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() {
110 add<KBPPKB>("KBPPKB");
111 add<KRPPKRP>("KRPPKRP");
114 Endgames::~Endgames() {
116 for_each(m1.begin(), m1.end(), delete_endgame<M1>);
117 for_each(m2.begin(), m2.end(), delete_endgame<M2>);
120 template<EndgameType E>
121 void Endgames::add(const string& code) {
123 map((Endgame<E>*)0)[key(code, WHITE)] = new Endgame<E>(WHITE);
124 map((Endgame<E>*)0)[key(code, BLACK)] = new Endgame<E>(BLACK);
128 /// Mate with KX vs K. This function is used to evaluate positions with
129 /// King and plenty of material vs a lone king. It simply gives the
130 /// attacking side a bonus for driving the defending king towards the edge
131 /// of the board, and for keeping the distance between the two kings small.
133 Value Endgame<KXK>::operator()(const Position& pos) const {
135 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
136 assert(!pos.count<PAWN>(weakerSide));
137 assert(!pos.checkers()); // Eval is never called when in check
139 // Stalemate detection with lone king
140 if (pos.side_to_move() == weakerSide && !MoveList<LEGAL>(pos).size())
143 Square winnerKSq = pos.king_square(strongerSide);
144 Square loserKSq = pos.king_square(weakerSide);
146 Value result = pos.non_pawn_material(strongerSide)
147 + pos.count<PAWN>(strongerSide) * PawnValueEg
148 + MateTable[loserKSq]
149 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
151 if ( pos.count<QUEEN>(strongerSide)
152 || pos.count<ROOK>(strongerSide)
153 || pos.bishop_pair(strongerSide))
154 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(strongerSide) == KnightValueMg + BishopValueMg);
166 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
167 assert(pos.count<BISHOP>(strongerSide) == 1);
168 assert(pos.count<KNIGHT>(strongerSide) == 1);
169 assert(pos.count< PAWN>(strongerSide) == 0);
170 assert(pos.count< PAWN>(weakerSide ) == 0);
172 Square winnerKSq = pos.king_square(strongerSide);
173 Square loserKSq = pos.king_square(weakerSide);
174 Square bishopSq = pos.list<BISHOP>(strongerSide)[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.count<PAWN>(strongerSide) == 1);
200 assert(pos.count<PAWN>(weakerSide ) == 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.list<PAWN>(WHITE)[0];
210 us = pos.side_to_move();
214 wksq = ~pos.king_square(BLACK);
215 bksq = ~pos.king_square(WHITE);
216 wpsq = ~pos.list<PAWN>(BLACK)[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.non_pawn_material(weakerSide) == 0);
245 assert(pos.count<PAWN>(strongerSide) == 0);
246 assert(pos.count<PAWN>(weakerSide ) == 1);
248 Square wksq, wrsq, bksq, bpsq;
249 int tempo = (pos.side_to_move() == strongerSide);
251 wksq = pos.king_square(strongerSide);
252 bksq = pos.king_square(weakerSide);
253 wrsq = pos.list<ROOK>(strongerSide)[0];
254 bpsq = pos.list<PAWN>(weakerSide)[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.non_pawn_material(weakerSide ) == BishopValueMg);
302 assert(pos.count<BISHOP>(weakerSide ) == 1);
303 assert(pos.count< PAWN>(weakerSide ) == 0);
304 assert(pos.count< PAWN>(strongerSide) == 0);
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.non_pawn_material(weakerSide ) == KnightValueMg);
318 assert(pos.count<KNIGHT>(weakerSide ) == 1);
319 assert(pos.count< PAWN>(weakerSide ) == 0);
320 assert(pos.count< PAWN>(strongerSide) == 0);
322 const int penalty[8] = { 0, 10, 14, 20, 30, 42, 58, 80 };
324 Square bksq = pos.king_square(weakerSide);
325 Square bnsq = pos.list<KNIGHT>(weakerSide)[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.non_pawn_material(weakerSide ) == VALUE_ZERO);
339 assert(pos.count<PAWN>(strongerSide) == 0);
340 assert(pos.count<PAWN>(weakerSide ) == 1);
342 Square winnerKSq = pos.king_square(strongerSide);
