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; }
88 /// Endgames members definitions
90 Endgames::Endgames() {
105 add<KBPPKB>("KBPPKB");
106 add<KRPPKRP>("KRPPKRP");
109 Endgames::~Endgames() {
111 for_each(m1.begin(), m1.end(), delete_endgame<M1>);
112 for_each(m2.begin(), m2.end(), delete_endgame<M2>);
115 template<EndgameType E>
116 void Endgames::add(const string& code) {
118 typedef typename eg_family<E>::type T;
120 map((T*)0)[key(code, WHITE)] = new Endgame<E>(WHITE);
121 map((T*)0)[key(code, BLACK)] = new Endgame<E>(BLACK);
125 /// Mate with KX vs K. This function is used to evaluate positions with
126 /// King and plenty of material vs a lone king. It simply gives the
127 /// attacking side a bonus for driving the defending king towards the edge
128 /// of the board, and for keeping the distance between the two kings small.
130 Value Endgame<KXK>::operator()(const Position& pos) const {
132 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
133 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
135 Square winnerKSq = pos.king_square(strongerSide);
136 Square loserKSq = pos.king_square(weakerSide);
138 Value result = pos.non_pawn_material(strongerSide)
139 + pos.piece_count(strongerSide, PAWN) * PawnValueEndgame
140 + MateTable[loserKSq]
141 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
143 if ( pos.piece_count(strongerSide, QUEEN)
144 || pos.piece_count(strongerSide, ROOK)
145 || pos.piece_count(strongerSide, BISHOP) > 1)
146 // TODO: check for two equal-colored bishops!
147 result += VALUE_KNOWN_WIN;
149 return strongerSide == pos.side_to_move() ? result : -result;
153 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
154 /// defending king towards a corner square of the right color.
156 Value Endgame<KBNK>::operator()(const Position& pos) const {
158 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
159 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
160 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame + BishopValueMidgame);
161 assert(pos.piece_count(strongerSide, BISHOP) == 1);
162 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
163 assert(pos.piece_count(strongerSide, PAWN) == 0);
165 Square winnerKSq = pos.king_square(strongerSide);
166 Square loserKSq = pos.king_square(weakerSide);
167 Square bishopSquare = pos.piece_list(strongerSide, BISHOP)[0];
169 // kbnk_mate_table() tries to drive toward corners A1 or H8,
170 // if we have a bishop that cannot reach the above squares we
171 // mirror the kings so to drive enemy toward corners A8 or H1.
172 if (opposite_colors(bishopSquare, SQ_A1))
174 winnerKSq = mirror(winnerKSq);
175 loserKSq = mirror(loserKSq);
178 Value result = VALUE_KNOWN_WIN
179 + DistanceBonus[square_distance(winnerKSq, loserKSq)]
180 + KBNKMateTable[loserKSq];
182 return strongerSide == pos.side_to_move() ? result : -result;
186 /// KP vs K. This endgame is evaluated with the help of a bitbase.
188 Value Endgame<KPK>::operator()(const Position& pos) const {
190 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
191 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
192 assert(pos.piece_count(strongerSide, PAWN) == 1);
193 assert(pos.piece_count(weakerSide, PAWN) == 0);
195 Square wksq, bksq, wpsq;
198 if (strongerSide == WHITE)
200 wksq = pos.king_square(WHITE);
201 bksq = pos.king_square(BLACK);
202 wpsq = pos.piece_list(WHITE, PAWN)[0];
203 stm = pos.side_to_move();
207 wksq = ~pos.king_square(BLACK);
208 bksq = ~pos.king_square(WHITE);
209 wpsq = ~pos.piece_list(BLACK, PAWN)[0];
210 stm = ~pos.side_to_move();
213 if (file_of(wpsq) >= FILE_E)
220 if (!probe_kpk_bitbase(wksq, wpsq, bksq, stm))
223 Value result = VALUE_KNOWN_WIN
225 + Value(rank_of(wpsq));
227 return strongerSide == pos.side_to_move() ? result : -result;
231 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
232 /// a bitbase. The function below returns drawish scores when the pawn is
233 /// far advanced with support of the king, while the attacking king is far
236 Value Endgame<KRKP>::operator()(const Position& pos) const {
238 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
239 assert(pos.piece_count(strongerSide, PAWN) == 0);
240 assert(pos.non_pawn_material(weakerSide) == 0);
241 assert(pos.piece_count(weakerSide, PAWN) == 1);
243 Square wksq, wrsq, bksq, bpsq;
244 int tempo = (pos.side_to_move() == strongerSide);
246 wksq = pos.king_square(strongerSide);
247 wrsq = pos.piece_list(strongerSide, ROOK)[0];
248 bksq = pos.king_square(weakerSide);
