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[SQUARE_NB] = {
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[SQUARE_NB] = {
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() {
106 add<KBPPKB>("KBPPKB");
107 add<KRPPKRP>("KRPPKRP");
110 Endgames::~Endgames() {
112 for_each(m1.begin(), m1.end(), delete_endgame<M1>);
113 for_each(m2.begin(), m2.end(), delete_endgame<M2>);
116 template<EndgameType E>
117 void Endgames::add(const string& code) {
119 map((Endgame<E>*)0)[key(code, WHITE)] = new Endgame<E>(WHITE);
120 map((Endgame<E>*)0)[key(code, BLACK)] = new Endgame<E>(BLACK);
124 /// Mate with KX vs K. This function is used to evaluate positions with
125 /// King and plenty of material vs a lone king. It simply gives the
126 /// attacking side a bonus for driving the defending king towards the edge
127 /// of the board, and for keeping the distance between the two kings small.
129 Value Endgame<KXK>::operator()(const Position& pos) const {
131 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
132 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
134 // Stalemate detection with lone king
135 if ( pos.side_to_move() == weakerSide
137 && !MoveList<LEGAL>(pos).size()) {
141 Square winnerKSq = pos.king_square(strongerSide);
142 Square loserKSq = pos.king_square(weakerSide);
144 Value result = pos.non_pawn_material(strongerSide)
145 + pos.piece_count(strongerSide, PAWN) * PawnValueEg
146 + MateTable[loserKSq]
147 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
149 if ( pos.piece_count(strongerSide, QUEEN)
150 || pos.piece_count(strongerSide, ROOK)
151 || pos.bishop_pair(strongerSide)) {
152 result += VALUE_KNOWN_WIN;
155 return strongerSide == pos.side_to_move() ? result : -result;
159 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
160 /// defending king towards a corner square of the right color.
162 Value Endgame<KBNK>::operator()(const Position& pos) const {
164 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
165 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
166 assert(pos.non_pawn_material(strongerSide) == KnightValueMg + BishopValueMg);
167 assert(pos.piece_count(strongerSide, BISHOP) == 1);
168 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
169 assert(pos.piece_count(strongerSide, PAWN) == 0);
171 Square winnerKSq = pos.king_square(strongerSide);
172 Square loserKSq = pos.king_square(weakerSide);
173 Square bishopSq = pos.piece_list(strongerSide, BISHOP)[0];
175 // kbnk_mate_table() tries to drive toward corners A1 or H8,
176 // if we have a bishop that cannot reach the above squares we
177 // mirror the kings so to drive enemy toward corners A8 or H1.
178 if (opposite_colors(bishopSq, SQ_A1))
180 winnerKSq = mirror(winnerKSq);
181 loserKSq = mirror(loserKSq);
184 Value result = VALUE_KNOWN_WIN
185 + DistanceBonus[square_distance(winnerKSq, loserKSq)]
186 + KBNKMateTable[loserKSq];
188 return strongerSide == pos.side_to_move() ? result : -result;
192 /// KP vs K. This endgame is evaluated with the help of a bitbase.
