2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
4 Copyright (C) 2008-2013 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() {
107 add<KBPPKB>("KBPPKB");
108 add<KRPPKRP>("KRPPKRP");
111 Endgames::~Endgames() {
113 for_each(m1.begin(), m1.end(), delete_endgame<M1>);
114 for_each(m2.begin(), m2.end(), delete_endgame<M2>);
117 template<EndgameType E>
118 void Endgames::add(const string& code) {
120 map((Endgame<E>*)0)[key(code, WHITE)] = new Endgame<E>(WHITE);
121 map((Endgame<E>*)0)[key(code, BLACK)] = new Endgame<E>(BLACK);
125 /// Mate with KX vs K. This function is used to evaluate positions with
126 /// King and plenty of material vs a lone king. It simply gives the
127 /// attacking side a bonus for driving the defending king towards the edge
128 /// of the board, and for keeping the distance between the two kings small.
130 Value Endgame<KXK>::operator()(const Position& pos) const {
132 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
133 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
135 // Stalemate detection with lone king
136 if ( pos.side_to_move() == weakerSide
138 && !MoveList<LEGAL>(pos).size()) {
142 Square winnerKSq = pos.king_square(strongerSide);
143 Square loserKSq = pos.king_square(weakerSide);
145 Value result = pos.non_pawn_material(strongerSide)
146 + pos.piece_count(strongerSide, PAWN) * PawnValueEg
147 + MateTable[loserKSq]
148 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
150 if ( pos.piece_count(strongerSide, QUEEN)
151 || pos.piece_count(strongerSide, ROOK)
152 || pos.bishop_pair(strongerSide)) {
153 result += VALUE_KNOWN_WIN;
156 return strongerSide == pos.side_to_move() ? result : -result;
160 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
161 /// defending king towards a corner square of the right color.
163 Value Endgame<KBNK>::operator()(const Position& pos) const {
165 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
166 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
167 assert(pos.non_pawn_material(strongerSide) == KnightValueMg + BishopValueMg);
168 assert(pos.piece_count(strongerSide, BISHOP) == 1);
169 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
170 assert(pos.piece_count(strongerSide, PAWN) == 0);
172 Square winnerKSq = pos.king_square(strongerSide);
173 Square loserKSq = pos.king_square(weakerSide);
174 Square bishopSq = pos.piece_list(strongerSide, BISHOP)[0];
176 // kbnk_mate_table() tries to drive toward corners A1 or H8,
177 // if we have a bishop that cannot reach the above squares we
178 // mirror the kings so to drive enemy toward corners A8 or H1.
179 if (opposite_colors(bishopSq, SQ_A1))
181 winnerKSq = mirror(winnerKSq);
182 loserKSq = mirror(loserKSq);
185 Value result = VALUE_KNOWN_WIN
186 + DistanceBonus[square_distance(winnerKSq, loserKSq)]
187 + KBNKMateTable[loserKSq];
189 return strongerSide == pos.side_to_move() ? result : -result;
193 /// KP vs K. This endgame is evaluated with the help of a bitbase.
195 Value Endgame<KPK>::operator()(const Position& pos) const {
197 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
198 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
199 assert(pos.piece_count(strongerSide, PAWN) == 1);
200 assert(pos.piece_count(weakerSide, PAWN) == 0);
202 Square wksq, bksq, wpsq;
205 if (strongerSide == WHITE)
207 wksq = pos.king_square(WHITE);
208 bksq = pos.king_square(BLACK);
209 wpsq = pos.piece_list(WHITE, PAWN)[0];
210 us = pos.side_to_move();
214 wksq = ~pos.king_square(BLACK);
215 bksq = ~pos.king_square(WHITE);
216 wpsq = ~pos.piece_list(BLACK, PAWN)[0];
217 us = ~pos.side_to_move();
220 if (file_of(wpsq) >= FILE_E)
227 if (!Bitbases::probe_kpk(wksq, wpsq, bksq, us))
230 Value result = VALUE_KNOWN_WIN + PawnValueEg + 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) == RookValueMg);
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 = RookValueEg - 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 = RookValueEg - 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) == RookValueMg);
301 assert(pos.piece_count(strongerSide, PAWN) == 0);
302 assert(pos.non_pawn_material(weakerSide) == BishopValueMg);
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) == RookValueMg);
317 assert(pos.piece_count(strongerSide, PAWN) == 0);
318 assert(pos.non_pawn_material(weakerSide) == KnightValueMg);
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 KP. In general, a win for the stronger side, however, there are a few
332 /// important exceptions. Pawn on 7th rank, A,C,F or H file, with king next can
333 /// be a draw, so we scale down to distance between kings only.
