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 // Stalemate detection with lone king
137 if ( pos.side_to_move() == weakerSide
139 && !MoveList<MV_LEGAL>(pos).size()) {
143 Square winnerKSq = pos.king_square(strongerSide);
144 Square loserKSq = pos.king_square(weakerSide);
146 Value result = pos.non_pawn_material(strongerSide)
147 + pos.piece_count(strongerSide, PAWN) * PawnValueEndgame
148 + MateTable[loserKSq]
149 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
151 if ( pos.piece_count(strongerSide, QUEEN)
152 || pos.piece_count(strongerSide, ROOK)
153 || pos.both_color_bishops(strongerSide)) {
154 result += VALUE_KNOWN_WIN;
157 return strongerSide == pos.side_to_move() ? result : -result;
161 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
162 /// defending king towards a corner square of the right color.
164 Value Endgame<KBNK>::operator()(const Position& pos) const {
166 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
167 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
168 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame + BishopValueMidgame);
169 assert(pos.piece_count(strongerSide, BISHOP) == 1);
170 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
171 assert(pos.piece_count(strongerSide, PAWN) == 0);
173 Square winnerKSq = pos.king_square(strongerSide);
174 Square loserKSq = pos.king_square(weakerSide);
175 Square bishopSquare = pos.piece_list(strongerSide, BISHOP)[0];
177 // kbnk_mate_table() tries to drive toward corners A1 or H8,
178 // if we have a bishop that cannot reach the above squares we
179 // mirror the kings so to drive enemy toward corners A8 or H1.
180 if (opposite_colors(bishopSquare, SQ_A1))
182 winnerKSq = mirror(winnerKSq);
183 loserKSq = mirror(loserKSq);
186 Value result = VALUE_KNOWN_WIN
187 + DistanceBonus[square_distance(winnerKSq, loserKSq)]
188 + KBNKMateTable[loserKSq];
190 return strongerSide == pos.side_to_move() ? result : -result;
194 /// KP vs K. This endgame is evaluated with the help of a bitbase.
196 Value Endgame<KPK>::operator()(const Position& pos) const {
198 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
199 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
200 assert(pos.piece_count(strongerSide, PAWN) == 1);
201 assert(pos.piece_count(weakerSide, PAWN) == 0);
203 Square wksq, bksq, wpsq;
206 if (strongerSide == WHITE)
208 wksq = pos.king_square(WHITE);
209 bksq = pos.king_square(BLACK);
210 wpsq = pos.piece_list(WHITE, PAWN)[0];
211 stm = pos.side_to_move();
215 wksq = ~pos.king_square(BLACK);
216 bksq = ~pos.king_square(WHITE);
217 wpsq = ~pos.piece_list(BLACK, PAWN)[0];
218 stm = ~pos.side_to_move();
221 if (file_of(wpsq) >= FILE_E)
228 if (!probe_kpk_bitbase(wksq, wpsq, bksq, stm))
231 Value result = VALUE_KNOWN_WIN
233 + Value(rank_of(wpsq));
235 return strongerSide == pos.side_to_move() ? result : -result;
239 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
240 /// a bitbase. The function below returns drawish scores when the pawn is
241 /// far advanced with support of the king, while the attacking king is far
244 Value Endgame<KRKP>::operator()(const Position& pos) const {
246 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
247 assert(pos.piece_count(strongerSide, PAWN) == 0);
248 assert(pos.non_pawn_material(weakerSide) == 0);
249 assert(pos.piece_count(weakerSide, PAWN) == 1);
251 Square wksq, wrsq, bksq, bpsq;
252 int tempo = (pos.side_to_move() == strongerSide);
254 wksq = pos.king_square(strongerSide);
255 wrsq = pos.piece_list(strongerSide, ROOK)[0];
256 bksq = pos.king_square(weakerSide);
257 bpsq = pos.piece_list(weakerSide, PAWN)[0];
259 if (strongerSide == BLACK)
267 Square queeningSq = make_square(file_of(bpsq), RANK_1);
270 // If the stronger side's king is in front of the pawn, it's a win
271 if (wksq < bpsq && file_of(wksq) == file_of(bpsq))
272 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
274 // If the weaker side's king is too far from the pawn and the rook,
276 else if ( square_distance(bksq, bpsq) - (tempo ^ 1) >= 3
277 && square_distance(bksq, wrsq) >= 3)
278 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
280 // If the pawn is far advanced and supported by the defending king,
281 // the position is drawish
282 else if ( rank_of(bksq) <= RANK_3
283 && square_distance(bksq, bpsq) == 1
284 && rank_of(wksq) >= RANK_4
285 && square_distance(wksq, bpsq) - tempo > 2)
286 result = Value(80 - square_distance(wksq, bpsq) * 8);
290 - Value(square_distance(wksq, bpsq + DELTA_S) * 8)
291 + Value(square_distance(bksq, bpsq + DELTA_S) * 8)
292 + Value(square_distance(bpsq, queeningSq) * 8);
294 return strongerSide == pos.side_to_move() ? result : -result;
298 /// KR vs KB. This is very simple, and always returns drawish scores. The
299 /// score is slightly bigger when the defending king is close to the edge.
