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, 0).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 typedef typename eg_family<E>::type T;
121 map((T*)0)[key(code, WHITE)] = new Endgame<E>(WHITE);
122 map((T*)0)[key(code, BLACK)] = new Endgame<E>(BLACK);
126 /// Mate with KX vs K. This function is used to evaluate positions with
127 /// King and plenty of material vs a lone king. It simply gives the
128 /// attacking side a bonus for driving the defending king towards the edge
129 /// of the board, and for keeping the distance between the two kings small.
131 Value Endgame<KXK>::operator()(const Position& pos) const {
133 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
134 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
136 Square winnerKSq = pos.king_square(strongerSide);
137 Square loserKSq = pos.king_square(weakerSide);
139 Value result = pos.non_pawn_material(strongerSide)
140 + pos.piece_count(strongerSide, PAWN) * PawnValueEndgame
141 + MateTable[loserKSq]
142 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
144 if ( pos.piece_count(strongerSide, QUEEN)
145 || pos.piece_count(strongerSide, ROOK)
146 || pos.piece_count(strongerSide, BISHOP) > 1)
147 // TODO: check for two equal-colored bishops!
148 result += VALUE_KNOWN_WIN;
150 return strongerSide == pos.side_to_move() ? result : -result;
154 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
155 /// defending king towards a corner square of the right color.
157 Value Endgame<KBNK>::operator()(const Position& pos) const {
159 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
160 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
161 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame + BishopValueMidgame);
162 assert(pos.piece_count(strongerSide, BISHOP) == 1);
163 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
164 assert(pos.piece_count(strongerSide, PAWN) == 0);
166 Square winnerKSq = pos.king_square(strongerSide);
167 Square loserKSq = pos.king_square(weakerSide);
168 Square bishopSquare = pos.piece_list(strongerSide, BISHOP)[0];
170 // kbnk_mate_table() tries to drive toward corners A1 or H8,
171 // if we have a bishop that cannot reach the above squares we
172 // mirror the kings so to drive enemy toward corners A8 or H1.
173 if (opposite_colors(bishopSquare, SQ_A1))
175 winnerKSq = mirror(winnerKSq);
176 loserKSq = mirror(loserKSq);
179 Value result = VALUE_KNOWN_WIN
180 + DistanceBonus[square_distance(winnerKSq, loserKSq)]
181 + KBNKMateTable[loserKSq];
183 return strongerSide == pos.side_to_move() ? result : -result;
187 /// KP vs K. This endgame is evaluated with the help of a bitbase.
189 Value Endgame<KPK>::operator()(const Position& pos) const {
191 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
192 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
193 assert(pos.piece_count(strongerSide, PAWN) == 1);
194 assert(pos.piece_count(weakerSide, PAWN) == 0);
196 Square wksq, bksq, wpsq;
199 if (strongerSide == WHITE)
201 wksq = pos.king_square(WHITE);
202 bksq = pos.king_square(BLACK);
203 wpsq = pos.piece_list(WHITE, PAWN)[0];
204 stm = pos.side_to_move();
208 wksq = flip(pos.king_square(BLACK));
209 bksq = flip(pos.king_square(WHITE));
210 wpsq = flip(pos.piece_list(BLACK, PAWN)[0]);
211 stm = flip(pos.side_to_move());
214 if (file_of(wpsq) >= FILE_E)
221 if (!probe_kpk_bitbase(wksq, wpsq, bksq, stm))
224 Value result = VALUE_KNOWN_WIN
226 + Value(rank_of(wpsq));
228 return strongerSide == pos.side_to_move() ? result : -result;
232 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
233 /// a bitbase. The function below returns drawish scores when the pawn is
234 /// far advanced with support of the king, while the attacking king is far
237 Value Endgame<KRKP>::operator()(const Position& pos) const {
239 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
240 assert(pos.piece_count(strongerSide, PAWN) == 0);
241 assert(pos.non_pawn_material(weakerSide) == 0);
242 assert(pos.piece_count(weakerSide, PAWN) == 1);
244 Square wksq, wrsq, bksq, bpsq;
245 int tempo = (pos.side_to_move() == strongerSide);
247 wksq = pos.king_square(strongerSide);
248 wrsq = pos.piece_list(strongerSide, ROOK)[0];
249 bksq = pos.king_square(weakerSide);
250 bpsq = pos.piece_list(weakerSide, PAWN)[0];
252 if (strongerSide == BLACK)
260 Square queeningSq = make_square(file_of(bpsq), RANK_1);
