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/>.
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 std::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, NULL).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 map((Endgame<E>*)0)[key(code, WHITE)] = new Endgame<E>(WHITE);
119 map((Endgame<E>*)0)[key(code, BLACK)] = new Endgame<E>(BLACK);
123 /// Mate with KX vs K. This function is used to evaluate positions with
124 /// King and plenty of material vs a lone king. It simply gives the
125 /// attacking side a bonus for driving the defending king towards the edge
126 /// of the board, and for keeping the distance between the two kings small.
128 Value Endgame<KXK>::operator()(const Position& pos) const {
130 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
131 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
133 // Stalemate detection with lone king
134 if ( pos.side_to_move() == weakerSide
136 && !MoveList<LEGAL>(pos).size()) {
140 Square winnerKSq = pos.king_square(strongerSide);
141 Square loserKSq = pos.king_square(weakerSide);
143 Value result = pos.non_pawn_material(strongerSide)
144 + pos.piece_count(strongerSide, PAWN) * PawnValueEndgame
145 + MateTable[loserKSq]
146 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
148 if ( pos.piece_count(strongerSide, QUEEN)
149 || pos.piece_count(strongerSide, ROOK)
150 || pos.bishop_pair(strongerSide)) {
151 result += VALUE_KNOWN_WIN;
154 return strongerSide == pos.side_to_move() ? result : -result;
158 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
159 /// defending king towards a corner square of the right color.
161 Value Endgame<KBNK>::operator()(const Position& pos) const {
163 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
164 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
165 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame + BishopValueMidgame);
166 assert(pos.piece_count(strongerSide, BISHOP) == 1);
167 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
168 assert(pos.piece_count(strongerSide, PAWN) == 0);
170 Square winnerKSq = pos.king_square(strongerSide);
171 Square loserKSq = pos.king_square(weakerSide);
172 Square bishopSquare = pos.piece_list(strongerSide, BISHOP)[0];
174 // kbnk_mate_table() tries to drive toward corners A1 or H8,
175 // if we have a bishop that cannot reach the above squares we
176 // mirror the kings so to drive enemy toward corners A8 or H1.
177 if (opposite_colors(bishopSquare, SQ_A1))
179 winnerKSq = mirror(winnerKSq);
180 loserKSq = mirror(loserKSq);
183 Value result = VALUE_KNOWN_WIN
184 + DistanceBonus[square_distance(winnerKSq, loserKSq)]
185 + KBNKMateTable[loserKSq];
187 return strongerSide == pos.side_to_move() ? result : -result;
191 /// KP vs K. This endgame is evaluated with the help of a bitbase.
193 Value Endgame<KPK>::operator()(const Position& pos) const {
195 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
196 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
197 assert(pos.piece_count(strongerSide, PAWN) == 1);
198 assert(pos.piece_count(weakerSide, PAWN) == 0);
200 Square wksq, bksq, wpsq;
203 if (strongerSide == WHITE)
205 wksq = pos.king_square(WHITE);
206 bksq = pos.king_square(BLACK);
207 wpsq = pos.piece_list(WHITE, PAWN)[0];
208 stm = pos.side_to_move();
212 wksq = ~pos.king_square(BLACK);
213 bksq = ~pos.king_square(WHITE);
214 wpsq = ~pos.piece_list(BLACK, PAWN)[0];
215 stm = ~pos.side_to_move();
218 if (file_of(wpsq) >= FILE_E)
225 if (!Bitbases::probe_kpk(wksq, wpsq, bksq, stm))
228 Value result = VALUE_KNOWN_WIN
230 + Value(rank_of(wpsq));
232 return strongerSide == pos.side_to_move() ? result : -result;
236 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
237 /// a bitbase. The function below returns drawish scores when the pawn is
238 /// far advanced with support of the king, while the attacking king is far
241 Value Endgame<KRKP>::operator()(const Position& pos) const {
243 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
244 assert(pos.piece_count(strongerSide, PAWN) == 0);
245 assert(pos.non_pawn_material(weakerSide) == 0);
246 assert(pos.piece_count(weakerSide, PAWN) == 1);
248 Square wksq, wrsq, bksq, bpsq;
249 int tempo = (pos.side_to_move() == strongerSide);
251 wksq = pos.king_square(strongerSide);
252 wrsq = pos.piece_list(strongerSide, ROOK)[0];
253 bksq = pos.king_square(weakerSide);
254 bpsq = pos.piece_list(weakerSide, PAWN)[0];
256 if (strongerSide == BLACK)