301 Value Endgame<KRKB>::operator()(const Position& pos) const {
303 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
304 assert(pos.piece_count(strongerSide, PAWN) == 0);
305 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
306 assert(pos.piece_count(weakerSide, PAWN) == 0);
307 assert(pos.piece_count(weakerSide, BISHOP) == 1);
309 Value result = Value(MateTable[pos.king_square(weakerSide)]);
310 return strongerSide == pos.side_to_move() ? result : -result;
314 /// KR vs KN. The attacking side has slightly better winning chances than
315 /// in KR vs KB, particularly if the king and the knight are far apart.
317 Value Endgame<KRKN>::operator()(const Position& pos) const {
319 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
320 assert(pos.piece_count(strongerSide, PAWN) == 0);
321 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
322 assert(pos.piece_count(weakerSide, PAWN) == 0);
323 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
325 const int penalty[8] = { 0, 10, 14, 20, 30, 42, 58, 80 };
327 Square bksq = pos.king_square(weakerSide);
328 Square bnsq = pos.piece_list(weakerSide, KNIGHT)[0];
329 Value result = Value(MateTable[bksq] + penalty[square_distance(bksq, bnsq)]);
330 return strongerSide == pos.side_to_move() ? result : -result;
334 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
335 /// king a bonus for having the kings close together, and for forcing the
336 /// defending king towards the edge. If we also take care to avoid null move
337 /// for the defending side in the search, this is usually sufficient to be
338 /// able to win KQ vs KR.
340 Value Endgame<KQKR>::operator()(const Position& pos) const {
342 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
343 assert(pos.piece_count(strongerSide, PAWN) == 0);
344 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
345 assert(pos.piece_count(weakerSide, PAWN) == 0);
347 Square winnerKSq = pos.king_square(strongerSide);
348 Square loserKSq = pos.king_square(weakerSide);
350 Value result = QueenValueEndgame
352 + MateTable[loserKSq]
353 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
355 return strongerSide == pos.side_to_move() ? result : -result;
359 Value Endgame<KBBKN>::operator()(const Position& pos) const {
361 assert(pos.piece_count(strongerSide, BISHOP) == 2);
362 assert(pos.non_pawn_material(strongerSide) == 2*BishopValueMidgame);
363 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
364 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
365 assert(!pos.pieces(PAWN));
367 Value result = BishopValueEndgame;
368 Square wksq = pos.king_square(strongerSide);
369 Square bksq = pos.king_square(weakerSide);
370 Square nsq = pos.piece_list(weakerSide, KNIGHT)[0];
372 // Bonus for attacking king close to defending king
373 result += Value(DistanceBonus[square_distance(wksq, bksq)]);
375 // Bonus for driving the defending king and knight apart
376 result += Value(square_distance(bksq, nsq) * 32);
378 // Bonus for restricting the knight's mobility
379 result += Value((8 - popcount<Max15>(pos.attacks_from<KNIGHT>(nsq))) * 8);
381 return strongerSide == pos.side_to_move() ? result : -result;
385 /// K and two minors vs K and one or two minors or K and two knights against
386 /// king alone are always draw.
