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/>.
29 extern uint32_t probe_kpk_bitbase(Square wksq, Square wpsq, Square bksq, Color stm);
33 // Table used to drive the defending king towards the edge of the board
34 // in KX vs K and KQ vs KR endgames.
35 const int MateTable[64] = {
36 100, 90, 80, 70, 70, 80, 90, 100,
37 90, 70, 60, 50, 50, 60, 70, 90,
38 80, 60, 40, 30, 30, 40, 60, 80,
39 70, 50, 30, 20, 20, 30, 50, 70,
40 70, 50, 30, 20, 20, 30, 50, 70,
41 80, 60, 40, 30, 30, 40, 60, 80,
42 90, 70, 60, 50, 50, 60, 70, 90,
43 100, 90, 80, 70, 70, 80, 90, 100,
46 // Table used to drive the defending king towards a corner square of the
47 // right color in KBN vs K endgames.
48 const int KBNKMateTable[64] = {
49 200, 190, 180, 170, 160, 150, 140, 130,
50 190, 180, 170, 160, 150, 140, 130, 140,
51 180, 170, 155, 140, 140, 125, 140, 150,
52 170, 160, 140, 120, 110, 140, 150, 160,
53 160, 150, 140, 110, 120, 140, 160, 170,
54 150, 140, 125, 140, 140, 155, 170, 180,
55 140, 130, 140, 150, 160, 170, 180, 190,
56 130, 140, 150, 160, 170, 180, 190, 200
59 // The attacking side is given a descending bonus based on distance between
60 // the two kings in basic endgames.
61 const int DistanceBonus[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
63 // Get the material key of a Position out of the given endgame key code
64 // like "KBPKN". The trick here is to first forge an ad-hoc fen string
65 // and then let a Position object to do the work for us. Note that the
66 // fen string could correspond to an illegal position.
67 Key key(const string& code, Color c) {
69 assert(code.length() > 0 && code.length() < 8);
70 assert(code[0] == 'K');
72 string sides[] = { code.substr(code.find('K', 1)), // Weaker
73 code.substr(0, code.find('K', 1)) }; // Stronger
75 transform(sides[c].begin(), sides[c].end(), sides[c].begin(), tolower);
77 string fen = sides[0] + char('0' + int(8 - code.length()))
78 + sides[1] + "/8/8/8/8/8/8/8 w - - 0 10";
80 return Position(fen, false, NULL).material_key();
84 void delete_endgame(const typename M::value_type& p) { delete p.second; }
89 /// Endgames members definitions
91 Endgames::Endgames() {
106 add<KBPPKB>("KBPPKB");
107 add<KRPPKRP>("KRPPKRP");
110 Endgames::~Endgames() {
112 for_each(m1.begin(), m1.end(), delete_endgame<M1>);
113 for_each(m2.begin(), m2.end(), delete_endgame<M2>);
116 template<EndgameType E>
117 void Endgames::add(const string& code) {
119 map((Endgame<E>*)0)[key(code, WHITE)] = new Endgame<E>(WHITE);
120 map((Endgame<E>*)0)[key(code, BLACK)] = new Endgame<E>(BLACK);
124 /// Mate with KX vs K. This function is used to evaluate positions with
125 /// King and plenty of material vs a lone king. It simply gives the
126 /// attacking side a bonus for driving the defending king towards the edge
127 /// of the board, and for keeping the distance between the two kings small.
129 Value Endgame<KXK>::operator()(const Position& pos) const {
131 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
132 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
134 // Stalemate detection with lone king
135 if ( pos.side_to_move() == weakerSide
137 && !MoveList<MV_LEGAL>(pos).size()) {
141 Square winnerKSq = pos.king_square(strongerSide);
142 Square loserKSq = pos.king_square(weakerSide);
144 Value result = pos.non_pawn_material(strongerSide)
145 + pos.piece_count(strongerSide, PAWN) * PawnValueEndgame
146 + MateTable[loserKSq]
147 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
149 if ( pos.piece_count(strongerSide, QUEEN)
150 || pos.piece_count(strongerSide, ROOK)
151 || pos.bishop_pair(strongerSide)) {
152 result += VALUE_KNOWN_WIN;
155 return strongerSide == pos.side_to_move() ? result : -result;
159 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
160 /// defending king towards a corner square of the right color.