249 bpsq = pos.piece_list(weakerSide, PAWN)[0];
251 if (strongerSide == BLACK)
259 Square queeningSq = make_square(file_of(bpsq), RANK_1);
262 // If the stronger side's king is in front of the pawn, it's a win
263 if (wksq < bpsq && file_of(wksq) == file_of(bpsq))
264 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
266 // If the weaker side's king is too far from the pawn and the rook,
268 else if ( square_distance(bksq, bpsq) - (tempo ^ 1) >= 3
269 && square_distance(bksq, wrsq) >= 3)
270 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
272 // If the pawn is far advanced and supported by the defending king,
273 // the position is drawish
274 else if ( rank_of(bksq) <= RANK_3
275 && square_distance(bksq, bpsq) == 1
276 && rank_of(wksq) >= RANK_4
277 && square_distance(wksq, bpsq) - tempo > 2)
278 result = Value(80 - square_distance(wksq, bpsq) * 8);
282 - Value(square_distance(wksq, bpsq + DELTA_S) * 8)
283 + Value(square_distance(bksq, bpsq + DELTA_S) * 8)
284 + Value(square_distance(bpsq, queeningSq) * 8);
286 return strongerSide == pos.side_to_move() ? result : -result;
290 /// KR vs KB. This is very simple, and always returns drawish scores. The
291 /// score is slightly bigger when the defending king is close to the edge.
293 Value Endgame<KRKB>::operator()(const Position& pos) const {
295 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
296 assert(pos.piece_count(strongerSide, PAWN) == 0);
297 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
298 assert(pos.piece_count(weakerSide, PAWN) == 0);
299 assert(pos.piece_count(weakerSide, BISHOP) == 1);
301 Value result = Value(MateTable[pos.king_square(weakerSide)]);
302 return strongerSide == pos.side_to_move() ? result : -result;
306 /// KR vs KN. The attacking side has slightly better winning chances than
307 /// in KR vs KB, particularly if the king and the knight are far apart.
309 Value Endgame<KRKN>::operator()(const Position& pos) const {
311 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
312 assert(pos.piece_count(strongerSide, PAWN) == 0);
313 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
314 assert(pos.piece_count(weakerSide, PAWN) == 0);
315 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
317 const int penalty[8] = { 0, 10, 14, 20, 30, 42, 58, 80 };
319 Square bksq = pos.king_square(weakerSide);
320 Square bnsq = pos.piece_list(weakerSide, KNIGHT)[0];
321 Value result = Value(MateTable[bksq] + penalty[square_distance(bksq, bnsq)]);
322 return strongerSide == pos.side_to_move() ? result : -result;
326 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
327 /// king a bonus for having the kings close together, and for forcing the
328 /// defending king towards the edge. If we also take care to avoid null move
329 /// for the defending side in the search, this is usually sufficient to be
330 /// able to win KQ vs KR.
332 Value Endgame<KQKR>::operator()(const Position& pos) const {
334 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
335 assert(pos.piece_count(strongerSide, PAWN) == 0);
336 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
337 assert(pos.piece_count(weakerSide, PAWN) == 0);
339 Square winnerKSq = pos.king_square(strongerSide);
340 Square loserKSq = pos.king_square(weakerSide);
342 Value result = QueenValueEndgame
344 + MateTable[loserKSq]
345 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
347 return strongerSide == pos.side_to_move() ? result : -result;
351 Value Endgame<KBBKN>::operator()(const Position& pos) const {
353 assert(pos.piece_count(strongerSide, BISHOP) == 2);
354 assert(pos.non_pawn_material(strongerSide) == 2*BishopValueMidgame);
355 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
356 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
357 assert(!pos.pieces(PAWN));
359 Value result = BishopValueEndgame;
360 Square wksq = pos.king_square(strongerSide);
361 Square bksq = pos.king_square(weakerSide);
362 Square nsq = pos.piece_list(weakerSide, KNIGHT)[0];
364 // Bonus for attacking king close to defending king
365 result += Value(DistanceBonus[square_distance(wksq, bksq)]);
367 // Bonus for driving the defending king and knight apart
368 result += Value(square_distance(bksq, nsq) * 32);
370 // Bonus for restricting the knight's mobility
371 result += Value((8 - popcount<Max15>(pos.attacks_from<KNIGHT>(nsq))) * 8);
373 return strongerSide == pos.side_to_move() ? result : -result;
377 /// K and two minors vs K and one or two minors or K and two knights against
378 /// king alone are always draw.