264 Square queeningSq = file_of(bpsq) | RANK_1;
267 // If the stronger side's king is in front of the pawn, it's a win
268 if (wksq < bpsq && file_of(wksq) == file_of(bpsq))
269 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
271 // If the weaker side's king is too far from the pawn and the rook,
273 else if ( square_distance(bksq, bpsq) - (tempo ^ 1) >= 3
274 && square_distance(bksq, wrsq) >= 3)
275 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
277 // If the pawn is far advanced and supported by the defending king,
278 // the position is drawish
279 else if ( rank_of(bksq) <= RANK_3
280 && square_distance(bksq, bpsq) == 1
281 && rank_of(wksq) >= RANK_4
282 && square_distance(wksq, bpsq) - tempo > 2)
283 result = Value(80 - square_distance(wksq, bpsq) * 8);
287 - Value(square_distance(wksq, bpsq + DELTA_S) * 8)
288 + Value(square_distance(bksq, bpsq + DELTA_S) * 8)
289 + Value(square_distance(bpsq, queeningSq) * 8);
291 return strongerSide == pos.side_to_move() ? result : -result;
295 /// KR vs KB. This is very simple, and always returns drawish scores. The
296 /// score is slightly bigger when the defending king is close to the edge.
298 Value Endgame<KRKB>::operator()(const Position& pos) const {
300 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
301 assert(pos.piece_count(strongerSide, PAWN) == 0);
302 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
303 assert(pos.piece_count(weakerSide, PAWN) == 0);
304 assert(pos.piece_count(weakerSide, BISHOP) == 1);
306 Value result = Value(MateTable[pos.king_square(weakerSide)]);
307 return strongerSide == pos.side_to_move() ? result : -result;
311 /// KR vs KN. The attacking side has slightly better winning chances than
312 /// in KR vs KB, particularly if the king and the knight are far apart.
314 Value Endgame<KRKN>::operator()(const Position& pos) const {
316 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
317 assert(pos.piece_count(strongerSide, PAWN) == 0);
318 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
319 assert(pos.piece_count(weakerSide, PAWN) == 0);
320 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
322 const int penalty[8] = { 0, 10, 14, 20, 30, 42, 58, 80 };
324 Square bksq = pos.king_square(weakerSide);
325 Square bnsq = pos.piece_list(weakerSide, KNIGHT)[0];
326 Value result = Value(MateTable[bksq] + penalty[square_distance(bksq, bnsq)]);
327 return strongerSide == pos.side_to_move() ? result : -result;
331 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
332 /// king a bonus for having the kings close together, and for forcing the
333 /// defending king towards the edge. If we also take care to avoid null move
334 /// for the defending side in the search, this is usually sufficient to be
335 /// able to win KQ vs KR.
337 Value Endgame<KQKR>::operator()(const Position& pos) const {
339 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
340 assert(pos.piece_count(strongerSide, PAWN) == 0);
341 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
342 assert(pos.piece_count(weakerSide, PAWN) == 0);
344 Square winnerKSq = pos.king_square(strongerSide);
345 Square loserKSq = pos.king_square(weakerSide);
347 Value result = QueenValueEndgame
349 + MateTable[loserKSq]
350 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
352 return strongerSide == pos.side_to_move() ? result : -result;
356 Value Endgame<KBBKN>::operator()(const Position& pos) const {
358 assert(pos.piece_count(strongerSide, BISHOP) == 2);
359 assert(pos.non_pawn_material(strongerSide) == 2*BishopValueMidgame);
360 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
361 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
362 assert(!pos.pieces(PAWN));
364 Value result = BishopValueEndgame;
365 Square wksq = pos.king_square(strongerSide);
366 Square bksq = pos.king_square(weakerSide);
367 Square nsq = pos.piece_list(weakerSide, KNIGHT)[0];
369 // Bonus for attacking king close to defending king
370 result += Value(DistanceBonus[square_distance(wksq, bksq)]);
372 // Bonus for driving the defending king and knight apart
373 result += Value(square_distance(bksq, nsq) * 32);
375 // Bonus for restricting the knight's mobility
376 result += Value((8 - popcount<Max15>(pos.attacks_from<KNIGHT>(nsq))) * 8);
378 return strongerSide == pos.side_to_move() ? result : -result;
382 /// K and two minors vs K and one or two minors or K and two knights against
383 /// king alone are always draw.