194 Value Endgame<KPK>::operator()(const Position& pos) const {
196 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
197 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
198 assert(pos.piece_count(strongerSide, PAWN) == 1);
199 assert(pos.piece_count(weakerSide, PAWN) == 0);
201 Square wksq, bksq, wpsq;
204 if (strongerSide == WHITE)
206 wksq = pos.king_square(WHITE);
207 bksq = pos.king_square(BLACK);
208 wpsq = pos.piece_list(WHITE, PAWN)[0];
209 stm = pos.side_to_move();
213 wksq = ~pos.king_square(BLACK);
214 bksq = ~pos.king_square(WHITE);
215 wpsq = ~pos.piece_list(BLACK, PAWN)[0];
216 stm = ~pos.side_to_move();
219 if (file_of(wpsq) >= FILE_E)
226 if (!Bitbases::probe_kpk(wksq, wpsq, bksq, stm))
229 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(wpsq));
231 return strongerSide == pos.side_to_move() ? result : -result;
235 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
236 /// a bitbase. The function below returns drawish scores when the pawn is
237 /// far advanced with support of the king, while the attacking king is far
240 Value Endgame<KRKP>::operator()(const Position& pos) const {
242 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
243 assert(pos.piece_count(strongerSide, PAWN) == 0);
244 assert(pos.non_pawn_material(weakerSide) == 0);
245 assert(pos.piece_count(weakerSide, PAWN) == 1);
247 Square wksq, wrsq, bksq, bpsq;
248 int tempo = (pos.side_to_move() == strongerSide);
250 wksq = pos.king_square(strongerSide);
251 wrsq = pos.piece_list(strongerSide, ROOK)[0];
252 bksq = pos.king_square(weakerSide);
253 bpsq = pos.piece_list(weakerSide, PAWN)[0];
255 if (strongerSide == BLACK)
263 Square queeningSq = file_of(bpsq) | RANK_1;
266 // If the stronger side's king is in front of the pawn, it's a win
267 if (wksq < bpsq && file_of(wksq) == file_of(bpsq))
268 result = RookValueEg - Value(square_distance(wksq, bpsq));
270 // If the weaker side's king is too far from the pawn and the rook,
272 else if ( square_distance(bksq, bpsq) - (tempo ^ 1) >= 3
273 && square_distance(bksq, wrsq) >= 3)
274 result = RookValueEg - Value(square_distance(wksq, bpsq));
276 // If the pawn is far advanced and supported by the defending king,
277 // the position is drawish
278 else if ( rank_of(bksq) <= RANK_3
279 && square_distance(bksq, bpsq) == 1
280 && rank_of(wksq) >= RANK_4
281 && square_distance(wksq, bpsq) - tempo > 2)
282 result = Value(80 - square_distance(wksq, bpsq) * 8);
286 - Value(square_distance(wksq, bpsq + DELTA_S) * 8)
287 + Value(square_distance(bksq, bpsq + DELTA_S) * 8)
288 + Value(square_distance(bpsq, queeningSq) * 8);
290 return strongerSide == pos.side_to_move() ? result : -result;
294 /// KR vs KB. This is very simple, and always returns drawish scores. The
295 /// score is slightly bigger when the defending king is close to the edge.
297 Value Endgame<KRKB>::operator()(const Position& pos) const {
299 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
300 assert(pos.piece_count(strongerSide, PAWN) == 0);
301 assert(pos.non_pawn_material(weakerSide) == BishopValueMg);
302 assert(pos.piece_count(weakerSide, PAWN) == 0);
303 assert(pos.piece_count(weakerSide, BISHOP) == 1);
305 Value result = Value(MateTable[pos.king_square(weakerSide)]);
306 return strongerSide == pos.side_to_move() ? result : -result;
310 /// KR vs KN. The attacking side has slightly better winning chances than
311 /// in KR vs KB, particularly if the king and the knight are far apart.
313 Value Endgame<KRKN>::operator()(const Position& pos) const {
315 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
316 assert(pos.piece_count(strongerSide, PAWN) == 0);
317 assert(pos.non_pawn_material(weakerSide) == KnightValueMg);
318 assert(pos.piece_count(weakerSide, PAWN) == 0);
319 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
321 const int penalty[8] = { 0, 10, 14, 20, 30, 42, 58, 80 };
323 Square bksq = pos.king_square(weakerSide);
324 Square bnsq = pos.piece_list(weakerSide, KNIGHT)[0];
325 Value result = Value(MateTable[bksq] + penalty[square_distance(bksq, bnsq)]);
326 return strongerSide == pos.side_to_move() ? result : -result;
330 /// KQ vs KP. In general, a win for the stronger side, however, there are a few
331 /// important exceptions. Pawn on 7th rank, A,C,F or H file, with king next can
332 /// be a draw, so we scale down to distance between kings only.