343 Square loserKSq = pos.king_square(weakerSide);
344 Square pawnSq = pos.list<PAWN>(weakerSide)[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.non_pawn_material(weakerSide ) == RookValueMg);
372 assert(pos.count<PAWN>(strongerSide) == 0);
373 assert(pos.count<PAWN>(weakerSide ) == 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.non_pawn_material(strongerSide) == 2 * BishopValueMg);
390 assert(pos.non_pawn_material(weakerSide ) == KnightValueMg);
391 assert(pos.count<BISHOP>(strongerSide) == 2);
392 assert(pos.count<KNIGHT>(weakerSide ) == 1);
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.list<KNIGHT>(weakerSide)[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 /// Some cases of trivial draws
414 template<> Value Endgame<KK>::operator()(const Position&) const { return VALUE_DRAW; }
415 template<> Value Endgame<KBK>::operator()(const Position&) const { return VALUE_DRAW; }
416 template<> Value Endgame<KNK>::operator()(const Position&) const { return VALUE_DRAW; }
417 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
418 template<> Value Endgame<KmmKm>::operator()(const Position&) const { return VALUE_DRAW; }
421 /// K, bishop and one or more pawns vs K. It checks for draws with rook pawns and
422 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
423 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
426 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
428 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
429 assert(pos.count<BISHOP>(strongerSide) == 1);
430 assert(pos.count< PAWN>(strongerSide) >= 1);
432 // No assertions about the material of weakerSide, because we want draws to
433 // be detected even when the weaker side has some pawns.
435 Bitboard pawns = pos.pieces(strongerSide, PAWN);
436 File pawnFile = file_of(pos.list<PAWN>(strongerSide)[0]);
438 // All pawns are on a single rook file ?
439 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
440 && !(pawns & ~file_bb(pawnFile)))
442 Square bishopSq = pos.list<BISHOP>(strongerSide)[0];
443 Square queeningSq = relative_square(strongerSide, pawnFile | RANK_8);
444 Square kingSq = pos.king_square(weakerSide);
446 if ( opposite_colors(queeningSq, bishopSq)
447 && abs(file_of(kingSq) - pawnFile) <= 1)
449 // The bishop has the wrong color, and the defending king is on the
450 // file of the pawn(s) or the adjacent file. Find the rank of the
453 if (strongerSide == WHITE)
455 for (rank = RANK_7; !(rank_bb(rank) & pawns); rank--) {}
456 assert(rank >= RANK_2 && rank <= RANK_7);
460 for (rank = RANK_2; !(rank_bb(rank) & pawns); rank++) {}
461 rank = Rank(rank ^ 7); // HACK to get the relative rank
462 assert(rank >= RANK_2 && rank <= RANK_7);
464 // If the defending king has distance 1 to the promotion square or
465 // is placed somewhere in front of the pawn, it's a draw.
466 if ( square_distance(kingSq, queeningSq) <= 1
467 || relative_rank(strongerSide, kingSq) >= rank)
468 return SCALE_FACTOR_DRAW;
472 // All pawns on same B or G file? Then potential draw
473 if ( (pawnFile == FILE_B || pawnFile == FILE_G)
474 && !(pos.pieces(PAWN) & ~file_bb(pawnFile))
475 && pos.non_pawn_material(weakerSide) == 0
476 && pos.count<PAWN>(weakerSide) >= 1)
478 // Get weaker pawn closest to opponent's queening square
479 Bitboard wkPawns = pos.pieces(weakerSide, PAWN);
480 Square weakerPawnSq = strongerSide == WHITE ? msb(wkPawns) : lsb(wkPawns);
482 Square strongerKingSq = pos.king_square(strongerSide);
483 Square weakerKingSq = pos.king_square(weakerSide);
484 Square bishopSq = pos.list<BISHOP>(strongerSide)[0];
486 // Draw if weaker pawn is on rank 7, bishop can't attack the pawn, and
487 // weaker king can stop opposing opponent's king from penetrating.