335 Value Endgame<KQKP>::operator()(const Position& pos) const {
337 assert(pos.non_pawn_material(strongerSide) == QueenValueMg);
338 assert(pos.piece_count(strongerSide, PAWN) == 0);
339 assert(pos.non_pawn_material(weakerSide) == 0);
340 assert(pos.piece_count(weakerSide, PAWN) == 1);
342 Square winnerKSq = pos.king_square(strongerSide);
343 Square loserKSq = pos.king_square(weakerSide);
344 Square pawnSq = pos.piece_list(weakerSide, PAWN)[0];
346 Value result = QueenValueEg
348 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
350 if ( square_distance(loserKSq, pawnSq) == 1
351 && relative_rank(weakerSide, pawnSq) == RANK_7)
353 File f = file_of(pawnSq);
355 if (f == FILE_A || f == FILE_C || f == FILE_F || f == FILE_H)
356 result = Value(DistanceBonus[square_distance(winnerKSq, loserKSq)]);
358 return strongerSide == pos.side_to_move() ? result : -result;
362 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
363 /// king a bonus for having the kings close together, and for forcing the
364 /// defending king towards the edge. If we also take care to avoid null move
365 /// for the defending side in the search, this is usually sufficient to be
366 /// able to win KQ vs KR.
368 Value Endgame<KQKR>::operator()(const Position& pos) const {
370 assert(pos.non_pawn_material(strongerSide) == QueenValueMg);
371 assert(pos.piece_count(strongerSide, PAWN) == 0);
372 assert(pos.non_pawn_material(weakerSide) == RookValueMg);
373 assert(pos.piece_count(weakerSide, PAWN) == 0);
375 Square winnerKSq = pos.king_square(strongerSide);
376 Square loserKSq = pos.king_square(weakerSide);
378 Value result = QueenValueEg
380 + MateTable[loserKSq]
381 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
383 return strongerSide == pos.side_to_move() ? result : -result;
387 Value Endgame<KBBKN>::operator()(const Position& pos) const {
389 assert(pos.piece_count(strongerSide, BISHOP) == 2);
390 assert(pos.non_pawn_material(strongerSide) == 2*BishopValueMg);
391 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
392 assert(pos.non_pawn_material(weakerSide) == KnightValueMg);
393 assert(!pos.pieces(PAWN));
395 Value result = BishopValueEg;
396 Square wksq = pos.king_square(strongerSide);
397 Square bksq = pos.king_square(weakerSide);
398 Square nsq = pos.piece_list(weakerSide, KNIGHT)[0];
400 // Bonus for attacking king close to defending king
401 result += Value(DistanceBonus[square_distance(wksq, bksq)]);
403 // Bonus for driving the defending king and knight apart
404 result += Value(square_distance(bksq, nsq) * 32);
406 // Bonus for restricting the knight's mobility
407 result += Value((8 - popcount<Max15>(pos.attacks_from<KNIGHT>(nsq))) * 8);
409 return strongerSide == pos.side_to_move() ? result : -result;
413 /// K and two minors vs K and one or two minors or K and two knights against
414 /// king alone are always draw.
416 Value Endgame<KmmKm>::operator()(const Position&) const {
421 Value Endgame<KNNK>::operator()(const Position&) const {
425 /// K, bishop and one or more pawns vs K. It checks for draws with rook pawns and
426 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
427 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
430 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
432 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
433 assert(pos.piece_count(strongerSide, BISHOP) == 1);
434 assert(pos.piece_count(strongerSide, PAWN) >= 1);
436 // No assertions about the material of weakerSide, because we want draws to
437 // be detected even when the weaker side has some pawns.
439 Bitboard pawns = pos.pieces(strongerSide, PAWN);
440 File pawnFile = file_of(pos.piece_list(strongerSide, PAWN)[0]);
442 // All pawns are on a single rook file ?