380 Value Endgame<KmmKm>::operator()(const Position&) const {
385 Value Endgame<KNNK>::operator()(const Position&) const {
389 /// K, bishop and one or more pawns vs K. It checks for draws with rook pawns and
390 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
391 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
394 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
396 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
397 assert(pos.piece_count(strongerSide, BISHOP) == 1);
398 assert(pos.piece_count(strongerSide, PAWN) >= 1);
400 // No assertions about the material of weakerSide, because we want draws to
401 // be detected even when the weaker side has some pawns.
403 Bitboard pawns = pos.pieces(PAWN, strongerSide);
404 File pawnFile = file_of(pos.piece_list(strongerSide, PAWN)[0]);
406 // All pawns are on a single rook file ?
407 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
408 && !(pawns & ~file_bb(pawnFile)))
410 Square bishopSq = pos.piece_list(strongerSide, BISHOP)[0];
411 Square queeningSq = relative_square(strongerSide, make_square(pawnFile, RANK_8));
412 Square kingSq = pos.king_square(weakerSide);
414 if ( opposite_colors(queeningSq, bishopSq)
415 && abs(file_of(kingSq) - pawnFile) <= 1)
417 // The bishop has the wrong color, and the defending king is on the
418 // file of the pawn(s) or the adjacent file. Find the rank of the
421 if (strongerSide == WHITE)
423 for (rank = RANK_7; !(rank_bb(rank) & pawns); rank--) {}
424 assert(rank >= RANK_2 && rank <= RANK_7);
428 for (rank = RANK_2; !(rank_bb(rank) & pawns); rank++) {}
429 rank = Rank(rank ^ 7); // HACK to get the relative rank
430 assert(rank >= RANK_2 && rank <= RANK_7);
432 // If the defending king has distance 1 to the promotion square or
433 // is placed somewhere in front of the pawn, it's a draw.
434 if ( square_distance(kingSq, queeningSq) <= 1
435 || relative_rank(strongerSide, kingSq) >= rank)
436 return SCALE_FACTOR_DRAW;
439 return SCALE_FACTOR_NONE;
443 /// K and queen vs K, rook and one or more pawns. It tests for fortress draws with
444 /// a rook on the third rank defended by a pawn.
446 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
448 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
449 assert(pos.piece_count(strongerSide, QUEEN) == 1);
450 assert(pos.piece_count(strongerSide, PAWN) == 0);
451 assert(pos.piece_count(weakerSide, ROOK) == 1);
452 assert(pos.piece_count(weakerSide, PAWN) >= 1);
454 Square kingSq = pos.king_square(weakerSide);
455 if ( relative_rank(weakerSide, kingSq) <= RANK_2
456 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
457 && (pos.pieces(ROOK, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_3)))
458 && (pos.pieces(PAWN, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_2)))
459 && (pos.attacks_from<KING>(kingSq) & pos.pieces(PAWN, weakerSide)))
461 Square rsq = pos.piece_list(weakerSide, ROOK)[0];
462 if (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(PAWN, weakerSide))
463 return SCALE_FACTOR_DRAW;
465 return SCALE_FACTOR_NONE;
469 /// K, rook and one pawn vs K and a rook. This function knows a handful of the
470 /// most important classes of drawn positions, but is far from perfect. It would
471 /// probably be a good idea to add more knowledge in the future.
473 /// It would also be nice to rewrite the actual code for this function,
474 /// which is mostly copied from Glaurung 1.x, and not very pretty.