385 Value Endgame<KmmKm>::operator()(const Position&) const {
390 Value Endgame<KNNK>::operator()(const Position&) const {
394 /// K, bishop and one or more pawns vs K. It checks for draws with rook pawns and
395 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
396 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
399 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
401 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
402 assert(pos.piece_count(strongerSide, BISHOP) == 1);
403 assert(pos.piece_count(strongerSide, PAWN) >= 1);
405 // No assertions about the material of weakerSide, because we want draws to
406 // be detected even when the weaker side has some pawns.
408 Bitboard pawns = pos.pieces(strongerSide, PAWN);
409 File pawnFile = file_of(pos.piece_list(strongerSide, PAWN)[0]);
411 // All pawns are on a single rook file ?
412 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
413 && !(pawns & ~file_bb(pawnFile)))
415 Square bishopSq = pos.piece_list(strongerSide, BISHOP)[0];
416 Square queeningSq = relative_square(strongerSide, pawnFile | RANK_8);
417 Square kingSq = pos.king_square(weakerSide);
419 if ( opposite_colors(queeningSq, bishopSq)
420 && abs(file_of(kingSq) - pawnFile) <= 1)
422 // The bishop has the wrong color, and the defending king is on the
423 // file of the pawn(s) or the adjacent file. Find the rank of the
426 if (strongerSide == WHITE)
428 for (rank = RANK_7; !(rank_bb(rank) & pawns); rank--) {}
429 assert(rank >= RANK_2 && rank <= RANK_7);
433 for (rank = RANK_2; !(rank_bb(rank) & pawns); rank++) {}
434 rank = Rank(rank ^ 7); // HACK to get the relative rank
435 assert(rank >= RANK_2 && rank <= RANK_7);
437 // If the defending king has distance 1 to the promotion square or
438 // is placed somewhere in front of the pawn, it's a draw.
439 if ( square_distance(kingSq, queeningSq) <= 1
440 || relative_rank(strongerSide, kingSq) >= rank)
441 return SCALE_FACTOR_DRAW;
444 return SCALE_FACTOR_NONE;
448 /// K and queen vs K, rook and one or more pawns. It tests for fortress draws with
449 /// a rook on the third rank defended by a pawn.
451 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
453 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
454 assert(pos.piece_count(strongerSide, QUEEN) == 1);
455 assert(pos.piece_count(strongerSide, PAWN) == 0);
456 assert(pos.piece_count(weakerSide, ROOK) == 1);
457 assert(pos.piece_count(weakerSide, PAWN) >= 1);
459 Square kingSq = pos.king_square(weakerSide);
460 if ( relative_rank(weakerSide, kingSq) <= RANK_2
461 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
462 && (pos.pieces(weakerSide, ROOK) & rank_bb(relative_rank(weakerSide, RANK_3)))
463 && (pos.pieces(weakerSide, PAWN) & rank_bb(relative_rank(weakerSide, RANK_2)))
464 && (pos.attacks_from<KING>(kingSq) & pos.pieces(weakerSide, PAWN)))
466 Square rsq = pos.piece_list(weakerSide, ROOK)[0];
467 if (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(weakerSide, PAWN))
468 return SCALE_FACTOR_DRAW;
470 return SCALE_FACTOR_NONE;
474 /// K, rook and one pawn vs K and a rook. This function knows a handful of the
475 /// most important classes of drawn positions, but is far from perfect. It would
476 /// probably be a good idea to add more knowledge in the future.
478 /// It would also be nice to rewrite the actual code for this function,
479 /// which is mostly copied from Glaurung 1.x, and not very pretty.
481 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
483 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
484 assert(pos.piece_count(strongerSide, PAWN) == 1);
485 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
486 assert(pos.piece_count(weakerSide, PAWN) == 0);
488 Square wksq = pos.king_square(strongerSide);
489 Square wrsq = pos.piece_list(strongerSide, ROOK)[0];
490 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
491 Square bksq = pos.king_square(weakerSide);
492 Square brsq = pos.piece_list(weakerSide, ROOK)[0];
494 // Orient the board in such a way that the stronger side is white, and the
495 // pawn is on the left half of the board.