443 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
444 && !(pawns & ~file_bb(pawnFile)))
446 Square bishopSq = pos.piece_list(strongerSide, BISHOP)[0];
447 Square queeningSq = relative_square(strongerSide, pawnFile | RANK_8);
448 Square kingSq = pos.king_square(weakerSide);
450 if ( opposite_colors(queeningSq, bishopSq)
451 && abs(file_of(kingSq) - pawnFile) <= 1)
453 // The bishop has the wrong color, and the defending king is on the
454 // file of the pawn(s) or the adjacent file. Find the rank of the
457 if (strongerSide == WHITE)
459 for (rank = RANK_7; !(rank_bb(rank) & pawns); rank--) {}
460 assert(rank >= RANK_2 && rank <= RANK_7);
464 for (rank = RANK_2; !(rank_bb(rank) & pawns); rank++) {}
465 rank = Rank(rank ^ 7); // HACK to get the relative rank
466 assert(rank >= RANK_2 && rank <= RANK_7);
468 // If the defending king has distance 1 to the promotion square or
469 // is placed somewhere in front of the pawn, it's a draw.
470 if ( square_distance(kingSq, queeningSq) <= 1
471 || relative_rank(strongerSide, kingSq) >= rank)
472 return SCALE_FACTOR_DRAW;
476 // All pawns on same B or G file? Then potential draw
477 if ( (pawnFile == FILE_B || pawnFile == FILE_G)
478 && !(pos.pieces(PAWN) & ~file_bb(pawnFile))
479 && pos.non_pawn_material(weakerSide) == 0
480 && pos.piece_count(weakerSide, PAWN) >= 1)
482 // Get weaker pawn closest to opponent's queening square
483 Bitboard wkPawns = pos.pieces(weakerSide, PAWN);
484 Square weakerPawnSq = strongerSide == WHITE ? msb(wkPawns) : lsb(wkPawns);
486 Square strongerKingSq = pos.king_square(strongerSide);
487 Square weakerKingSq = pos.king_square(weakerSide);
488 Square bishopSq = pos.piece_list(strongerSide, BISHOP)[0];
490 // Draw if weaker pawn is on rank 7, bishop can't attack the pawn, and
491 // weaker king can stop opposing opponent's king from penetrating.
492 if ( relative_rank(strongerSide, weakerPawnSq) == RANK_7
493 && opposite_colors(bishopSq, weakerPawnSq)
494 && square_distance(weakerPawnSq, weakerKingSq) <= square_distance(weakerPawnSq, strongerKingSq))
495 return SCALE_FACTOR_DRAW;
498 return SCALE_FACTOR_NONE;
502 /// K and queen vs K, rook and one or more pawns. It tests for fortress draws with
503 /// a rook on the third rank defended by a pawn.
505 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
507 assert(pos.non_pawn_material(strongerSide) == QueenValueMg);
508 assert(pos.piece_count(strongerSide, QUEEN) == 1);
509 assert(pos.piece_count(strongerSide, PAWN) == 0);
510 assert(pos.piece_count(weakerSide, ROOK) == 1);
511 assert(pos.piece_count(weakerSide, PAWN) >= 1);
513 Square kingSq = pos.king_square(weakerSide);
514 if ( relative_rank(weakerSide, kingSq) <= RANK_2
515 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
516 && (pos.pieces(weakerSide, ROOK) & rank_bb(relative_rank(weakerSide, RANK_3)))
517 && (pos.pieces(weakerSide, PAWN) & rank_bb(relative_rank(weakerSide, RANK_2)))
518 && (pos.attacks_from<KING>(kingSq) & pos.pieces(weakerSide, PAWN)))
520 Square rsq = pos.piece_list(weakerSide, ROOK)[0];
521 if (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(weakerSide, PAWN))
522 return SCALE_FACTOR_DRAW;
524 return SCALE_FACTOR_NONE;
528 /// K, rook and one pawn vs K and a rook. This function knows a handful of the
529 /// most important classes of drawn positions, but is far from perfect. It would
530 /// probably be a good idea to add more knowledge in the future.
532 /// It would also be nice to rewrite the actual code for this function,
533 /// which is mostly copied from Glaurung 1.x, and not very pretty.
535 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
537 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
538 assert(pos.piece_count(strongerSide, PAWN) == 1);
539 assert(pos.non_pawn_material(weakerSide) == RookValueMg);
540 assert(pos.piece_count(weakerSide, PAWN) == 0);
542 Square wksq = pos.king_square(strongerSide);
543 Square wrsq = pos.piece_list(strongerSide, ROOK)[0];
544 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
545 Square bksq = pos.king_square(weakerSide);
546 Square brsq = pos.piece_list(weakerSide, ROOK)[0];
548 // Orient the board in such a way that the stronger side is white, and the
549 // pawn is on the left half of the board.