263 // If the stronger side's king is in front of the pawn, it's a win
264 if (wksq < bpsq && file_of(wksq) == file_of(bpsq))
265 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
267 // If the weaker side's king is too far from the pawn and the rook,
269 else if ( square_distance(bksq, bpsq) - (tempo ^ 1) >= 3
270 && square_distance(bksq, wrsq) >= 3)
271 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
273 // If the pawn is far advanced and supported by the defending king,
274 // the position is drawish
275 else if ( rank_of(bksq) <= RANK_3
276 && square_distance(bksq, bpsq) == 1
277 && rank_of(wksq) >= RANK_4
278 && square_distance(wksq, bpsq) - tempo > 2)
279 result = Value(80 - square_distance(wksq, bpsq) * 8);
283 - Value(square_distance(wksq, bpsq + DELTA_S) * 8)
284 + Value(square_distance(bksq, bpsq + DELTA_S) * 8)
285 + Value(square_distance(bpsq, queeningSq) * 8);
287 return strongerSide == pos.side_to_move() ? result : -result;
291 /// KR vs KB. This is very simple, and always returns drawish scores. The
292 /// score is slightly bigger when the defending king is close to the edge.
294 Value Endgame<KRKB>::operator()(const Position& pos) const {
296 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
297 assert(pos.piece_count(strongerSide, PAWN) == 0);
298 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
299 assert(pos.piece_count(weakerSide, PAWN) == 0);
300 assert(pos.piece_count(weakerSide, BISHOP) == 1);
302 Value result = Value(MateTable[pos.king_square(weakerSide)]);
303 return strongerSide == pos.side_to_move() ? result : -result;
307 /// KR vs KN. The attacking side has slightly better winning chances than
308 /// in KR vs KB, particularly if the king and the knight are far apart.
310 Value Endgame<KRKN>::operator()(const Position& pos) const {
312 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
313 assert(pos.piece_count(strongerSide, PAWN) == 0);
314 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
315 assert(pos.piece_count(weakerSide, PAWN) == 0);
316 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
318 const int penalty[8] = { 0, 10, 14, 20, 30, 42, 58, 80 };
320 Square bksq = pos.king_square(weakerSide);
321 Square bnsq = pos.piece_list(weakerSide, KNIGHT)[0];
322 Value result = Value(MateTable[bksq] + penalty[square_distance(bksq, bnsq)]);
323 return strongerSide == pos.side_to_move() ? result : -result;
327 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
328 /// king a bonus for having the kings close together, and for forcing the
329 /// defending king towards the edge. If we also take care to avoid null move
330 /// for the defending side in the search, this is usually sufficient to be
331 /// able to win KQ vs KR.
333 Value Endgame<KQKR>::operator()(const Position& pos) const {
335 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
336 assert(pos.piece_count(strongerSide, PAWN) == 0);
337 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
338 assert(pos.piece_count(weakerSide, PAWN) == 0);
340 Square winnerKSq = pos.king_square(strongerSide);
341 Square loserKSq = pos.king_square(weakerSide);
343 Value result = QueenValueEndgame
345 + MateTable[loserKSq]
346 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
348 return strongerSide == pos.side_to_move() ? result : -result;
352 Value Endgame<KBBKN>::operator()(const Position& pos) const {
354 assert(pos.piece_count(strongerSide, BISHOP) == 2);
355 assert(pos.non_pawn_material(strongerSide) == 2*BishopValueMidgame);
356 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
357 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
358 assert(!pos.pieces(PAWN));
360 Value result = BishopValueEndgame;
361 Square wksq = pos.king_square(strongerSide);
362 Square bksq = pos.king_square(weakerSide);
363 Square nsq = pos.piece_list(weakerSide, KNIGHT)[0];
365 // Bonus for attacking king close to defending king
366 result += Value(DistanceBonus[square_distance(wksq, bksq)]);
368 // Bonus for driving the defending king and knight apart
369 result += Value(square_distance(bksq, nsq) * 32);
371 // Bonus for restricting the knight's mobility
372 result += Value((8 - popcount<Max15>(pos.attacks_from<KNIGHT>(nsq))) * 8);
374 return strongerSide == pos.side_to_move() ? result : -result;
378 /// K and two minors vs K and one or two minors or K and two knights against
379 /// king alone are always draw.
