender firmly controls
780 // some square in the frontmost pawn's path.
781 if ( file_of(ksq) == file_of(blockSq1)
782 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
783 && opposite_colors(ksq, wbsq))
784 return SCALE_FACTOR_DRAW;
786 return SCALE_FACTOR_NONE;
789 // Pawns on adjacent files. Draw if defender firmly controls the square
790 // in front of the frontmost pawn's path, and the square diagonally behind
791 // this square on the file of the other pawn.
793 && opposite_colors(ksq, wbsq)
794 && ( bbsq == blockSq2
795 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(BISHOP, weakerSide))
796 || abs(r1 - r2) >= 2))
797 return SCALE_FACTOR_DRAW;
799 else if ( ksq == blockSq2
800 && opposite_colors(ksq, wbsq)
801 && ( bbsq == blockSq1
802 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(BISHOP, weakerSide))))
803 return SCALE_FACTOR_DRAW;
805 return SCALE_FACTOR_NONE;
808 // The pawns are not on the same file or adjacent files. No scaling.
809 return SCALE_FACTOR_NONE;
814 /// K, bisop and a pawn vs K and knight. There is a single rule: If the defending
815 /// king is somewhere along the path of the pawn, and the square of the king is
816 /// not of the same color as the stronger side's bishop, it's a draw.
818 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
820 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
821 assert(pos.piece_count(strongerSide, BISHOP) == 1);
822 assert(pos.piece_count(strongerSide, PAWN) == 1);
823 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
824 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
825 assert(pos.piece_count(weakerSide, PAWN) == 0);
827 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
828 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
829 Square weakerKingSq = pos.king_square(weakerSide);
831 if ( file_of(weakerKingSq) == file_of(pawnSq)
832 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
833 && ( opposite_colors(weakerKingSq, strongerBishopSq)
834 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
835 return SCALE_FACTOR_DRAW;
837 return SCALE_FACTOR_NONE;
841 /// K, knight and a pawn vs K. There is a single rule: If the pawn is a rook pawn
842 /// on the 7th rank and the defending king prevents the pawn from advancing, the
843 /// position is drawn.
845 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
847 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame);
848 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
849 assert(pos.piece_count(strongerSide, PAWN) == 1);
850 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
851 assert(pos.piece_count(weakerSide, PAWN) == 0);
853 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
854 Square weakerKingSq = pos.king_square(weakerSide);
856 if ( pawnSq == relative_square(strongerSide, SQ_A7)
857 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
858 return SCALE_FACTOR_DRAW;
860 if ( pawnSq == relative_square(strongerSide, SQ_H7)
861 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
862 return SCALE_FACTOR_DRAW;
864 return SCALE_FACTOR_NONE;
868 /// K and a pawn vs K and a pawn. This is done by removing the weakest side's
869 /// pawn and probing the KP vs K bitbase: If the weakest side has a draw without
870 /// the pawn, she probably has at least a draw with the pawn as well. The exception
871 /// is when the stronger side's pawn is far advanced and not on a rook file; in
872 /// this case it is often possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
874 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
876 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
877 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
878 assert(pos.piece_count(WHITE, PAWN) == 1);
879 assert(pos.piece_count(BLACK, PAWN) == 1);
881 Square wksq = pos.king_square(strongerSide);
882 Square bksq = pos.king_square(weakerSide);
883 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
884 Color stm = pos.side_to_move();
886 if (strongerSide == BLACK)
894 if (file_of(wpsq) >= FILE_E)
901 // If the pawn has advanced to the fifth rank or further, and is not a
902 // rook pawn, it's too dangerous to assume that it's at least a draw.
903 if ( rank_of(wpsq) >= RANK_5
904 && file_of(wpsq) != FILE_A)
905 return SCALE_FACTOR_NONE;
907 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
908 // it's probably at least a draw even with the pawn.
909 return probe_kpk_bitbase(wksq, wpsq, bksq, stm) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;