550 if (strongerSide == BLACK)
558 if (file_of(wpsq) > FILE_D)
567 File f = file_of(wpsq);
568 Rank r = rank_of(wpsq);
569 Square queeningSq = f | RANK_8;
570 int tempo = (pos.side_to_move() == strongerSide);
572 // If the pawn is not too far advanced and the defending king defends the
573 // queening square, use the third-rank defence.
575 && square_distance(bksq, queeningSq) <= 1
577 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
578 return SCALE_FACTOR_DRAW;
580 // The defending side saves a draw by checking from behind in case the pawn
581 // has advanced to the 6th rank with the king behind.
583 && square_distance(bksq, queeningSq) <= 1
584 && rank_of(wksq) + tempo <= RANK_6
585 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
586 return SCALE_FACTOR_DRAW;
589 && bksq == queeningSq
590 && rank_of(brsq) == RANK_1
591 && (!tempo || square_distance(wksq, wpsq) >= 2))
592 return SCALE_FACTOR_DRAW;
594 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
595 // and the black rook is behind the pawn.
598 && (bksq == SQ_H7 || bksq == SQ_G7)
599 && file_of(brsq) == FILE_A
600 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
601 return SCALE_FACTOR_DRAW;
603 // If the defending king blocks the pawn and the attacking king is too far
604 // away, it's a draw.
606 && bksq == wpsq + DELTA_N
607 && square_distance(wksq, wpsq) - tempo >= 2
608 && square_distance(wksq, brsq) - tempo >= 2)
609 return SCALE_FACTOR_DRAW;
611 // Pawn on the 7th rank supported by the rook from behind usually wins if the
612 // attacking king is closer to the queening square than the defending king,
613 // and the defending king cannot gain tempi by threatening the attacking rook.
616 && file_of(wrsq) == f
617 && wrsq != queeningSq
618 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
619 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
620 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
622 // Similar to the above, but with the pawn further back
624 && file_of(wrsq) == f
626 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
627 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
628 && ( square_distance(bksq, wrsq) + tempo >= 3
629 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
630 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
631 return ScaleFactor( SCALE_FACTOR_MAX
632 - 8 * square_distance(wpsq, queeningSq)
633 - 2 * square_distance(wksq, queeningSq));
635 // If the pawn is not far advanced, and the defending king is somewhere in
636 // the pawn's path, it's probably a draw.
637 if (r <= RANK_4 && bksq > wpsq)
639 if (file_of(bksq) == file_of(wpsq))
640 return ScaleFactor(10);
641 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
642 && square_distance(wksq, bksq) > 2)
643 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
645 return SCALE_FACTOR_NONE;
649 /// K, rook and two pawns vs K, rook and one pawn. There is only a single
650 /// pattern: If the stronger side has no passed pawns and the defending king
651 /// is actively placed, the position is drawish.
653 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
655 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
656 assert(pos.piece_count(strongerSide, PAWN) == 2);
657 assert(pos.non_pawn_material(weakerSide) == RookValueMg);
658 assert(pos.piece_count(weakerSide, PAWN) == 1);
660 Square wpsq1 = pos.piece_list(strongerSide, PAWN)[0];
661 Square wpsq2 = pos.piece_list(strongerSide, PAWN)[1];
662 Square bksq = pos.king_square(weakerSide);
664 // Does the stronger side have a passed pawn?
665 if ( pos.pawn_is_passed(strongerSide, wpsq1)
666 || pos.pawn_is_passed(strongerSide, wpsq2))
667 return SCALE_FACTOR_NONE;
669 Rank r = std::max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
671 if ( file_distance(bksq, wpsq1) <= 1
672 && file_distance(bksq, wpsq2) <= 1
673 && relative_rank(strongerSide, bksq) > r)
676 case RANK_2: return ScaleFactor(10);
677 case RANK_3: return ScaleFactor(10);
678 case RANK_4: return ScaleFactor(15);
679 case RANK_5: return ScaleFactor(20);
680 case RANK_6: return ScaleFactor(40);
681 default: assert(false);
684 return SCALE_FACTOR_NONE;
688 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
689 /// are on the same rook file and are blocked by the defending king, it's a draw.
691 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
693 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
694 assert(pos.piece_count(strongerSide, PAWN) >= 2);
695 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
696 assert(pos.piece_count(weakerSide, PAWN) == 0);
698 Square ksq = pos.king_square(weakerSide);
699 Bitboard pawns = pos.pieces(strongerSide, PAWN);
701 // Are all pawns on the 'a' file?