381 Value Endgame<KmmKm>::operator()(const Position&) const {
386 Value Endgame<KNNK>::operator()(const Position&) const {
390 /// K, bishop and one or more pawns vs K. It checks for draws with rook pawns and
391 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
392 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
395 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
397 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
398 assert(pos.piece_count(strongerSide, BISHOP) == 1);
399 assert(pos.piece_count(strongerSide, PAWN) >= 1);
401 // No assertions about the material of weakerSide, because we want draws to
402 // be detected even when the weaker side has some pawns.
404 Bitboard pawns = pos.pieces(PAWN, strongerSide);
405 File pawnFile = file_of(pos.piece_list(strongerSide, PAWN)[0]);
407 // All pawns are on a single rook file ?
408 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
409 && !(pawns & ~file_bb(pawnFile)))
411 Square bishopSq = pos.piece_list(strongerSide, BISHOP)[0];
412 Square queeningSq = relative_square(strongerSide, make_square(pawnFile, RANK_8));
413 Square kingSq = pos.king_square(weakerSide);
415 if ( opposite_colors(queeningSq, bishopSq)
416 && abs(file_of(kingSq) - pawnFile) <= 1)
418 // The bishop has the wrong color, and the defending king is on the
419 // file of the pawn(s) or the neighboring file. Find the rank of the
422 if (strongerSide == WHITE)
424 for (rank = RANK_7; !(rank_bb(rank) & pawns); rank--) {}
425 assert(rank >= RANK_2 && rank <= RANK_7);
429 for (rank = RANK_2; !(rank_bb(rank) & pawns); rank++) {}
430 rank = Rank(rank ^ 7); // HACK to get the relative rank
431 assert(rank >= RANK_2 && rank <= RANK_7);
433 // If the defending king has distance 1 to the promotion square or
434 // is placed somewhere in front of the pawn, it's a draw.
435 if ( square_distance(kingSq, queeningSq) <= 1
436 || relative_rank(strongerSide, kingSq) >= rank)
437 return SCALE_FACTOR_DRAW;
440 return SCALE_FACTOR_NONE;
444 /// K and queen vs K, rook and one or more pawns. It tests for fortress draws with
445 /// a rook on the third rank defended by a pawn.
447 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
449 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
450 assert(pos.piece_count(strongerSide, QUEEN) == 1);
451 assert(pos.piece_count(strongerSide, PAWN) == 0);
452 assert(pos.piece_count(weakerSide, ROOK) == 1);
453 assert(pos.piece_count(weakerSide, PAWN) >= 1);
455 Square kingSq = pos.king_square(weakerSide);
456 if ( relative_rank(weakerSide, kingSq) <= RANK_2
457 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
458 && (pos.pieces(ROOK, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_3)))
459 && (pos.pieces(PAWN, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_2)))
460 && (pos.attacks_from<KING>(kingSq) & pos.pieces(PAWN, weakerSide)))
462 Square rsq = pos.piece_list(weakerSide, ROOK)[0];
463 if (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(PAWN, weakerSide))
464 return SCALE_FACTOR_DRAW;
466 return SCALE_FACTOR_NONE;
470 /// K, rook and one pawn vs K and a rook. This function knows a handful of the
471 /// most important classes of drawn positions, but is far from perfect. It would
472 /// probably be a good idea to add more knowledge in the future.
474 /// It would also be nice to rewrite the actual code for this function,
475 /// which is mostly copied from Glaurung 1.x, and not very pretty.
477 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
479 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
480 assert(pos.piece_count(strongerSide, PAWN) == 1);
481 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
482 assert(pos.piece_count(weakerSide, PAWN) == 0);
484 Square wksq = pos.king_square(strongerSide);
485 Square wrsq = pos.piece_list(strongerSide, ROOK)[0];
486 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
487 Square bksq = pos.king_square(weakerSide);
488 Square brsq = pos.piece_list(weakerSide, ROOK)[0];
490 // Orient the board in such a way that the stronger side is white, and the
491 // pawn is on the left half of the board.