388 Value Endgame<KmmKm>::operator()(const Position&) const {
393 Value Endgame<KNNK>::operator()(const Position&) const {
397 /// K, bishop and one or more pawns vs K. It checks for draws with rook pawns and
398 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
399 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
402 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
404 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
405 assert(pos.piece_count(strongerSide, BISHOP) == 1);
406 assert(pos.piece_count(strongerSide, PAWN) >= 1);
408 // No assertions about the material of weakerSide, because we want draws to
409 // be detected even when the weaker side has some pawns.
411 Bitboard pawns = pos.pieces(PAWN, strongerSide);
412 File pawnFile = file_of(pos.piece_list(strongerSide, PAWN)[0]);
414 // All pawns are on a single rook file ?
415 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
416 && !(pawns & ~file_bb(pawnFile)))
418 Square bishopSq = pos.piece_list(strongerSide, BISHOP)[0];
419 Square queeningSq = relative_square(strongerSide, make_square(pawnFile, RANK_8));
420 Square kingSq = pos.king_square(weakerSide);
422 if ( opposite_colors(queeningSq, bishopSq)
423 && abs(file_of(kingSq) - pawnFile) <= 1)
425 // The bishop has the wrong color, and the defending king is on the
426 // file of the pawn(s) or the adjacent file. Find the rank of the
429 if (strongerSide == WHITE)
431 for (rank = RANK_7; !(rank_bb(rank) & pawns); rank--) {}
432 assert(rank >= RANK_2 && rank <= RANK_7);
436 for (rank = RANK_2; !(rank_bb(rank) & pawns); rank++) {}
437 rank = Rank(rank ^ 7); // HACK to get the relative rank
438 assert(rank >= RANK_2 && rank <= RANK_7);
440 // If the defending king has distance 1 to the promotion square or
441 // is placed somewhere in front of the pawn, it's a draw.
442 if ( square_distance(kingSq, queeningSq) <= 1
443 || relative_rank(strongerSide, kingSq) >= rank)
444 return SCALE_FACTOR_DRAW;
447 return SCALE_FACTOR_NONE;
451 /// K and queen vs K, rook and one or more pawns. It tests for fortress draws with
452 /// a rook on the third rank defended by a pawn.
454 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
456 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
457 assert(pos.piece_count(strongerSide, QUEEN) == 1);
458 assert(pos.piece_count(strongerSide, PAWN) == 0);
459 assert(pos.piece_count(weakerSide, ROOK) == 1);
460 assert(pos.piece_count(weakerSide, PAWN) >= 1);
462 Square kingSq = pos.king_square(weakerSide);
463 if ( relative_rank(weakerSide, kingSq) <= RANK_2
464 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
465 && (pos.pieces(ROOK, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_3)))
466 && (pos.pieces(PAWN, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_2)))
467 && (pos.attacks_from<KING>(kingSq) & pos.pieces(PAWN, weakerSide)))
469 Square rsq = pos.piece_list(weakerSide, ROOK)[0];
470 if (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(PAWN, weakerSide))
471 return SCALE_FACTOR_DRAW;
473 return SCALE_FACTOR_NONE;
477 /// K, rook and one pawn vs K and a rook. This function knows a handful of the
478 /// most important classes of drawn positions, but is far from perfect. It would
479 /// probably be a good idea to add more knowledge in the future.
481 /// It would also be nice to rewrite the actual code for this function,
482 /// which is mostly copied from Glaurung 1.x, and not very pretty.
484 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
486 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
487 assert(pos.piece_count(strongerSide, PAWN) == 1);
488 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
489 assert(pos.piece_count(weakerSide, PAWN) == 0);
491 Square wksq = pos.king_square(strongerSide);
492 Square wrsq = pos.piece_list(strongerSide, ROOK)[0];
493 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
494 Square bksq = pos.king_square(weakerSide);
495 Square brsq = pos.piece_list(weakerSide, ROOK)[0];
497 // Orient the board in such a way that the stronger side is white, and the
498 // pawn is on the left half of the board.