702 if (!(pawns & ~FileABB))
704 // Does the defending king block the pawns?
705 if ( square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
706 || ( file_of(ksq) == FILE_A
707 && !(in_front_bb(strongerSide, ksq) & pawns)))
708 return SCALE_FACTOR_DRAW;
710 // Are all pawns on the 'h' file?
711 else if (!(pawns & ~FileHBB))
713 // Does the defending king block the pawns?
714 if ( square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
715 || ( file_of(ksq) == FILE_H
716 && !(in_front_bb(strongerSide, ksq) & pawns)))
717 return SCALE_FACTOR_DRAW;
719 return SCALE_FACTOR_NONE;
723 /// K, bishop and a pawn vs K and a bishop. There are two rules: If the defending
724 /// king is somewhere along the path of the pawn, and the square of the king is
725 /// not of the same color as the stronger side's bishop, it's a draw. If the two
726 /// bishops have opposite color, it's almost always a draw.
728 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
730 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
731 assert(pos.piece_count(strongerSide, BISHOP) == 1);
732 assert(pos.piece_count(strongerSide, PAWN) == 1);
733 assert(pos.non_pawn_material(weakerSide) == BishopValueMg);
734 assert(pos.piece_count(weakerSide, BISHOP) == 1);
735 assert(pos.piece_count(weakerSide, PAWN) == 0);
737 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
738 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
739 Square weakerBishopSq = pos.piece_list(weakerSide, BISHOP)[0];
740 Square weakerKingSq = pos.king_square(weakerSide);
742 // Case 1: Defending king blocks the pawn, and cannot be driven away
743 if ( file_of(weakerKingSq) == file_of(pawnSq)
744 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
745 && ( opposite_colors(weakerKingSq, strongerBishopSq)
746 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
747 return SCALE_FACTOR_DRAW;
749 // Case 2: Opposite colored bishops
750 if (opposite_colors(strongerBishopSq, weakerBishopSq))
752 // We assume that the position is drawn in the following three situations:
754 // a. The pawn is on rank 5 or further back.
755 // b. The defending king is somewhere in the pawn's path.
756 // c. The defending bishop attacks some square along the pawn's path,
757 // and is at least three squares away from the pawn.
759 // These rules are probably not perfect, but in practice they work
762 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
763 return SCALE_FACTOR_DRAW;
766 Bitboard path = forward_bb(strongerSide, pawnSq);
768 if (path & pos.pieces(weakerSide, KING))
769 return SCALE_FACTOR_DRAW;
771 if ( (pos.attacks_from<BISHOP>(weakerBishopSq) & path)
772 && square_distance(weakerBishopSq, pawnSq) >= 3)
773 return SCALE_FACTOR_DRAW;
776 return SCALE_FACTOR_NONE;
780 /// K, bishop and two pawns vs K and bishop. It detects a few basic draws with
781 /// opposite-colored bishops.
783 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
785 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
786 assert(pos.piece_count(strongerSide, BISHOP) == 1);
787 assert(pos.piece_count(strongerSide, PAWN) == 2);
788 assert(pos.non_pawn_material(weakerSide) == BishopValueMg);
789 assert(pos.piece_count(weakerSide, BISHOP) == 1);
790 assert(pos.piece_count(weakerSide, PAWN) == 0);
792 Square wbsq = pos.piece_list(strongerSide, BISHOP)[0];
793 Square bbsq = pos.piece_list(weakerSide, BISHOP)[0];
795 if (!opposite_colors(wbsq, bbsq))
796 return SCALE_FACTOR_NONE;
798 Square ksq = pos.king_square(weakerSide);
799 Square psq1 = pos.piece_list(strongerSide, PAWN)[0];
800 Square psq2 = pos.piece_list(strongerSide, PAWN)[1];
801 Rank r1 = rank_of(psq1);
802 Rank r2 = rank_of(psq2);
803 Square blockSq1, blockSq2;
805 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
807 blockSq1 = psq1 + pawn_push(strongerSide);
808 blockSq2 = file_of(psq2) | rank_of(psq1);
812 blockSq1 = psq2 + pawn_push(strongerSide);
813 blockSq2 = file_of(psq1) | rank_of(psq2);
816 switch (file_distance(psq1, psq2))
819 // Both pawns are on the same file. Easy draw if defender firmly controls
820 // some square in the frontmost pawn's path.