334 Value Endgame<KQKP>::operator()(const Position& pos) const {
336 assert(pos.non_pawn_material(strongerSide) == QueenValueMg);
337 assert(pos.piece_count(strongerSide, PAWN) == 0);
338 assert(pos.non_pawn_material(weakerSide) == 0);
339 assert(pos.piece_count(weakerSide, PAWN) == 1);
341 Square winnerKSq = pos.king_square(strongerSide);
342 Square loserKSq = pos.king_square(weakerSide);
343 Square pawnSq = pos.piece_list(weakerSide, PAWN)[0];
345 Value result = QueenValueEg
347 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
349 if ( square_distance(loserKSq, pawnSq) == 1
350 && relative_rank(weakerSide, pawnSq) == RANK_7)
352 File f = file_of(pawnSq);
354 if (f == FILE_A || f == FILE_C || f == FILE_F || f == FILE_H)
355 result = Value(DistanceBonus[square_distance(winnerKSq, loserKSq)]);
357 return strongerSide == pos.side_to_move() ? result : -result;
361 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
362 /// king a bonus for having the kings close together, and for forcing the
363 /// defending king towards the edge. If we also take care to avoid null move
364 /// for the defending side in the search, this is usually sufficient to be
365 /// able to win KQ vs KR.
367 Value Endgame<KQKR>::operator()(const Position& pos) const {
369 assert(pos.non_pawn_material(strongerSide) == QueenValueMg);
370 assert(pos.piece_count(strongerSide, PAWN) == 0);
371 assert(pos.non_pawn_material(weakerSide) == RookValueMg);
372 assert(pos.piece_count(weakerSide, PAWN) == 0);
374 Square winnerKSq = pos.king_square(strongerSide);
375 Square loserKSq = pos.king_square(weakerSide);
377 Value result = QueenValueEg
379 + MateTable[loserKSq]
380 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
382 return strongerSide == pos.side_to_move() ? result : -result;
386 Value Endgame<KBBKN>::operator()(const Position& pos) const {
388 assert(pos.piece_count(strongerSide, BISHOP) == 2);
389 assert(pos.non_pawn_material(strongerSide) == 2*BishopValueMg);
390 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
391 assert(pos.non_pawn_material(weakerSide) == KnightValueMg);
392 assert(!pos.pieces(PAWN));
394 Value result = BishopValueEg;
395 Square wksq = pos.king_square(strongerSide);
396 Square bksq = pos.king_square(weakerSide);
397 Square nsq = pos.piece_list(weakerSide, KNIGHT)[0];
399 // Bonus for attacking king close to defending king
400 result += Value(DistanceBonus[square_distance(wksq, bksq)]);
402 // Bonus for driving the defending king and knight apart
403 result += Value(square_distance(bksq, nsq) * 32);
405 // Bonus for restricting the knight's mobility
406 result += Value((8 - popcount<Max15>(pos.attacks_from<KNIGHT>(nsq))) * 8);
408 return strongerSide == pos.side_to_move() ? result : -result;
412 /// K and two minors vs K and one or two minors or K and two knights against
413 /// king alone are always draw.
415 Value Endgame<KmmKm>::operator()(const Position&) const {
420 Value Endgame<KNNK>::operator()(const Position&) const {
424 /// K, bishop and one or more pawns vs K. It checks for draws with rook pawns and
425 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
426 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
429 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
431 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
432 assert(pos.piece_count(strongerSide, BISHOP) == 1);
433 assert(pos.piece_count(strongerSide, PAWN) >= 1);
435 // No assertions about the material of weakerSide, because we want draws to
436 // be detected even when the weaker side has some pawns.
438 Bitboard pawns = pos.pieces(strongerSide, PAWN);
439 File pawnFile = file_of(pos.piece_list(strongerSide, PAWN)[0]);
441 // All pawns are on a single rook file ?