162 Value Endgame<KBNK>::operator()(const Position& pos) const {
164 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
165 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
166 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame + BishopValueMidgame);
167 assert(pos.piece_count(strongerSide, BISHOP) == 1);
168 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
169 assert(pos.piece_count(strongerSide, PAWN) == 0);
171 Square winnerKSq = pos.king_square(strongerSide);
172 Square loserKSq = pos.king_square(weakerSide);
173 Square bishopSquare = pos.piece_list(strongerSide, BISHOP)[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(bishopSquare, SQ_A1))
180 winnerKSq = mirror(winnerKSq);
181 loserKSq = mirror(loserKSq);
184 Value result = VALUE_KNOWN_WIN
185 + DistanceBonus[square_distance(winnerKSq, loserKSq)]
186 + KBNKMateTable[loserKSq];
188 return strongerSide == 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(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
197 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
198 assert(pos.piece_count(strongerSide, PAWN) == 1);
199 assert(pos.piece_count(weakerSide, PAWN) == 0);
201 Square wksq, bksq, wpsq;
204 if (strongerSide == WHITE)
206 wksq = pos.king_square(WHITE);
207 bksq = pos.king_square(BLACK);
208 wpsq = pos.piece_list(WHITE, PAWN)[0];
209 stm = pos.side_to_move();
213 wksq = ~pos.king_square(BLACK);
214 bksq = ~pos.king_square(WHITE);
215 wpsq = ~pos.piece_list(BLACK, PAWN)[0];
216 stm = ~pos.side_to_move();
219 if (file_of(wpsq) >= FILE_E)
226 if (!probe_kpk_bitbase(wksq, wpsq, bksq, stm))
229 Value result = VALUE_KNOWN_WIN
231 + Value(rank_of(wpsq));
233 return strongerSide == pos.side_to_move() ? result : -result;
237 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
238 /// a bitbase. The function below returns drawish scores when the pawn is
239 /// far advanced with support of the king, while the attacking king is far
242 Value Endgame<KRKP>::operator()(const Position& pos) const {
244 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
245 assert(pos.piece_count(strongerSide, PAWN) == 0);
246 assert(pos.non_pawn_material(weakerSide) == 0);
247 assert(pos.piece_count(weakerSide, PAWN) == 1);
249 Square wksq, wrsq, bksq, bpsq;
250 int tempo = (pos.side_to_move() == strongerSide);
252 wksq = pos.king_square(strongerSide);
253 wrsq = pos.piece_list(strongerSide, ROOK)[0];
254 bksq = pos.king_square(weakerSide);
255 bpsq = pos.piece_list(weakerSide, PAWN)[0];
257 if (strongerSide == BLACK)
265 Square queeningSq = make_square(file_of(bpsq), RANK_1);
268 // If the stronger side's king is in front of the pawn, it's a win
269 if (wksq < bpsq && file_of(wksq) == file_of(bpsq))
270 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
272 // If the weaker side's king is too far from the pawn and the rook,
274 else if ( square_distance(bksq, bpsq) - (tempo ^ 1) >= 3
275 && square_distance(bksq, wrsq) >= 3)
276 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
278 // If the pawn is far advanced and supported by the defending king,
279 // the position is drawish
280 else if ( rank_of(bksq) <= RANK_3
281 && square_distance(bksq, bpsq) == 1
282 && rank_of(wksq) >= RANK_4
283 && square_distance(wksq, bpsq) - tempo > 2)
284 result = Value(80 - square_distance(wksq, bpsq) * 8);
288 - Value(square_distance(wksq, bpsq + DELTA_S) * 8)
289 + Value(square_distance(bksq, bpsq + DELTA_S) * 8)
290 + Value(square_distance(bpsq, queeningSq) * 8);
292 return strongerSide == pos.side_to_move() ? result : -result;
296 /// KR vs KB. This is very simple, and always returns drawish scores. The
297 /// score is slightly bigger when the defending king is close to the edge.