476 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
478 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
479 assert(pos.piece_count(strongerSide, PAWN) == 1);
480 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
481 assert(pos.piece_count(weakerSide, PAWN) == 0);
483 Square wksq = pos.king_square(strongerSide);
484 Square wrsq = pos.piece_list(strongerSide, ROOK)[0];
485 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
486 Square bksq = pos.king_square(weakerSide);
487 Square brsq = pos.piece_list(weakerSide, ROOK)[0];
489 // Orient the board in such a way that the stronger side is white, and the
490 // pawn is on the left half of the board.
491 if (strongerSide == BLACK)
499 if (file_of(wpsq) > FILE_D)
508 File f = file_of(wpsq);
509 Rank r = rank_of(wpsq);
510 Square queeningSq = make_square(f, RANK_8);
511 int tempo = (pos.side_to_move() == strongerSide);
513 // If the pawn is not too far advanced and the defending king defends the
514 // queening square, use the third-rank defence.
516 && square_distance(bksq, queeningSq) <= 1
518 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
519 return SCALE_FACTOR_DRAW;
521 // The defending side saves a draw by checking from behind in case the pawn
522 // has advanced to the 6th rank with the king behind.
524 && square_distance(bksq, queeningSq) <= 1
525 && rank_of(wksq) + tempo <= RANK_6
526 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
527 return SCALE_FACTOR_DRAW;
530 && bksq == queeningSq
531 && rank_of(brsq) == RANK_1
532 && (!tempo || square_distance(wksq, wpsq) >= 2))
533 return SCALE_FACTOR_DRAW;
535 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
536 // and the black rook is behind the pawn.
539 && (bksq == SQ_H7 || bksq == SQ_G7)
540 && file_of(brsq) == FILE_A
541 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
542 return SCALE_FACTOR_DRAW;
544 // If the defending king blocks the pawn and the attacking king is too far
545 // away, it's a draw.
547 && bksq == wpsq + DELTA_N
548 && square_distance(wksq, wpsq) - tempo >= 2
549 && square_distance(wksq, brsq) - tempo >= 2)
550 return SCALE_FACTOR_DRAW;
552 // Pawn on the 7th rank supported by the rook from behind usually wins if the
553 // attacking king is closer to the queening square than the defending king,
554 // and the defending king cannot gain tempi by threatening the attacking rook.
557 && file_of(wrsq) == f
558 && wrsq != queeningSq
559 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
560 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
561 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
563 // Similar to the above, but with the pawn further back
565 && file_of(wrsq) == f
567 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
568 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
569 && ( square_distance(bksq, wrsq) + tempo >= 3
570 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
571 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
572 return ScaleFactor( SCALE_FACTOR_MAX
573 - 8 * square_distance(wpsq, queeningSq)
574 - 2 * square_distance(wksq, queeningSq));
576 // If the pawn is not far advanced, and the defending king is somewhere in
577 // the pawn's path, it's probably a draw.
578 if (r <= RANK_4 && bksq > wpsq)
580 if (file_of(bksq) == file_of(wpsq))
581 return ScaleFactor(10);
582 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
583 && square_distance(wksq, bksq) > 2)
584 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
586 return SCALE_FACTOR_NONE;
590 /// K, rook and two pawns vs K, rook and one pawn. There is only a single
591 /// pattern: If the stronger side has no passed pawns and the defending king
592 /// is actively placed, the position is drawish.
594 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
596 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
597 assert(pos.piece_count(strongerSide, PAWN) == 2);
598 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
599 assert(pos.piece_count(weakerSide, PAWN) == 1);
601 Square wpsq1 = pos.piece_list(strongerSide, PAWN)[0];
602 Square wpsq2 = pos.piece_list(strongerSide, PAWN)[1];
603 Square bksq = pos.king_square(weakerSide);
605 // Does the stronger side have a passed pawn?
606 if ( pos.pawn_is_passed(strongerSide, wpsq1)
607 || pos.pawn_is_passed(strongerSide, wpsq2))
608 return SCALE_FACTOR_NONE;
610 Rank r = std::max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
612 if ( file_distance(bksq, wpsq1) <= 1
613 && file_distance(bksq, wpsq2) <= 1
614 && relative_rank(strongerSide, bksq) > r)
617 case RANK_2: return ScaleFactor(10);
618 case RANK_3: return ScaleFactor(10);
619 case RANK_4: return ScaleFactor(15);
620 case RANK_5: return ScaleFactor(20);
621 case RANK_6: return ScaleFactor(40);
622 default: assert(false);
625 return SCALE_FACTOR_NONE;
629 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
630 /// are on the same rook file and are blocked by the defending king, it's a draw.