442 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
443 && !(pawns & ~file_bb(pawnFile)))
445 Square bishopSq = pos.piece_list(strongerSide, BISHOP)[0];
446 Square queeningSq = relative_square(strongerSide, pawnFile | RANK_8);
447 Square kingSq = pos.king_square(weakerSide);
449 if ( opposite_colors(queeningSq, bishopSq)
450 && abs(file_of(kingSq) - pawnFile) <= 1)
452 // The bishop has the wrong color, and the defending king is on the
453 // file of the pawn(s) or the adjacent file. Find the rank of the
456 if (strongerSide == WHITE)
458 for (rank = RANK_7; !(rank_bb(rank) & pawns); rank--) {}
459 assert(rank >= RANK_2 && rank <= RANK_7);
463 for (rank = RANK_2; !(rank_bb(rank) & pawns); rank++) {}
464 rank = Rank(rank ^ 7); // HACK to get the relative rank
465 assert(rank >= RANK_2 && rank <= RANK_7);
467 // If the defending king has distance 1 to the promotion square or
468 // is placed somewhere in front of the pawn, it's a draw.
469 if ( square_distance(kingSq, queeningSq) <= 1
470 || relative_rank(strongerSide, kingSq) >= rank)
471 return SCALE_FACTOR_DRAW;
474 return SCALE_FACTOR_NONE;
478 /// K and queen vs K, rook and one or more pawns. It tests for fortress draws with
479 /// a rook on the third rank defended by a pawn.
481 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
483 assert(pos.non_pawn_material(strongerSide) == QueenValueMg);
484 assert(pos.piece_count(strongerSide, QUEEN) == 1);
485 assert(pos.piece_count(strongerSide, PAWN) == 0);
486 assert(pos.piece_count(weakerSide, ROOK) == 1);
487 assert(pos.piece_count(weakerSide, PAWN) >= 1);
489 Square kingSq = pos.king_square(weakerSide);
490 if ( relative_rank(weakerSide, kingSq) <= RANK_2
491 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
492 && (pos.pieces(weakerSide, ROOK) & rank_bb(relative_rank(weakerSide, RANK_3)))
493 && (pos.pieces(weakerSide, PAWN) & rank_bb(relative_rank(weakerSide, RANK_2)))
494 && (pos.attacks_from<KING>(kingSq) & pos.pieces(weakerSide, PAWN)))
496 Square rsq = pos.piece_list(weakerSide, ROOK)[0];
497 if (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(weakerSide, PAWN))
498 return SCALE_FACTOR_DRAW;
500 return SCALE_FACTOR_NONE;
504 /// K, rook and one pawn vs K and a rook. This function knows a handful of the
505 /// most important classes of drawn positions, but is far from perfect. It would
506 /// probably be a good idea to add more knowledge in the future.
508 /// It would also be nice to rewrite the actual code for this function,
509 /// which is mostly copied from Glaurung 1.x, and not very pretty.
511 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
513 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
514 assert(pos.piece_count(strongerSide, PAWN) == 1);
515 assert(pos.non_pawn_material(weakerSide) == RookValueMg);
516 assert(pos.piece_count(weakerSide, PAWN) == 0);
518 Square wksq = pos.king_square(strongerSide);
519 Square wrsq = pos.piece_list(strongerSide, ROOK)[0];
520 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
521 Square bksq = pos.king_square(weakerSide);
522 Square brsq = pos.piece_list(weakerSide, ROOK)[0];
524 // Orient the board in such a way that the stronger side is white, and the
525 // pawn is on the left half of the board.
526 if (strongerSide == BLACK)
534 if (file_of(wpsq) > FILE_D)
543 File f = file_of(wpsq);
544 Rank r = rank_of(wpsq);
545 Square queeningSq = f | RANK_8;
546 int tempo = (pos.side_to_move() == strongerSide);
548 // If the pawn is not too far advanced and the defending king defends the
549 // queening square, use the third-rank defence.
551 && square_distance(bksq, queeningSq) <= 1
553 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
554 return SCALE_FACTOR_DRAW;
556 // The defending side saves a draw by checking from behind in case the pawn
557 // has advanced to the 6th rank with the king behind.