299 Value Endgame<KRKB>::operator()(const Position& pos) const {
301 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
302 assert(pos.piece_count(strongerSide, PAWN) == 0);
303 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
304 assert(pos.piece_count(weakerSide, PAWN) == 0);
305 assert(pos.piece_count(weakerSide, BISHOP) == 1);
307 Value result = Value(MateTable[pos.king_square(weakerSide)]);
308 return strongerSide == pos.side_to_move() ? result : -result;
312 /// KR vs KN. The attacking side has slightly better winning chances than
313 /// in KR vs KB, particularly if the king and the knight are far apart.
315 Value Endgame<KRKN>::operator()(const Position& pos) const {
317 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
318 assert(pos.piece_count(strongerSide, PAWN) == 0);
319 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
320 assert(pos.piece_count(weakerSide, PAWN) == 0);
321 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
323 const int penalty[8] = { 0, 10, 14, 20, 30, 42, 58, 80 };
325 Square bksq = pos.king_square(weakerSide);
326 Square bnsq = pos.piece_list(weakerSide, KNIGHT)[0];
327 Value result = Value(MateTable[bksq] + penalty[square_distance(bksq, bnsq)]);
328 return strongerSide == pos.side_to_move() ? result : -result;
332 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
333 /// king a bonus for having the kings close together, and for forcing the
334 /// defending king towards the edge. If we also take care to avoid null move
335 /// for the defending side in the search, this is usually sufficient to be
336 /// able to win KQ vs KR.
338 Value Endgame<KQKR>::operator()(const Position& pos) const {
340 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
341 assert(pos.piece_count(strongerSide, PAWN) == 0);
342 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
343 assert(pos.piece_count(weakerSide, PAWN) == 0);
345 Square winnerKSq = pos.king_square(strongerSide);
346 Square loserKSq = pos.king_square(weakerSide);
348 Value result = QueenValueEndgame
350 + MateTable[loserKSq]
351 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
353 return strongerSide == pos.side_to_move() ? result : -result;
357 Value Endgame<KBBKN>::operator()(const Position& pos) const {
359 assert(pos.piece_count(strongerSide, BISHOP) == 2);
360 assert(pos.non_pawn_material(strongerSide) == 2*BishopValueMidgame);
361 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
362 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
363 assert(!pos.pieces(PAWN));
365 Value result = BishopValueEndgame;
366 Square wksq = pos.king_square(strongerSide);
367 Square bksq = pos.king_square(weakerSide);
368 Square nsq = pos.piece_list(weakerSide, KNIGHT)[0];
370 // Bonus for attacking king close to defending king
371 result += Value(DistanceBonus[square_distance(wksq, bksq)]);
373 // Bonus for driving the defending king and knight apart
374 result += Value(square_distance(bksq, nsq) * 32);
376 // Bonus for restricting the knight's mobility
377 result += Value((8 - popcount<Max15>(pos.attacks_from<KNIGHT>(nsq))) * 8);
379 return strongerSide == pos.side_to_move() ? result : -result;
383 /// K and two minors vs K and one or two minors or K and two knights against
384 /// king alone are always draw.
386 Value Endgame<KmmKm>::operator()(const Position&) const {
391 Value Endgame<KNNK>::operator()(const Position&) const {
395 /// K, bishop and one or more pawns vs K. It checks for draws with rook pawns and
396 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
397 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
400 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
402 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
403 assert(pos.piece_count(strongerSide, BISHOP) == 1);
404 assert(pos.piece_count(strongerSide, PAWN) >= 1);
406 // No assertions about the material of weakerSide, because we want draws to
407 // be detected even when the weaker side has some pawns.