492 if (strongerSide == BLACK)
500 if (file_of(wpsq) > FILE_D)
509 File f = file_of(wpsq);
510 Rank r = rank_of(wpsq);
511 Square queeningSq = make_square(f, RANK_8);
512 int tempo = (pos.side_to_move() == strongerSide);
514 // If the pawn is not too far advanced and the defending king defends the
515 // queening square, use the third-rank defence.
517 && square_distance(bksq, queeningSq) <= 1
519 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
520 return SCALE_FACTOR_DRAW;
522 // The defending side saves a draw by checking from behind in case the pawn
523 // has advanced to the 6th rank with the king behind.
525 && square_distance(bksq, queeningSq) <= 1
526 && rank_of(wksq) + tempo <= RANK_6
527 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
528 return SCALE_FACTOR_DRAW;
531 && bksq == queeningSq
532 && rank_of(brsq) == RANK_1
533 && (!tempo || square_distance(wksq, wpsq) >= 2))
534 return SCALE_FACTOR_DRAW;
536 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
537 // and the black rook is behind the pawn.
540 && (bksq == SQ_H7 || bksq == SQ_G7)
541 && file_of(brsq) == FILE_A
542 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
543 return SCALE_FACTOR_DRAW;
545 // If the defending king blocks the pawn and the attacking king is too far
546 // away, it's a draw.
548 && bksq == wpsq + DELTA_N
549 && square_distance(wksq, wpsq) - tempo >= 2
550 && square_distance(wksq, brsq) - tempo >= 2)
551 return SCALE_FACTOR_DRAW;
553 // Pawn on the 7th rank supported by the rook from behind usually wins if the
554 // attacking king is closer to the queening square than the defending king,
555 // and the defending king cannot gain tempi by threatening the attacking rook.
558 && file_of(wrsq) == f
559 && wrsq != queeningSq
560 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
561 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
562 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
564 // Similar to the above, but with the pawn further back
566 && file_of(wrsq) == f
568 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
569 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
570 && ( square_distance(bksq, wrsq) + tempo >= 3
571 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
572 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
573 return ScaleFactor( SCALE_FACTOR_MAX
574 - 8 * square_distance(wpsq, queeningSq)
575 - 2 * square_distance(wksq, queeningSq));
577 // If the pawn is not far advanced, and the defending king is somewhere in
578 // the pawn's path, it's probably a draw.
579 if (r <= RANK_4 && bksq > wpsq)
581 if (file_of(bksq) == file_of(wpsq))
582 return ScaleFactor(10);
583 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
584 && square_distance(wksq, bksq) > 2)
585 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
587 return SCALE_FACTOR_NONE;
591 /// K, rook and two pawns vs K, rook and one pawn. There is only a single
592 /// pattern: If the stronger side has no passed pawns and the defending king
593 /// is actively placed, the position is drawish.
595 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
597 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
598 assert(pos.piece_count(strongerSide, PAWN) == 2);
599 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
600 assert(pos.piece_count(weakerSide, PAWN) == 1);
602 Square wpsq1 = pos.piece_list(strongerSide, PAWN)[0];
603 Square wpsq2 = pos.piece_list(strongerSide, PAWN)[1];
604 Square bksq = pos.king_square(weakerSide);
606 // Does the stronger side have a passed pawn?
607 if ( pos.pawn_is_passed(strongerSide, wpsq1)
608 || pos.pawn_is_passed(strongerSide, wpsq2))
609 return SCALE_FACTOR_NONE;
611 Rank r = std::max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
613 if ( file_distance(bksq, wpsq1) <= 1
614 && file_distance(bksq, wpsq2) <= 1
615 && relative_rank(strongerSide, bksq) > r)
618 case RANK_2: return ScaleFactor(10);
619 case RANK_3: return ScaleFactor(10);
620 case RANK_4: return ScaleFactor(15);
621 case RANK_5: return ScaleFactor(20);
622 case RANK_6: return ScaleFactor(40);
623 default: assert(false);
626 return SCALE_FACTOR_NONE;
630 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
631 /// are on the same rook file and are blocked by the defending king, it's a draw.