559 && square_distance(bksq, queeningSq) <= 1
560 && rank_of(wksq) + tempo <= RANK_6
561 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
562 return SCALE_FACTOR_DRAW;
565 && bksq == queeningSq
566 && rank_of(brsq) == RANK_1
567 && (!tempo || square_distance(wksq, wpsq) >= 2))
568 return SCALE_FACTOR_DRAW;
570 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
571 // and the black rook is behind the pawn.
574 && (bksq == SQ_H7 || bksq == SQ_G7)
575 && file_of(brsq) == FILE_A
576 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
577 return SCALE_FACTOR_DRAW;
579 // If the defending king blocks the pawn and the attacking king is too far
580 // away, it's a draw.
582 && bksq == wpsq + DELTA_N
583 && square_distance(wksq, wpsq) - tempo >= 2
584 && square_distance(wksq, brsq) - tempo >= 2)
585 return SCALE_FACTOR_DRAW;
587 // Pawn on the 7th rank supported by the rook from behind usually wins if the
588 // attacking king is closer to the queening square than the defending king,
589 // and the defending king cannot gain tempi by threatening the attacking rook.
592 && file_of(wrsq) == f
593 && wrsq != queeningSq
594 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
595 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
596 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
598 // Similar to the above, but with the pawn further back
600 && file_of(wrsq) == f
602 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
603 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
604 && ( square_distance(bksq, wrsq) + tempo >= 3
605 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
606 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
607 return ScaleFactor( SCALE_FACTOR_MAX
608 - 8 * square_distance(wpsq, queeningSq)
609 - 2 * square_distance(wksq, queeningSq));
611 // If the pawn is not far advanced, and the defending king is somewhere in
612 // the pawn's path, it's probably a draw.
613 if (r <= RANK_4 && bksq > wpsq)
615 if (file_of(bksq) == file_of(wpsq))
616 return ScaleFactor(10);
617 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
618 && square_distance(wksq, bksq) > 2)
619 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
621 return SCALE_FACTOR_NONE;
625 /// K, rook and two pawns vs K, rook and one pawn. There is only a single
626 /// pattern: If the stronger side has no passed pawns and the defending king
627 /// is actively placed, the position is drawish.
629 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
631 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
632 assert(pos.piece_count(strongerSide, PAWN) == 2);
633 assert(pos.non_pawn_material(weakerSide) == RookValueMg);
634 assert(pos.piece_count(weakerSide, PAWN) == 1);
636 Square wpsq1 = pos.piece_list(strongerSide, PAWN)[0];
637 Square wpsq2 = pos.piece_list(strongerSide, PAWN)[1];
638 Square bksq = pos.king_square(weakerSide);
640 // Does the stronger side have a passed pawn?
641 if ( pos.pawn_is_passed(strongerSide, wpsq1)
642 || pos.pawn_is_passed(strongerSide, wpsq2))
643 return SCALE_FACTOR_NONE;
645 Rank r = std::max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
647 if ( file_distance(bksq, wpsq1) <= 1
648 && file_distance(bksq, wpsq2) <= 1
649 && relative_rank(strongerSide, bksq) > r)
652 case RANK_2: return ScaleFactor(10);
653 case RANK_3: return ScaleFactor(10);
654 case RANK_4: return ScaleFactor(15);
655 case RANK_5: return ScaleFactor(20);
656 case RANK_6: return ScaleFactor(40);
657 default: assert(false);
660 return SCALE_FACTOR_NONE;
664 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
665 /// are on the same rook file and are blocked by the defending king, it's a draw.
667 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
669 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
670 assert(pos.piece_count(strongerSide, PAWN) >= 2);
671 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
672 assert(pos.piece_count(weakerSide, PAWN) == 0);
674 Square ksq = pos.king_square(weakerSide);
675 Bitboard pawns = pos.pieces(strongerSide, PAWN);
677 // Are all pawns on the 'a' file?
678 if (!(pawns & ~FileABB))
680 // Does the defending king block the pawns?
681 if ( square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
682 || ( file_of(ksq) == FILE_A
683 && !(in_front_bb(strongerSide, ksq) & pawns)))
684 return SCALE_FACTOR_DRAW;
686 // Are all pawns on the 'h' file?