409 Bitboard pawns = pos.pieces(PAWN, strongerSide);
410 File pawnFile = file_of(pos.piece_list(strongerSide, PAWN)[0]);
412 // All pawns are on a single rook file ?
413 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
414 && !(pawns & ~file_bb(pawnFile)))
416 Square bishopSq = pos.piece_list(strongerSide, BISHOP)[0];
417 Square queeningSq = relative_square(strongerSide, make_square(pawnFile, RANK_8));
418 Square kingSq = pos.king_square(weakerSide);
420 if ( opposite_colors(queeningSq, bishopSq)
421 && abs(file_of(kingSq) - pawnFile) <= 1)
423 // The bishop has the wrong color, and the defending king is on the
424 // file of the pawn(s) or the adjacent file. Find the rank of the
427 if (strongerSide == WHITE)
429 for (rank = RANK_7; !(rank_bb(rank) & pawns); rank--) {}
430 assert(rank >= RANK_2 && rank <= RANK_7);
434 for (rank = RANK_2; !(rank_bb(rank) & pawns); rank++) {}
435 rank = Rank(rank ^ 7); // HACK to get the relative rank
436 assert(rank >= RANK_2 && rank <= RANK_7);
438 // If the defending king has distance 1 to the promotion square or
439 // is placed somewhere in front of the pawn, it's a draw.
440 if ( square_distance(kingSq, queeningSq) <= 1
441 || relative_rank(strongerSide, kingSq) >= rank)
442 return SCALE_FACTOR_DRAW;
445 return SCALE_FACTOR_NONE;
449 /// K and queen vs K, rook and one or more pawns. It tests for fortress draws with
450 /// a rook on the third rank defended by a pawn.
452 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
454 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
455 assert(pos.piece_count(strongerSide, QUEEN) == 1);
456 assert(pos.piece_count(strongerSide, PAWN) == 0);
457 assert(pos.piece_count(weakerSide, ROOK) == 1);
458 assert(pos.piece_count(weakerSide, PAWN) >= 1);
460 Square kingSq = pos.king_square(weakerSide);
461 if ( relative_rank(weakerSide, kingSq) <= RANK_2
462 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
463 && (pos.pieces(ROOK, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_3)))
464 && (pos.pieces(PAWN, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_2)))
465 && (pos.attacks_from<KING>(kingSq) & pos.pieces(PAWN, weakerSide)))
467 Square rsq = pos.piece_list(weakerSide, ROOK)[0];
468 if (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(PAWN, weakerSide))
469 return SCALE_FACTOR_DRAW;
471 return SCALE_FACTOR_NONE;
475 /// K, rook and one pawn vs K and a rook. This function knows a handful of the
476 /// most important classes of drawn positions, but is far from perfect. It would
477 /// probably be a good idea to add more knowledge in the future.
479 /// It would also be nice to rewrite the actual code for this function,
480 /// which is mostly copied from Glaurung 1.x, and not very pretty.
482 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
484 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
485 assert(pos.piece_count(strongerSide, PAWN) == 1);
486 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
487 assert(pos.piece_count(weakerSide, PAWN) == 0);
489 Square wksq = pos.king_square(strongerSide);
490 Square wrsq = pos.piece_list(strongerSide, ROOK)[0];
491 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
492 Square bksq = pos.king_square(weakerSide);
493 Square brsq = pos.piece_list(weakerSide, ROOK)[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 (strongerSide == BLACK)
505 if (file_of(wpsq) > FILE_D)
514 File f = file_of(wpsq);
515 Rank r = rank_of(wpsq);
516 Square queeningSq = make_square(f, RANK_8);
517 int tempo = (pos.side_to_move() == strongerSide);
519 // If the pawn is not too far advanced and the defending king defends the
520 // queening square, use the third-rank defence.
522 && square_distance(bksq, queeningSq) <= 1
524 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
525 return SCALE_FACTOR_DRAW;
527 // The defending side saves a draw by checking from behind in case the pawn
528 // has advanced to the 6th rank with the king behind.