633 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
635 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
636 assert(pos.piece_count(strongerSide, PAWN) >= 2);
637 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
638 assert(pos.piece_count(weakerSide, PAWN) == 0);
640 Square ksq = pos.king_square(weakerSide);
641 Bitboard pawns = pos.pieces(PAWN, strongerSide);
643 // Are all pawns on the 'a' file?
644 if (!(pawns & ~FileABB))
646 // Does the defending king block the pawns?
647 if ( square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
648 || ( file_of(ksq) == FILE_A
649 && !in_front_bb(strongerSide, ksq) & pawns))
650 return SCALE_FACTOR_DRAW;
652 // Are all pawns on the 'h' file?
653 else if (!(pawns & ~FileHBB))
655 // Does the defending king block the pawns?
656 if ( square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
657 || ( file_of(ksq) == FILE_H
658 && !in_front_bb(strongerSide, ksq) & pawns))
659 return SCALE_FACTOR_DRAW;
661 return SCALE_FACTOR_NONE;
665 /// K, bishop and a pawn vs K and a bishop. There are two rules: If the defending
666 /// king is somewhere along the path of the pawn, and the square of the king is
667 /// not of the same color as the stronger side's bishop, it's a draw. If the two
668 /// bishops have opposite color, it's almost always a draw.
670 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
672 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
673 assert(pos.piece_count(strongerSide, BISHOP) == 1);
674 assert(pos.piece_count(strongerSide, PAWN) == 1);
675 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
676 assert(pos.piece_count(weakerSide, BISHOP) == 1);
677 assert(pos.piece_count(weakerSide, PAWN) == 0);
679 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
680 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
681 Square weakerBishopSq = pos.piece_list(weakerSide, BISHOP)[0];
682 Square weakerKingSq = pos.king_square(weakerSide);
684 // Case 1: Defending king blocks the pawn, and cannot be driven away
685 if ( file_of(weakerKingSq) == file_of(pawnSq)
686 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
687 && ( opposite_colors(weakerKingSq, strongerBishopSq)
688 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
689 return SCALE_FACTOR_DRAW;
691 // Case 2: Opposite colored bishops
692 if (opposite_colors(strongerBishopSq, weakerBishopSq))
694 // We assume that the position is drawn in the following three situations:
696 // a. The pawn is on rank 5 or further back.
697 // b. The defending king is somewhere in the pawn's path.
698 // c. The defending bishop attacks some square along the pawn's path,
699 // and is at least three squares away from the pawn.
701 // These rules are probably not perfect, but in practice they work
704 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
705 return SCALE_FACTOR_DRAW;
708 Bitboard path = squares_in_front_of(strongerSide, pawnSq);
710 if (path & pos.pieces(KING, weakerSide))
711 return SCALE_FACTOR_DRAW;
713 if ( (pos.attacks_from<BISHOP>(weakerBishopSq) & path)
714 && square_distance(weakerBishopSq, pawnSq) >= 3)
715 return SCALE_FACTOR_DRAW;
718 return SCALE_FACTOR_NONE;
722 /// K, bishop and two pawns vs K and bishop. It detects a few basic draws with
723 /// opposite-colored bishops.
725 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
727 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
728 assert(pos.piece_count(strongerSide, BISHOP) == 1);
729 assert(pos.piece_count(strongerSide, PAWN) == 2);
730 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
731 assert(pos.piece_count(weakerSide, BISHOP) == 1);
732 assert(pos.piece_count(weakerSide, PAWN) == 0);
734 Square wbsq = pos.piece_list(strongerSide, BISHOP)[0];
735 Square bbsq = pos.piece_list(weakerSide, BISHOP)[0];
737 if (!opposite_colors(wbsq, bbsq))
738 return SCALE_FACTOR_NONE;
740 Square ksq = pos.king_square(weakerSide);
741 Square psq1 = pos.piece_list(strongerSide, PAWN)[0];
742 Square psq2 = pos.piece_list(strongerSide, PAWN)[1];
743 Rank r1 = rank_of(psq1);
744 Rank r2 = rank_of(psq2);
745 Square blockSq1, blockSq2;
747 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
749 blockSq1 = psq1 + pawn_push(strongerSide);
750 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
754 blockSq1 = psq2 + pawn_push(strongerSide);
755 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
758 switch (file_distance(psq1, psq2))
761 // Both pawns are on the same file. Easy draw if defender firmly controls
762 // some square in the frontmost pawn's path.