687 else if (!(pawns & ~FileHBB))
689 // Does the defending king block the pawns?
690 if ( square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
691 || ( file_of(ksq) == FILE_H
692 && !(in_front_bb(strongerSide, ksq) & pawns)))
693 return SCALE_FACTOR_DRAW;
695 return SCALE_FACTOR_NONE;
699 /// K, bishop and a pawn vs K and a bishop. There are two rules: If the defending
700 /// king is somewhere along the path of the pawn, and the square of the king is
701 /// not of the same color as the stronger side's bishop, it's a draw. If the two
702 /// bishops have opposite color, it's almost always a draw.
704 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
706 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
707 assert(pos.piece_count(strongerSide, BISHOP) == 1);
708 assert(pos.piece_count(strongerSide, PAWN) == 1);
709 assert(pos.non_pawn_material(weakerSide) == BishopValueMg);
710 assert(pos.piece_count(weakerSide, BISHOP) == 1);
711 assert(pos.piece_count(weakerSide, PAWN) == 0);
713 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
714 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
715 Square weakerBishopSq = pos.piece_list(weakerSide, BISHOP)[0];
716 Square weakerKingSq = pos.king_square(weakerSide);
718 // Case 1: Defending king blocks the pawn, and cannot be driven away
719 if ( file_of(weakerKingSq) == file_of(pawnSq)
720 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
721 && ( opposite_colors(weakerKingSq, strongerBishopSq)
722 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
723 return SCALE_FACTOR_DRAW;
725 // Case 2: Opposite colored bishops
726 if (opposite_colors(strongerBishopSq, weakerBishopSq))
728 // We assume that the position is drawn in the following three situations:
730 // a. The pawn is on rank 5 or further back.
731 // b. The defending king is somewhere in the pawn's path.
732 // c. The defending bishop attacks some square along the pawn's path,
733 // and is at least three squares away from the pawn.
735 // These rules are probably not perfect, but in practice they work
738 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
739 return SCALE_FACTOR_DRAW;
742 Bitboard path = forward_bb(strongerSide, pawnSq);
744 if (path & pos.pieces(weakerSide, KING))
745 return SCALE_FACTOR_DRAW;
747 if ( (pos.attacks_from<BISHOP>(weakerBishopSq) & path)
748 && square_distance(weakerBishopSq, pawnSq) >= 3)
749 return SCALE_FACTOR_DRAW;
752 return SCALE_FACTOR_NONE;
756 /// K, bishop and two pawns vs K and bishop. It detects a few basic draws with
757 /// opposite-colored bishops.
759 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
761 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
762 assert(pos.piece_count(strongerSide, BISHOP) == 1);
763 assert(pos.piece_count(strongerSide, PAWN) == 2);
764 assert(pos.non_pawn_material(weakerSide) == BishopValueMg);
765 assert(pos.piece_count(weakerSide, BISHOP) == 1);
766 assert(pos.piece_count(weakerSide, PAWN) == 0);
768 Square wbsq = pos.piece_list(strongerSide, BISHOP)[0];
769 Square bbsq = pos.piece_list(weakerSide, BISHOP)[0];
771 if (!opposite_colors(wbsq, bbsq))
772 return SCALE_FACTOR_NONE;
774 Square ksq = pos.king_square(weakerSide);
775 Square psq1 = pos.piece_list(strongerSide, PAWN)[0];
776 Square psq2 = pos.piece_list(strongerSide, PAWN)[1];
777 Rank r1 = rank_of(psq1);
778 Rank r2 = rank_of(psq2);
779 Square blockSq1, blockSq2;
781 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
783 blockSq1 = psq1 + pawn_push(strongerSide);
784 blockSq2 = file_of(psq2) | rank_of(psq1);
788 blockSq1 = psq2 + pawn_push(strongerSide);
789 blockSq2 = file_of(psq1) | rank_of(psq2);
792 switch (file_distance(psq1, psq2))
795 // Both pawns are on the same file. Easy draw if defender firmly controls
796 // some square in the frontmost pawn's path.