496 if (strongerSide == BLACK)
504 if (file_of(wpsq) > FILE_D)
513 File f = file_of(wpsq);
514 Rank r = rank_of(wpsq);
515 Square queeningSq = f | RANK_8;
516 int tempo = (pos.side_to_move() == strongerSide);
518 // If the pawn is not too far advanced and the defending king defends the
519 // queening square, use the third-rank defence.
521 && square_distance(bksq, queeningSq) <= 1
523 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
524 return SCALE_FACTOR_DRAW;
526 // The defending side saves a draw by checking from behind in case the pawn
527 // has advanced to the 6th rank with the king behind.
529 && square_distance(bksq, queeningSq) <= 1
530 && rank_of(wksq) + tempo <= RANK_6
531 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
532 return SCALE_FACTOR_DRAW;
535 && bksq == queeningSq
536 && rank_of(brsq) == RANK_1
537 && (!tempo || square_distance(wksq, wpsq) >= 2))
538 return SCALE_FACTOR_DRAW;
540 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
541 // and the black rook is behind the pawn.
544 && (bksq == SQ_H7 || bksq == SQ_G7)
545 && file_of(brsq) == FILE_A
546 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
547 return SCALE_FACTOR_DRAW;
549 // If the defending king blocks the pawn and the attacking king is too far
550 // away, it's a draw.
552 && bksq == wpsq + DELTA_N
553 && square_distance(wksq, wpsq) - tempo >= 2
554 && square_distance(wksq, brsq) - tempo >= 2)
555 return SCALE_FACTOR_DRAW;
557 // Pawn on the 7th rank supported by the rook from behind usually wins if the
558 // attacking king is closer to the queening square than the defending king,
559 // and the defending king cannot gain tempi by threatening the attacking rook.
562 && file_of(wrsq) == f
563 && wrsq != queeningSq
564 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
565 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
566 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
568 // Similar to the above, but with the pawn further back
570 && file_of(wrsq) == f
572 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
573 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
574 && ( square_distance(bksq, wrsq) + tempo >= 3
575 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
576 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
577 return ScaleFactor( SCALE_FACTOR_MAX
578 - 8 * square_distance(wpsq, queeningSq)
579 - 2 * square_distance(wksq, queeningSq));
581 // If the pawn is not far advanced, and the defending king is somewhere in
582 // the pawn's path, it's probably a draw.
583 if (r <= RANK_4 && bksq > wpsq)
585 if (file_of(bksq) == file_of(wpsq))
586 return ScaleFactor(10);
587 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
588 && square_distance(wksq, bksq) > 2)
589 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
591 return SCALE_FACTOR_NONE;
595 /// K, rook and two pawns vs K, rook and one pawn. There is only a single
596 /// pattern: If the stronger side has no passed pawns and the defending king
597 /// is actively placed, the position is drawish.
599 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
601 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
602 assert(pos.piece_count(strongerSide, PAWN) == 2);
603 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
604 assert(pos.piece_count(weakerSide, PAWN) == 1);
606 Square wpsq1 = pos.piece_list(strongerSide, PAWN)[0];
607 Square wpsq2 = pos.piece_list(strongerSide, PAWN)[1];
608 Square bksq = pos.king_square(weakerSide);
610 // Does the stronger side have a passed pawn?
611 if ( pos.pawn_is_passed(strongerSide, wpsq1)
612 || pos.pawn_is_passed(strongerSide, wpsq2))
613 return SCALE_FACTOR_NONE;
615 Rank r = std::max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
617 if ( file_distance(bksq, wpsq1) <= 1
618 && file_distance(bksq, wpsq2) <= 1
619 && relative_rank(strongerSide, bksq) > r)
622 case RANK_2: return ScaleFactor(10);
623 case RANK_3: return ScaleFactor(10);
624 case RANK_4: return ScaleFactor(15);
625 case RANK_5: return ScaleFactor(20);
626 case RANK_6: return ScaleFactor(40);
627 default: assert(false);
630 return SCALE_FACTOR_NONE;
634 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
635 /// are on the same rook file and are blocked by the defending king, it's a draw.