530 && square_distance(bksq, queeningSq) <= 1
531 && rank_of(wksq) + tempo <= RANK_6
532 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
533 return SCALE_FACTOR_DRAW;
536 && bksq == queeningSq
537 && rank_of(brsq) == RANK_1
538 && (!tempo || square_distance(wksq, wpsq) >= 2))
539 return SCALE_FACTOR_DRAW;
541 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
542 // and the black rook is behind the pawn.
545 && (bksq == SQ_H7 || bksq == SQ_G7)
546 && file_of(brsq) == FILE_A
547 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
548 return SCALE_FACTOR_DRAW;
550 // If the defending king blocks the pawn and the attacking king is too far
551 // away, it's a draw.
553 && bksq == wpsq + DELTA_N
554 && square_distance(wksq, wpsq) - tempo >= 2
555 && square_distance(wksq, brsq) - tempo >= 2)
556 return SCALE_FACTOR_DRAW;
558 // Pawn on the 7th rank supported by the rook from behind usually wins if the
559 // attacking king is closer to the queening square than the defending king,
560 // and the defending king cannot gain tempi by threatening the attacking rook.
563 && file_of(wrsq) == f
564 && wrsq != queeningSq
565 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
566 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
567 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
569 // Similar to the above, but with the pawn further back
571 && file_of(wrsq) == f
573 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
574 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
575 && ( square_distance(bksq, wrsq) + tempo >= 3
576 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
577 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
578 return ScaleFactor( SCALE_FACTOR_MAX
579 - 8 * square_distance(wpsq, queeningSq)
580 - 2 * square_distance(wksq, queeningSq));
582 // If the pawn is not far advanced, and the defending king is somewhere in
583 // the pawn's path, it's probably a draw.
584 if (r <= RANK_4 && bksq > wpsq)
586 if (file_of(bksq) == file_of(wpsq))
587 return ScaleFactor(10);
588 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
589 && square_distance(wksq, bksq) > 2)
590 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
592 return SCALE_FACTOR_NONE;
596 /// K, rook and two pawns vs K, rook and one pawn. There is only a single
597 /// pattern: If the stronger side has no passed pawns and the defending king
598 /// is actively placed, the position is drawish.
600 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
602 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
603 assert(pos.piece_count(strongerSide, PAWN) == 2);
604 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
605 assert(pos.piece_count(weakerSide, PAWN) == 1);
607 Square wpsq1 = pos.piece_list(strongerSide, PAWN)[0];
608 Square wpsq2 = pos.piece_list(strongerSide, PAWN)[1];
609 Square bksq = pos.king_square(weakerSide);
611 // Does the stronger side have a passed pawn?
612 if ( pos.pawn_is_passed(strongerSide, wpsq1)
613 || pos.pawn_is_passed(strongerSide, wpsq2))
614 return SCALE_FACTOR_NONE;
616 Rank r = std::max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
618 if ( file_distance(bksq, wpsq1) <= 1
619 && file_distance(bksq, wpsq2) <= 1
620 && relative_rank(strongerSide, bksq) > r)
623 case RANK_2: return ScaleFactor(10);
624 case RANK_3: return ScaleFactor(10);
625 case RANK_4: return ScaleFactor(15);
626 case RANK_5: return ScaleFactor(20);
627 case RANK_6: return ScaleFactor(40);
628 default: assert(false);
631 return SCALE_FACTOR_NONE;
635 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
636 /// are on the same rook file and are blocked by the defending king, it's a draw.
638 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
640 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
641 assert(pos.piece_count(strongerSide, PAWN) >= 2);
642 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
643 assert(pos.piece_count(weakerSide, PAWN) == 0);
645 Square ksq = pos.king_square(weakerSide);
646 Bitboard pawns = pos.pieces(PAWN, strongerSide);
648 // Are all pawns on the 'a' file?