763 if ( file_of(ksq) == file_of(blockSq1)
764 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
765 && opposite_colors(ksq, wbsq))
766 return SCALE_FACTOR_DRAW;
768 return SCALE_FACTOR_NONE;
771 // Pawns on neighboring files. Draw if defender firmly controls the square
772 // in front of the frontmost pawn's path, and the square diagonally behind
773 // this square on the file of the other pawn.
775 && opposite_colors(ksq, wbsq)
776 && ( bbsq == blockSq2
777 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(BISHOP, weakerSide))
778 || abs(r1 - r2) >= 2))
779 return SCALE_FACTOR_DRAW;
781 else if ( ksq == blockSq2
782 && opposite_colors(ksq, wbsq)
783 && ( bbsq == blockSq1
784 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(BISHOP, weakerSide))))
785 return SCALE_FACTOR_DRAW;
787 return SCALE_FACTOR_NONE;
790 // The pawns are not on the same file or adjacent files. No scaling.
791 return SCALE_FACTOR_NONE;
796 /// K, bisop and a pawn vs K and knight. There is a single rule: If the defending
797 /// king is somewhere along the path of the pawn, and the square of the king is
798 /// not of the same color as the stronger side's bishop, it's a draw.
800 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
802 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
803 assert(pos.piece_count(strongerSide, BISHOP) == 1);
804 assert(pos.piece_count(strongerSide, PAWN) == 1);
805 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
806 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
807 assert(pos.piece_count(weakerSide, PAWN) == 0);
809 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
810 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
811 Square weakerKingSq = pos.king_square(weakerSide);
813 if ( file_of(weakerKingSq) == file_of(pawnSq)
814 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
815 && ( opposite_colors(weakerKingSq, strongerBishopSq)
816 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
817 return SCALE_FACTOR_DRAW;
819 return SCALE_FACTOR_NONE;
823 /// K, knight and a pawn vs K. There is a single rule: If the pawn is a rook pawn
824 /// on the 7th rank and the defending king prevents the pawn from advancing, the
825 /// position is drawn.
827 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
829 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame);
830 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
831 assert(pos.piece_count(strongerSide, PAWN) == 1);
832 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
833 assert(pos.piece_count(weakerSide, PAWN) == 0);
835 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
836 Square weakerKingSq = pos.king_square(weakerSide);
838 if ( pawnSq == relative_square(strongerSide, SQ_A7)
839 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
840 return SCALE_FACTOR_DRAW;
842 if ( pawnSq == relative_square(strongerSide, SQ_H7)
843 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
844 return SCALE_FACTOR_DRAW;
846 return SCALE_FACTOR_NONE;
850 /// K and a pawn vs K and a pawn. This is done by removing the weakest side's
851 /// pawn and probing the KP vs K bitbase: If the weakest side has a draw without
852 /// the pawn, she probably has at least a draw with the pawn as well. The exception
853 /// is when the stronger side's pawn is far advanced and not on a rook file; in
854 /// this case it is often possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
856 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
858 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
859 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
860 assert(pos.piece_count(WHITE, PAWN) == 1);
861 assert(pos.piece_count(BLACK, PAWN) == 1);
863 Square wksq = pos.king_square(strongerSide);
864 Square bksq = pos.king_square(weakerSide);
865 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
866 Color stm = pos.side_to_move();
868 if (strongerSide == BLACK)
876 if (file_of(wpsq) >= FILE_E)
883 // If the pawn has advanced to the fifth rank or further, and is not a
884 // rook pawn, it's too dangerous to assume that it's at least a draw.
885 if ( rank_of(wpsq) >= RANK_5
886 && file_of(wpsq) != FILE_A)
887 return SCALE_FACTOR_NONE;
889 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
890 // it's probably at least a draw even with the pawn.
891 return probe_kpk_bitbase(wksq, wpsq, bksq, stm) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;