637 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
639 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
640 assert(pos.piece_count(strongerSide, PAWN) >= 2);
641 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
642 assert(pos.piece_count(weakerSide, PAWN) == 0);
644 Square ksq = pos.king_square(weakerSide);
645 Bitboard pawns = pos.pieces(strongerSide, PAWN);
647 // Are all pawns on the 'a' file?
648 if (!(pawns & ~FileABB))
650 // Does the defending king block the pawns?
651 if ( square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
652 || ( file_of(ksq) == FILE_A
653 && !in_front_bb(strongerSide, ksq) & pawns))
654 return SCALE_FACTOR_DRAW;
656 // Are all pawns on the 'h' file?
657 else if (!(pawns & ~FileHBB))
659 // Does the defending king block the pawns?
660 if ( square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
661 || ( file_of(ksq) == FILE_H
662 && !in_front_bb(strongerSide, ksq) & pawns))
663 return SCALE_FACTOR_DRAW;
665 return SCALE_FACTOR_NONE;
669 /// K, bishop and a pawn vs K and a bishop. There are two rules: If the defending
670 /// king is somewhere along the path of the pawn, and the square of the king is
671 /// not of the same color as the stronger side's bishop, it's a draw. If the two
672 /// bishops have opposite color, it's almost always a draw.
674 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
676 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
677 assert(pos.piece_count(strongerSide, BISHOP) == 1);
678 assert(pos.piece_count(strongerSide, PAWN) == 1);
679 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
680 assert(pos.piece_count(weakerSide, BISHOP) == 1);
681 assert(pos.piece_count(weakerSide, PAWN) == 0);
683 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
684 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
685 Square weakerBishopSq = pos.piece_list(weakerSide, BISHOP)[0];
686 Square weakerKingSq = pos.king_square(weakerSide);
688 // Case 1: Defending king blocks the pawn, and cannot be driven away
689 if ( file_of(weakerKingSq) == file_of(pawnSq)
690 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
691 && ( opposite_colors(weakerKingSq, strongerBishopSq)
692 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
693 return SCALE_FACTOR_DRAW;
695 // Case 2: Opposite colored bishops
696 if (opposite_colors(strongerBishopSq, weakerBishopSq))
698 // We assume that the position is drawn in the following three situations:
700 // a. The pawn is on rank 5 or further back.
701 // b. The defending king is somewhere in the pawn's path.
702 // c. The defending bishop attacks some square along the pawn's path,
703 // and is at least three squares away from the pawn.
705 // These rules are probably not perfect, but in practice they work
708 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
709 return SCALE_FACTOR_DRAW;
712 Bitboard path = forward_bb(strongerSide, pawnSq);
714 if (path & pos.pieces(weakerSide, KING))
715 return SCALE_FACTOR_DRAW;
717 if ( (pos.attacks_from<BISHOP>(weakerBishopSq) & path)
718 && square_distance(weakerBishopSq, pawnSq) >= 3)
719 return SCALE_FACTOR_DRAW;
722 return SCALE_FACTOR_NONE;
726 /// K, bishop and two pawns vs K and bishop. It detects a few basic draws with
727 /// opposite-colored bishops.
729 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
731 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
732 assert(pos.piece_count(strongerSide, BISHOP) == 1);
733 assert(pos.piece_count(strongerSide, PAWN) == 2);
734 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
735 assert(pos.piece_count(weakerSide, BISHOP) == 1);
736 assert(pos.piece_count(weakerSide, PAWN) == 0);
738 Square wbsq = pos.piece_list(strongerSide, BISHOP)[0];
739 Square bbsq = pos.piece_list(weakerSide, BISHOP)[0];
741 if (!opposite_colors(wbsq, bbsq))
742 return SCALE_FACTOR_NONE;
744 Square ksq = pos.king_square(weakerSide);
745 Square psq1 = pos.piece_list(strongerSide, PAWN)[0];
746 Square psq2 = pos.piece_list(strongerSide, PAWN)[1];
747 Rank r1 = rank_of(psq1);
748 Rank r2 = rank_of(psq2);
749 Square blockSq1, blockSq2;
751 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
753 blockSq1 = psq1 + pawn_push(strongerSide);
754 blockSq2 = file_of(psq2) | rank_of(psq1);
758 blockSq1 = psq2 + pawn_push(strongerSide);
759 blockSq2 = file_of(psq1) | rank_of(psq2);
762 switch (file_distance(psq1, psq2))
765 // Both pawns are on the same file. Easy draw if defender firmly controls
766 // some square in the frontmost pawn's path.