649 if (!(pawns & ~FileABB))
651 // Does the defending king block the pawns?
652 if ( square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
653 || ( file_of(ksq) == FILE_A
654 && !in_front_bb(strongerSide, ksq) & pawns))
655 return SCALE_FACTOR_DRAW;
657 // Are all pawns on the 'h' file?
658 else if (!(pawns & ~FileHBB))
660 // Does the defending king block the pawns?
661 if ( square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
662 || ( file_of(ksq) == FILE_H
663 && !in_front_bb(strongerSide, ksq) & pawns))
664 return SCALE_FACTOR_DRAW;
666 return SCALE_FACTOR_NONE;
670 /// K, bishop and a pawn vs K and a bishop. There are two rules: If the defending
671 /// king is somewhere along the path of the pawn, and the square of the king is
672 /// not of the same color as the stronger side's bishop, it's a draw. If the two
673 /// bishops have opposite color, it's almost always a draw.
675 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
677 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
678 assert(pos.piece_count(strongerSide, BISHOP) == 1);
679 assert(pos.piece_count(strongerSide, PAWN) == 1);
680 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
681 assert(pos.piece_count(weakerSide, BISHOP) == 1);
682 assert(pos.piece_count(weakerSide, PAWN) == 0);
684 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
685 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
686 Square weakerBishopSq = pos.piece_list(weakerSide, BISHOP)[0];
687 Square weakerKingSq = pos.king_square(weakerSide);
689 // Case 1: Defending king blocks the pawn, and cannot be driven away
690 if ( file_of(weakerKingSq) == file_of(pawnSq)
691 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
692 && ( opposite_colors(weakerKingSq, strongerBishopSq)
693 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
694 return SCALE_FACTOR_DRAW;
696 // Case 2: Opposite colored bishops
697 if (opposite_colors(strongerBishopSq, weakerBishopSq))
699 // We assume that the position is drawn in the following three situations:
701 // a. The pawn is on rank 5 or further back.
702 // b. The defending king is somewhere in the pawn's path.
703 // c. The defending bishop attacks some square along the pawn's path,
704 // and is at least three squares away from the pawn.
706 // These rules are probably not perfect, but in practice they work
709 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
710 return SCALE_FACTOR_DRAW;
713 Bitboard path = forward_bb(strongerSide, pawnSq);
715 if (path & pos.pieces(KING, weakerSide))
716 return SCALE_FACTOR_DRAW;
718 if ( (pos.attacks_from<BISHOP>(weakerBishopSq) & path)
719 && square_distance(weakerBishopSq, pawnSq) >= 3)
720 return SCALE_FACTOR_DRAW;
723 return SCALE_FACTOR_NONE;
727 /// K, bishop and two pawns vs K and bishop. It detects a few basic draws with
728 /// opposite-colored bishops.
730 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
732 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
733 assert(pos.piece_count(strongerSide, BISHOP) == 1);
734 assert(pos.piece_count(strongerSide, PAWN) == 2);
735 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
736 assert(pos.piece_count(weakerSide, BISHOP) == 1);
737 assert(pos.piece_count(weakerSide, PAWN) == 0);
739 Square wbsq = pos.piece_list(strongerSide, BISHOP)[0];
740 Square bbsq = pos.piece_list(weakerSide, BISHOP)[0];
742 if (!opposite_colors(wbsq, bbsq))
743 return SCALE_FACTOR_NONE;
745 Square ksq = pos.king_square(weakerSide);
746 Square psq1 = pos.piece_list(strongerSide, PAWN)[0];
747 Square psq2 = pos.piece_list(strongerSide, PAWN)[1];
748 Rank r1 = rank_of(psq1);
749 Rank r2 = rank_of(psq2);
750 Square blockSq1, blockSq2;
752 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
754 blockSq1 = psq1 + pawn_push(strongerSide);
755 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
759 blockSq1 = psq2 + pawn_push(strongerSide);
760 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
763 switch (file_distance(psq1, psq2))
766 // Both pawns are on the same file. Easy draw if defender firmly controls
767 // some square in the frontmost pawn's path.