821 if ( file_of(ksq) == file_of(blockSq1)
822 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
823 && opposite_colors(ksq, wbsq))
824 return SCALE_FACTOR_DRAW;
826 return SCALE_FACTOR_NONE;
829 // Pawns on adjacent files. Draw if defender firmly controls the square
830 // in front of the frontmost pawn's path, and the square diagonally behind
831 // this square on the file of the other pawn.
833 && opposite_colors(ksq, wbsq)
834 && ( bbsq == blockSq2
835 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakerSide, BISHOP))
836 || abs(r1 - r2) >= 2))
837 return SCALE_FACTOR_DRAW;
839 else if ( ksq == blockSq2
840 && opposite_colors(ksq, wbsq)
841 && ( bbsq == blockSq1
842 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakerSide, BISHOP))))
843 return SCALE_FACTOR_DRAW;
845 return SCALE_FACTOR_NONE;
848 // The pawns are not on the same file or adjacent files. No scaling.
849 return SCALE_FACTOR_NONE;
854 /// K, bisop and a pawn vs K and knight. There is a single rule: If the defending
855 /// king is somewhere along the path of the pawn, and the square of the king is
856 /// not of the same color as the stronger side's bishop, it's a draw.
858 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
860 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
861 assert(pos.piece_count(strongerSide, BISHOP) == 1);
862 assert(pos.piece_count(strongerSide, PAWN) == 1);
863 assert(pos.non_pawn_material(weakerSide) == KnightValueMg);
864 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
865 assert(pos.piece_count(weakerSide, PAWN) == 0);
867 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
868 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
869 Square weakerKingSq = pos.king_square(weakerSide);
871 if ( file_of(weakerKingSq) == file_of(pawnSq)
872 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
873 && ( opposite_colors(weakerKingSq, strongerBishopSq)
874 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
875 return SCALE_FACTOR_DRAW;
877 return SCALE_FACTOR_NONE;
881 /// K, knight and a pawn vs K. There is a single rule: If the pawn is a rook pawn
882 /// on the 7th rank and the defending king prevents the pawn from advancing, the
883 /// position is drawn.
885 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
887 assert(pos.non_pawn_material(strongerSide) == KnightValueMg);
888 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
889 assert(pos.piece_count(strongerSide, PAWN) == 1);
890 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
891 assert(pos.piece_count(weakerSide, PAWN) == 0);
893 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
894 Square weakerKingSq = pos.king_square(weakerSide);
896 if ( pawnSq == relative_square(strongerSide, SQ_A7)
897 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
898 return SCALE_FACTOR_DRAW;
900 if ( pawnSq == relative_square(strongerSide, SQ_H7)
901 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
902 return SCALE_FACTOR_DRAW;
904 return SCALE_FACTOR_NONE;
908 /// K, knight and a pawn vs K and bishop. If knight can block bishop from taking
909 /// pawn, it's a win. Otherwise, drawn.
911 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
913 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
914 Square bishopSq = pos.piece_list(weakerSide, BISHOP)[0];
915 Square weakerKingSq = pos.king_square(weakerSide);
917 // King needs to get close to promoting pawn to prevent knight from blocking.
918 // Rules for this are very tricky, so just approximate.
919 if (forward_bb(strongerSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
920 return ScaleFactor(square_distance(weakerKingSq, pawnSq));
922 return SCALE_FACTOR_NONE;
926 /// K and a pawn vs K and a pawn. This is done by removing the weakest side's
927 /// pawn and probing the KP vs K bitbase: If the weakest side has a draw without
928 /// the pawn, she probably has at least a draw with the pawn as well. The exception
929 /// is when the stronger side's pawn is far advanced and not on a rook file; in
930 /// this case it is often possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
932 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
934 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
935 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
936 assert(pos.piece_count(WHITE, PAWN) == 1);
937 assert(pos.piece_count(BLACK, PAWN) == 1);
939 Square wksq = pos.king_square(strongerSide);
940 Square bksq = pos.king_square(weakerSide);
941 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
942 Color us = pos.side_to_move();
944 if (strongerSide == BLACK)
952 if (file_of(wpsq) >= FILE_E)
959 // If the pawn has advanced to the fifth rank or further, and is not a
960 // rook pawn, it's too dangerous to assume that it's at least a draw.
961 if ( rank_of(wpsq) >= RANK_5
962 && file_of(wpsq) != FILE_A)
963 return SCALE_FACTOR_NONE;
965 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
966 // it's probably at least a draw even with the pawn.
967 return Bitbases::probe_kpk(wksq, wpsq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;