797 if ( file_of(ksq) == file_of(blockSq1)
798 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
799 && opposite_colors(ksq, wbsq))
800 return SCALE_FACTOR_DRAW;
802 return SCALE_FACTOR_NONE;
805 // Pawns on adjacent files. Draw if defender firmly controls the square
806 // in front of the frontmost pawn's path, and the square diagonally behind
807 // this square on the file of the other pawn.
809 && opposite_colors(ksq, wbsq)
810 && ( bbsq == blockSq2
811 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakerSide, BISHOP))
812 || abs(r1 - r2) >= 2))
813 return SCALE_FACTOR_DRAW;
815 else if ( ksq == blockSq2
816 && opposite_colors(ksq, wbsq)
817 && ( bbsq == blockSq1
818 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakerSide, BISHOP))))
819 return SCALE_FACTOR_DRAW;
821 return SCALE_FACTOR_NONE;
824 // The pawns are not on the same file or adjacent files. No scaling.
825 return SCALE_FACTOR_NONE;
830 /// K, bisop and a pawn vs K and knight. There is a single rule: If the defending
831 /// king is somewhere along the path of the pawn, and the square of the king is
832 /// not of the same color as the stronger side's bishop, it's a draw.
834 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
836 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
837 assert(pos.piece_count(strongerSide, BISHOP) == 1);
838 assert(pos.piece_count(strongerSide, PAWN) == 1);
839 assert(pos.non_pawn_material(weakerSide) == KnightValueMg);
840 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
841 assert(pos.piece_count(weakerSide, PAWN) == 0);
843 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
844 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
845 Square weakerKingSq = pos.king_square(weakerSide);
847 if ( file_of(weakerKingSq) == file_of(pawnSq)
848 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
849 && ( opposite_colors(weakerKingSq, strongerBishopSq)
850 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
851 return SCALE_FACTOR_DRAW;
853 return SCALE_FACTOR_NONE;
857 /// K, knight and a pawn vs K. There is a single rule: If the pawn is a rook pawn
858 /// on the 7th rank and the defending king prevents the pawn from advancing, the
859 /// position is drawn.
861 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
863 assert(pos.non_pawn_material(strongerSide) == KnightValueMg);
864 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
865 assert(pos.piece_count(strongerSide, PAWN) == 1);
866 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
867 assert(pos.piece_count(weakerSide, PAWN) == 0);
869 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
870 Square weakerKingSq = pos.king_square(weakerSide);
872 if ( pawnSq == relative_square(strongerSide, SQ_A7)
873 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
874 return SCALE_FACTOR_DRAW;
876 if ( pawnSq == relative_square(strongerSide, SQ_H7)
877 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
878 return SCALE_FACTOR_DRAW;
880 return SCALE_FACTOR_NONE;
884 /// K and a pawn vs K and a pawn. This is done by removing the weakest side's
885 /// pawn and probing the KP vs K bitbase: If the weakest side has a draw without
886 /// the pawn, she probably has at least a draw with the pawn as well. The exception
887 /// is when the stronger side's pawn is far advanced and not on a rook file; in
888 /// this case it is often possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
890 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
892 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
893 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
894 assert(pos.piece_count(WHITE, PAWN) == 1);
895 assert(pos.piece_count(BLACK, PAWN) == 1);
897 Square wksq = pos.king_square(strongerSide);
898 Square bksq = pos.king_square(weakerSide);
899 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
900 Color stm = pos.side_to_move();
902 if (strongerSide == BLACK)
910 if (file_of(wpsq) >= FILE_E)
917 // If the pawn has advanced to the fifth rank or further, and is not a
918 // rook pawn, it's too dangerous to assume that it's at least a draw.
919 if ( rank_of(wpsq) >= RANK_5
920 && file_of(wpsq) != FILE_A)
921 return SCALE_FACTOR_NONE;
923 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
924 // it's probably at least a draw even with the pawn.
925 return Bitbases::probe_kpk(wksq, wpsq, bksq, stm) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;