768 if ( file_of(ksq) == file_of(blockSq1)
769 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
770 && opposite_colors(ksq, wbsq))
771 return SCALE_FACTOR_DRAW;
773 return SCALE_FACTOR_NONE;
776 // Pawns on adjacent files. Draw if defender firmly controls the square
777 // in front of the frontmost pawn's path, and the square diagonally behind
778 // this square on the file of the other pawn.
780 && opposite_colors(ksq, wbsq)
781 && ( bbsq == blockSq2
782 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(BISHOP, weakerSide))
783 || abs(r1 - r2) >= 2))
784 return SCALE_FACTOR_DRAW;
786 else if ( ksq == blockSq2
787 && opposite_colors(ksq, wbsq)
788 && ( bbsq == blockSq1
789 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(BISHOP, weakerSide))))
790 return SCALE_FACTOR_DRAW;
792 return SCALE_FACTOR_NONE;
795 // The pawns are not on the same file or adjacent files. No scaling.
796 return SCALE_FACTOR_NONE;
801 /// K, bisop and a pawn vs K and knight. There is a single rule: If the defending
802 /// king is somewhere along the path of the pawn, and the square of the king is
803 /// not of the same color as the stronger side's bishop, it's a draw.
805 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
807 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
808 assert(pos.piece_count(strongerSide, BISHOP) == 1);
809 assert(pos.piece_count(strongerSide, PAWN) == 1);
810 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
811 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
812 assert(pos.piece_count(weakerSide, PAWN) == 0);
814 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
815 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
816 Square weakerKingSq = pos.king_square(weakerSide);
818 if ( file_of(weakerKingSq) == file_of(pawnSq)
819 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
820 && ( opposite_colors(weakerKingSq, strongerBishopSq)
821 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
822 return SCALE_FACTOR_DRAW;
824 return SCALE_FACTOR_NONE;
828 /// K, knight and a pawn vs K. There is a single rule: If the pawn is a rook pawn
829 /// on the 7th rank and the defending king prevents the pawn from advancing, the
830 /// position is drawn.
832 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
834 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame);
835 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
836 assert(pos.piece_count(strongerSide, PAWN) == 1);
837 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
838 assert(pos.piece_count(weakerSide, PAWN) == 0);
840 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
841 Square weakerKingSq = pos.king_square(weakerSide);
843 if ( pawnSq == relative_square(strongerSide, SQ_A7)
844 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
845 return SCALE_FACTOR_DRAW;
847 if ( pawnSq == relative_square(strongerSide, SQ_H7)
848 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
849 return SCALE_FACTOR_DRAW;
851 return SCALE_FACTOR_NONE;
855 /// K and a pawn vs K and a pawn. This is done by removing the weakest side's
856 /// pawn and probing the KP vs K bitbase: If the weakest side has a draw without
857 /// the pawn, she probably has at least a draw with the pawn as well. The exception
858 /// is when the stronger side's pawn is far advanced and not on a rook file; in
859 /// this case it is often possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
861 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
863 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
864 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
865 assert(pos.piece_count(WHITE, PAWN) == 1);
866 assert(pos.piece_count(BLACK, PAWN) == 1);
868 Square wksq = pos.king_square(strongerSide);
869 Square bksq = pos.king_square(weakerSide);
870 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
871 Color stm = pos.side_to_move();
873 if (strongerSide == BLACK)
881 if (file_of(wpsq) >= FILE_E)
888 // If the pawn has advanced to the fifth rank or further, and is not a
889 // rook pawn, it's too dangerous to assume that it's at least a draw.
890 if ( rank_of(wpsq) >= RANK_5
891 && file_of(wpsq) != FILE_A)
892 return SCALE_FACTOR_NONE;
894 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
895 // it's probably at least a draw even with the pawn.
896 return probe_kpk_bitbase(wksq, wpsq, bksq, stm) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;