499 if (strongerSide == BLACK)
507 if (file_of(wpsq) > FILE_D)
516 File f = file_of(wpsq);
517 Rank r = rank_of(wpsq);
518 Square queeningSq = make_square(f, RANK_8);
519 int tempo = (pos.side_to_move() == strongerSide);
521 // If the pawn is not too far advanced and the defending king defends the
522 // queening square, use the third-rank defence.
524 && square_distance(bksq, queeningSq) <= 1
526 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
527 return SCALE_FACTOR_DRAW;
529 // The defending side saves a draw by checking from behind in case the pawn
530 // has advanced to the 6th rank with the king behind.
532 && square_distance(bksq, queeningSq) <= 1
533 && rank_of(wksq) + tempo <= RANK_6
534 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
535 return SCALE_FACTOR_DRAW;
538 && bksq == queeningSq
539 && rank_of(brsq) == RANK_1
540 && (!tempo || square_distance(wksq, wpsq) >= 2))
541 return SCALE_FACTOR_DRAW;
543 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
544 // and the black rook is behind the pawn.
547 && (bksq == SQ_H7 || bksq == SQ_G7)
548 && file_of(brsq) == FILE_A
549 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
550 return SCALE_FACTOR_DRAW;
552 // If the defending king blocks the pawn and the attacking king is too far
553 // away, it's a draw.
555 && bksq == wpsq + DELTA_N
556 && square_distance(wksq, wpsq) - tempo >= 2
557 && square_distance(wksq, brsq) - tempo >= 2)
558 return SCALE_FACTOR_DRAW;
560 // Pawn on the 7th rank supported by the rook from behind usually wins if the
561 // attacking king is closer to the queening square than the defending king,
562 // and the defending king cannot gain tempi by threatening the attacking rook.
565 && file_of(wrsq) == f
566 && wrsq != queeningSq
567 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
568 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
569 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
571 // Similar to the above, but with the pawn further back
573 && file_of(wrsq) == f
575 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
576 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
577 && ( square_distance(bksq, wrsq) + tempo >= 3
578 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
579 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
580 return ScaleFactor( SCALE_FACTOR_MAX
581 - 8 * square_distance(wpsq, queeningSq)
582 - 2 * square_distance(wksq, queeningSq));
584 // If the pawn is not far advanced, and the defending king is somewhere in
585 // the pawn's path, it's probably a draw.
586 if (r <= RANK_4 && bksq > wpsq)
588 if (file_of(bksq) == file_of(wpsq))
589 return ScaleFactor(10);
590 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
591 && square_distance(wksq, bksq) > 2)
592 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
594 return SCALE_FACTOR_NONE;
598 /// K, rook and two pawns vs K, rook and one pawn. There is only a single
599 /// pattern: If the stronger side has no passed pawns and the defending king
600 /// is actively placed, the position is drawish.
602 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
604 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
605 assert(pos.piece_count(strongerSide, PAWN) == 2);
606 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
607 assert(pos.piece_count(weakerSide, PAWN) == 1);
609 Square wpsq1 = pos.piece_list(strongerSide, PAWN)[0];
610 Square wpsq2 = pos.piece_list(strongerSide, PAWN)[1];
611 Square bksq = pos.king_square(weakerSide);
613 // Does the stronger side have a passed pawn?
614 if ( pos.pawn_is_passed(strongerSide, wpsq1)
615 || pos.pawn_is_passed(strongerSide, wpsq2))
616 return SCALE_FACTOR_NONE;
618 Rank r = std::max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
620 if ( file_distance(bksq, wpsq1) <= 1
621 && file_distance(bksq, wpsq2) <= 1
622 && relative_rank(strongerSide, bksq) > r)
625 case RANK_2: return ScaleFactor(10);
626 case RANK_3: return ScaleFactor(10);
627 case RANK_4: return ScaleFactor(15);
628 case RANK_5: return ScaleFactor(20);
629 case RANK_6: return ScaleFactor(40);
630 default: assert(false);
633 return SCALE_FACTOR_NONE;
637 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
638 /// are on the same rook file and are blocked by the defending king, it's a draw.