632 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
634 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
635 assert(pos.piece_count(strongerSide, PAWN) >= 2);
636 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
637 assert(pos.piece_count(weakerSide, PAWN) == 0);
639 Square ksq = pos.king_square(weakerSide);
640 Bitboard pawns = pos.pieces(PAWN, strongerSide);
642 // Are all pawns on the 'a' file?
643 if (!(pawns & ~FileABB))
645 // Does the defending king block the pawns?
646 if ( square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
647 || ( file_of(ksq) == FILE_A
648 && !in_front_bb(strongerSide, ksq) & pawns))
649 return SCALE_FACTOR_DRAW;
651 // Are all pawns on the 'h' file?
652 else if (!(pawns & ~FileHBB))
654 // Does the defending king block the pawns?
655 if ( square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
656 || ( file_of(ksq) == FILE_H
657 && !in_front_bb(strongerSide, ksq) & pawns))
658 return SCALE_FACTOR_DRAW;
660 return SCALE_FACTOR_NONE;
664 /// K, bishop and a pawn vs K and a bishop. There are two rules: If the defending
665 /// king is somewhere along the path of the pawn, and the square of the king is
666 /// not of the same color as the stronger side's bishop, it's a draw. If the two
667 /// bishops have opposite color, it's almost always a draw.
669 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
671 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
672 assert(pos.piece_count(strongerSide, BISHOP) == 1);
673 assert(pos.piece_count(strongerSide, PAWN) == 1);
674 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
675 assert(pos.piece_count(weakerSide, BISHOP) == 1);
676 assert(pos.piece_count(weakerSide, PAWN) == 0);
678 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
679 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
680 Square weakerBishopSq = pos.piece_list(weakerSide, BISHOP)[0];
681 Square weakerKingSq = pos.king_square(weakerSide);
683 // Case 1: Defending king blocks the pawn, and cannot be driven away
684 if ( file_of(weakerKingSq) == file_of(pawnSq)
685 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
686 && ( opposite_colors(weakerKingSq, strongerBishopSq)
687 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
688 return SCALE_FACTOR_DRAW;
690 // Case 2: Opposite colored bishops
691 if (opposite_colors(strongerBishopSq, weakerBishopSq))
693 // We assume that the position is drawn in the following three situations:
695 // a. The pawn is on rank 5 or further back.
696 // b. The defending king is somewhere in the pawn's path.
697 // c. The defending bishop attacks some square along the pawn's path,
698 // and is at least three squares away from the pawn.
700 // These rules are probably not perfect, but in practice they work
703 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
704 return SCALE_FACTOR_DRAW;
707 Bitboard path = squares_in_front_of(strongerSide, pawnSq);
709 if (path & pos.pieces(KING, weakerSide))
710 return SCALE_FACTOR_DRAW;
712 if ( (pos.attacks_from<BISHOP>(weakerBishopSq) & path)
713 && square_distance(weakerBishopSq, pawnSq) >= 3)
714 return SCALE_FACTOR_DRAW;
717 return SCALE_FACTOR_NONE;
721 /// K, bishop and two pawns vs K and bishop. It detects a few basic draws with
722 /// opposite-colored bishops.
724 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
726 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
727 assert(pos.piece_count(strongerSide, BISHOP) == 1);
728 assert(pos.piece_count(strongerSide, PAWN) == 2);
729 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
730 assert(pos.piece_count(weakerSide, BISHOP) == 1);
731 assert(pos.piece_count(weakerSide, PAWN) == 0);
733 Square wbsq = pos.piece_list(strongerSide, BISHOP)[0];
734 Square bbsq = pos.piece_list(weakerSide, BISHOP)[0];
736 if (!opposite_colors(wbsq, bbsq))
737 return SCALE_FACTOR_NONE;
739 Square ksq = pos.king_square(weakerSide);
740 Square psq1 = pos.piece_list(strongerSide, PAWN)[0];
741 Square psq2 = pos.piece_list(strongerSide, PAWN)[1];
742 Rank r1 = rank_of(psq1);
743 Rank r2 = rank_of(psq2);
744 Square blockSq1, blockSq2;
746 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
748 blockSq1 = psq1 + pawn_push(strongerSide);
749 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
753 blockSq1 = psq2 + pawn_push(strongerSide);
754 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
757 switch (file_distance(psq1, psq2))
760 // Both pawns are on the same file. Easy draw if defender firmly controls
761 // some square in the frontmost pawn's path.