767 if ( file_of(ksq) == file_of(blockSq1)
768 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
769 && opposite_colors(ksq, wbsq))
770 return SCALE_FACTOR_DRAW;
772 return SCALE_FACTOR_NONE;
775 // Pawns on adjacent files. Draw if defender firmly controls the square
776 // in front of the frontmost pawn's path, and the square diagonally behind
777 // this square on the file of the other pawn.
779 && opposite_colors(ksq, wbsq)
780 && ( bbsq == blockSq2
781 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakerSide, BISHOP))
782 || abs(r1 - r2) >= 2))
783 return SCALE_FACTOR_DRAW;
785 else if ( ksq == blockSq2
786 && opposite_colors(ksq, wbsq)
787 && ( bbsq == blockSq1
788 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakerSide, BISHOP))))
789 return SCALE_FACTOR_DRAW;
791 return SCALE_FACTOR_NONE;
794 // The pawns are not on the same file or adjacent files. No scaling.
795 return SCALE_FACTOR_NONE;
800 /// K, bisop and a pawn vs K and knight. There is a single rule: If the defending
801 /// king is somewhere along the path of the pawn, and the square of the king is
802 /// not of the same color as the stronger side's bishop, it's a draw.
804 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
806 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
807 assert(pos.piece_count(strongerSide, BISHOP) == 1);
808 assert(pos.piece_count(strongerSide, PAWN) == 1);
809 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
810 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
811 assert(pos.piece_count(weakerSide, PAWN) == 0);
813 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
814 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
815 Square weakerKingSq = pos.king_square(weakerSide);
817 if ( file_of(weakerKingSq) == file_of(pawnSq)
818 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
819 && ( opposite_colors(weakerKingSq, strongerBishopSq)
820 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
821 return SCALE_FACTOR_DRAW;
823 return SCALE_FACTOR_NONE;
827 /// K, knight and a pawn vs K. There is a single rule: If the pawn is a rook pawn
828 /// on the 7th rank and the defending king prevents the pawn from advancing, the
829 /// position is drawn.
831 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
833 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame);
834 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
835 assert(pos.piece_count(strongerSide, PAWN) == 1);
836 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
837 assert(pos.piece_count(weakerSide, PAWN) == 0);
839 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
840 Square weakerKingSq = pos.king_square(weakerSide);
842 if ( pawnSq == relative_square(strongerSide, SQ_A7)
843 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
844 return SCALE_FACTOR_DRAW;
846 if ( pawnSq == relative_square(strongerSide, SQ_H7)
847 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
848 return SCALE_FACTOR_DRAW;
850 return SCALE_FACTOR_NONE;
854 /// K and a pawn vs K and a pawn. This is done by removing the weakest side's
855 /// pawn and probing the KP vs K bitbase: If the weakest side has a draw without
856 /// the pawn, she probably has at least a draw with the pawn as well. The exception
857 /// is when the stronger side's pawn is far advanced and not on a rook file; in
858 /// this case it is often possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
860 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
862 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
863 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
864 assert(pos.piece_count(WHITE, PAWN) == 1);
865 assert(pos.piece_count(BLACK, PAWN) == 1);
867 Square wksq = pos.king_square(strongerSide);
868 Square bksq = pos.king_square(weakerSide);
869 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
870 Color stm = pos.side_to_move();
872 if (strongerSide == BLACK)
880 if (file_of(wpsq) >= FILE_E)
887 // If the pawn has advanced to the fifth rank or further, and is not a
888 // rook pawn, it's too dangerous to assume that it's at least a draw.
889 if ( rank_of(wpsq) >= RANK_5
890 && file_of(wpsq) != FILE_A)
891 return SCALE_FACTOR_NONE;
893 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
894 // it's probably at least a draw even with the pawn.
895 return Bitbases::probe_kpk(wksq, wpsq, bksq, stm) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;