640 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
642 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
643 assert(pos.piece_count(strongerSide, PAWN) >= 2);
644 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
645 assert(pos.piece_count(weakerSide, PAWN) == 0);
647 Square ksq = pos.king_square(weakerSide);
648 Bitboard pawns = pos.pieces(PAWN, strongerSide);
650 // Are all pawns on the 'a' file?
651 if (!(pawns & ~FileABB))
653 // Does the defending king block the pawns?
654 if ( square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
655 || ( file_of(ksq) == FILE_A
656 && !in_front_bb(strongerSide, ksq) & pawns))
657 return SCALE_FACTOR_DRAW;
659 // Are all pawns on the 'h' file?
660 else if (!(pawns & ~FileHBB))
662 // Does the defending king block the pawns?
663 if ( square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
664 || ( file_of(ksq) == FILE_H
665 && !in_front_bb(strongerSide, ksq) & pawns))
666 return SCALE_FACTOR_DRAW;
668 return SCALE_FACTOR_NONE;
672 /// K, bishop and a pawn vs K and a bishop. There are two rules: If the defending
673 /// king is somewhere along the path of the pawn, and the square of the king is
674 /// not of the same color as the stronger side's bishop, it's a draw. If the two
675 /// bishops have opposite color, it's almost always a draw.
677 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
679 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
680 assert(pos.piece_count(strongerSide, BISHOP) == 1);
681 assert(pos.piece_count(strongerSide, PAWN) == 1);
682 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
683 assert(pos.piece_count(weakerSide, BISHOP) == 1);
684 assert(pos.piece_count(weakerSide, PAWN) == 0);
686 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
687 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
688 Square weakerBishopSq = pos.piece_list(weakerSide, BISHOP)[0];
689 Square weakerKingSq = pos.king_square(weakerSide);
691 // Case 1: Defending king blocks the pawn, and cannot be driven away
692 if ( file_of(weakerKingSq) == file_of(pawnSq)
693 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
694 && ( opposite_colors(weakerKingSq, strongerBishopSq)
695 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
696 return SCALE_FACTOR_DRAW;
698 // Case 2: Opposite colored bishops
699 if (opposite_colors(strongerBishopSq, weakerBishopSq))
701 // We assume that the position is drawn in the following three situations:
703 // a. The pawn is on rank 5 or further back.
704 // b. The defending king is somewhere in the pawn's path.
705 // c. The defending bishop attacks some square along the pawn's path,
706 // and is at least three squares away from the pawn.
708 // These rules are probably not perfect, but in practice they work
711 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
712 return SCALE_FACTOR_DRAW;
715 Bitboard path = squares_in_front_of(strongerSide, pawnSq);
717 if (path & pos.pieces(KING, weakerSide))
718 return SCALE_FACTOR_DRAW;
720 if ( (pos.attacks_from<BISHOP>(weakerBishopSq) & path)
721 && square_distance(weakerBishopSq, pawnSq) >= 3)
722 return SCALE_FACTOR_DRAW;
725 return SCALE_FACTOR_NONE;
729 /// K, bishop and two pawns vs K and bishop. It detects a few basic draws with
730 /// opposite-colored bishops.
732 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
734 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
735 assert(pos.piece_count(strongerSide, BISHOP) == 1);
736 assert(pos.piece_count(strongerSide, PAWN) == 2);
737 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
738 assert(pos.piece_count(weakerSide, BISHOP) == 1);
739 assert(pos.piece_count(weakerSide, PAWN) == 0);
741 Square wbsq = pos.piece_list(strongerSide, BISHOP)[0];
742 Square bbsq = pos.piece_list(weakerSide, BISHOP)[0];
744 if (!opposite_colors(wbsq, bbsq))
745 return SCALE_FACTOR_NONE;
747 Square ksq = pos.king_square(weakerSide);
748 Square psq1 = pos.piece_list(strongerSide, PAWN)[0];
749 Square psq2 = pos.piece_list(strongerSide, PAWN)[1];
750 Rank r1 = rank_of(psq1);
751 Rank r2 = rank_of(psq2);
752 Square blockSq1, blockSq2;
754 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
756 blockSq1 = psq1 + pawn_push(strongerSide);
757 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
761 blockSq1 = psq2 + pawn_push(strongerSide);
762 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
765 switch (file_distance(psq1, psq2))
768 // Both pawns are on the same file. Easy draw if defender firmly controls
769 // some square in the frontmost pawn's path.