762 if ( file_of(ksq) == file_of(blockSq1)
763 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
764 && opposite_colors(ksq, wbsq))
765 return SCALE_FACTOR_DRAW;
767 return SCALE_FACTOR_NONE;
770 // Pawns on adjacent files. Draw if defender firmly controls the square
771 // in front of the frontmost pawn's path, and the square diagonally behind
772 // this square on the file of the other pawn.
774 && opposite_colors(ksq, wbsq)
775 && ( bbsq == blockSq2
776 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(BISHOP, weakerSide))
777 || abs(r1 - r2) >= 2))
778 return SCALE_FACTOR_DRAW;
780 else if ( ksq == blockSq2
781 && opposite_colors(ksq, wbsq)
782 && ( bbsq == blockSq1
783 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(BISHOP, weakerSide))))
784 return SCALE_FACTOR_DRAW;
786 return SCALE_FACTOR_NONE;
789 // The pawns are not on the same file or adjacent files. No scaling.
790 return SCALE_FACTOR_NONE;
795 /// K, bisop and a pawn vs K and knight. There is a single rule: If the defending
796 /// king is somewhere along the path of the pawn, and the square of the king is
797 /// not of the same color as the stronger side's bishop, it's a draw.
799 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
801 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
802 assert(pos.piece_count(strongerSide, BISHOP) == 1);
803 assert(pos.piece_count(strongerSide, PAWN) == 1);
804 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
805 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
806 assert(pos.piece_count(weakerSide, PAWN) == 0);
808 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
809 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
810 Square weakerKingSq = pos.king_square(weakerSide);
812 if ( file_of(weakerKingSq) == file_of(pawnSq)
813 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
814 && ( opposite_colors(weakerKingSq, strongerBishopSq)
815 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
816 return SCALE_FACTOR_DRAW;
818 return SCALE_FACTOR_NONE;
822 /// K, knight and a pawn vs K. There is a single rule: If the pawn is a rook pawn
823 /// on the 7th rank and the defending king prevents the pawn from advancing, the
824 /// position is drawn.
826 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
828 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame);
829 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
830 assert(pos.piece_count(strongerSide, PAWN) == 1);
831 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
832 assert(pos.piece_count(weakerSide, PAWN) == 0);
834 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
835 Square weakerKingSq = pos.king_square(weakerSide);
837 if ( pawnSq == relative_square(strongerSide, SQ_A7)
838 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
839 return SCALE_FACTOR_DRAW;
841 if ( pawnSq == relative_square(strongerSide, SQ_H7)
842 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
843 return SCALE_FACTOR_DRAW;
845 return SCALE_FACTOR_NONE;
849 /// K and a pawn vs K and a pawn. This is done by removing the weakest side's
850 /// pawn and probing the KP vs K bitbase: If the weakest side has a draw without
851 /// the pawn, she probably has at least a draw with the pawn as well. The exception
852 /// is when the stronger side's pawn is far advanced and not on a rook file; in
853 /// this case it is often possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
855 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
857 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
858 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
859 assert(pos.piece_count(WHITE, PAWN) == 1);
860 assert(pos.piece_count(BLACK, PAWN) == 1);
862 Square wksq = pos.king_square(strongerSide);
863 Square bksq = pos.king_square(weakerSide);
864 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
865 Color stm = pos.side_to_move();
867 if (strongerSide == BLACK)
875 if (file_of(wpsq) >= FILE_E)
882 // If the pawn has advanced to the fifth rank or further, and is not a
883 // rook pawn, it's too dangerous to assume that it's at least a draw.
884 if ( rank_of(wpsq) >= RANK_5
885 && file_of(wpsq) != FILE_A)
886 return SCALE_FACTOR_NONE;
888 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
889 // it's probably at least a draw even with the pawn.
890 return probe_kpk_bitbase(wksq, wpsq, bksq, stm) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;