770 if ( file_of(ksq) == file_of(blockSq1)
771 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
772 && opposite_colors(ksq, wbsq))
773 return SCALE_FACTOR_DRAW;
775 return SCALE_FACTOR_NONE;
778 // Pawns on adjacent files. Draw if defender firmly controls the square
779 // in front of the frontmost pawn's path, and the square diagonally behind
780 // this square on the file of the other pawn.
782 && opposite_colors(ksq, wbsq)
783 && ( bbsq == blockSq2
784 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(BISHOP, weakerSide))
785 || abs(r1 - r2) >= 2))
786 return SCALE_FACTOR_DRAW;
788 else if ( ksq == blockSq2
789 && opposite_colors(ksq, wbsq)
790 && ( bbsq == blockSq1
791 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(BISHOP, weakerSide))))
792 return SCALE_FACTOR_DRAW;
794 return SCALE_FACTOR_NONE;
797 // The pawns are not on the same file or adjacent files. No scaling.
798 return SCALE_FACTOR_NONE;
803 /// K, bisop and a pawn vs K and knight. There is a single rule: If the defending
804 /// king is somewhere along the path of the pawn, and the square of the king is
805 /// not of the same color as the stronger side's bishop, it's a draw.
807 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
809 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
810 assert(pos.piece_count(strongerSide, BISHOP) == 1);
811 assert(pos.piece_count(strongerSide, PAWN) == 1);
812 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
813 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
814 assert(pos.piece_count(weakerSide, PAWN) == 0);
816 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
817 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
818 Square weakerKingSq = pos.king_square(weakerSide);
820 if ( file_of(weakerKingSq) == file_of(pawnSq)
821 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
822 && ( opposite_colors(weakerKingSq, strongerBishopSq)
823 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
824 return SCALE_FACTOR_DRAW;
826 return SCALE_FACTOR_NONE;
830 /// K, knight and a pawn vs K. There is a single rule: If the pawn is a rook pawn
831 /// on the 7th rank and the defending king prevents the pawn from advancing, the
832 /// position is drawn.
834 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
836 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame);
837 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
838 assert(pos.piece_count(strongerSide, PAWN) == 1);
839 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
840 assert(pos.piece_count(weakerSide, PAWN) == 0);
842 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
843 Square weakerKingSq = pos.king_square(weakerSide);
845 if ( pawnSq == relative_square(strongerSide, SQ_A7)
846 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
847 return SCALE_FACTOR_DRAW;
849 if ( pawnSq == relative_square(strongerSide, SQ_H7)
850 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
851 return SCALE_FACTOR_DRAW;
853 return SCALE_FACTOR_NONE;
857 /// K and a pawn vs K and a pawn. This is done by removing the weakest side's
858 /// pawn and probing the KP vs K bitbase: If the weakest side has a draw without
859 /// the pawn, she probably has at least a draw with the pawn as well. The exception
860 /// is when the stronger side's pawn is far advanced and not on a rook file; in
861 /// this case it is often possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
863 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
865 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
866 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
867 assert(pos.piece_count(WHITE, PAWN) == 1);
868 assert(pos.piece_count(BLACK, PAWN) == 1);
870 Square wksq = pos.king_square(strongerSide);
871 Square bksq = pos.king_square(weakerSide);
872 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
873 Color stm = pos.side_to_move();
875 if (strongerSide == BLACK)
883 if (file_of(wpsq) >= FILE_E)
890 // If the pawn has advanced to the fifth rank or further, and is not a
891 // rook pawn, it's too dangerous to assume that it's at least a draw.
892 if ( rank_of(wpsq) >= RANK_5
893 && file_of(wpsq) != FILE_A)
894 return SCALE_FACTOR_NONE;
896 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
897 // it's probably at least a draw even with the pawn.
898 return probe_kpk_bitbase(wksq, wpsq, bksq, stm) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;