488 if ( relative_rank(strongerSide, weakerPawnSq) == RANK_7
489 && opposite_colors(bishopSq, weakerPawnSq)
490 && square_distance(weakerPawnSq, weakerKingSq) <= square_distance(weakerPawnSq, strongerKingSq))
491 return SCALE_FACTOR_DRAW;
494 return SCALE_FACTOR_NONE;
498 /// K and queen vs K, rook and one or more pawns. It tests for fortress draws with
499 /// a rook on the third rank defended by a pawn.
501 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
503 assert(pos.non_pawn_material(strongerSide) == QueenValueMg);
504 assert(pos.count<QUEEN>(strongerSide) == 1);
505 assert(pos.count< PAWN>(strongerSide) == 0);
506 assert(pos.count< ROOK>(weakerSide ) == 1);
507 assert(pos.count< PAWN>(weakerSide ) >= 1);
509 Square kingSq = pos.king_square(weakerSide);
510 if ( relative_rank(weakerSide, kingSq) <= RANK_2
511 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
512 && (pos.pieces(weakerSide, ROOK) & rank_bb(relative_rank(weakerSide, RANK_3)))
513 && (pos.pieces(weakerSide, PAWN) & rank_bb(relative_rank(weakerSide, RANK_2)))
514 && (pos.attacks_from<KING>(kingSq) & pos.pieces(weakerSide, PAWN)))
516 Square rsq = pos.list<ROOK>(weakerSide)[0];
517 if (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(weakerSide, PAWN))
518 return SCALE_FACTOR_DRAW;
520 return SCALE_FACTOR_NONE;
524 /// K, rook and one pawn vs K and a rook. This function knows a handful of the
525 /// most important classes of drawn positions, but is far from perfect. It would
526 /// probably be a good idea to add more knowledge in the future.
528 /// It would also be nice to rewrite the actual code for this function,
529 /// which is mostly copied from Glaurung 1.x, and not very pretty.
531 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
533 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
534 assert(pos.non_pawn_material(weakerSide) == RookValueMg);
535 assert(pos.count<PAWN>(strongerSide) == 1);
536 assert(pos.count<PAWN>(weakerSide ) == 0);
538 Square wksq = pos.king_square(strongerSide);
539 Square bksq = pos.king_square(weakerSide);
540 Square wrsq = pos.list<ROOK>(strongerSide)[0];
541 Square wpsq = pos.list<PAWN>(strongerSide)[0];
542 Square brsq = pos.list<ROOK>(weakerSide)[0];
544 // Orient the board in such a way that the stronger side is white, and the
545 // pawn is on the left half of the board.
546 if (strongerSide == BLACK)
554 if (file_of(wpsq) > FILE_D)
563 File f = file_of(wpsq);
564 Rank r = rank_of(wpsq);
565 Square queeningSq = f | RANK_8;
566 int tempo = (pos.side_to_move() == strongerSide);
568 // If the pawn is not too far advanced and the defending king defends the
569 // queening square, use the third-rank defence.
571 && square_distance(bksq, queeningSq) <= 1
573 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
574 return SCALE_FACTOR_DRAW;
576 // The defending side saves a draw by checking from behind in case the pawn
577 // has advanced to the 6th rank with the king behind.
579 && square_distance(bksq, queeningSq) <= 1
580 && rank_of(wksq) + tempo <= RANK_6
581 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
582 return SCALE_FACTOR_DRAW;
585 && bksq == queeningSq
586 && rank_of(brsq) == RANK_1
587 && (!tempo || square_distance(wksq, wpsq) >= 2))
588 return SCALE_FACTOR_DRAW;
590 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
591 // and the black rook is behind the pawn.
594 && (bksq == SQ_H7 || bksq == SQ_G7)
595 && file_of(brsq) == FILE_A
596 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
597 return SCALE_FACTOR_DRAW;
599 // If the defending king blocks the pawn and the attacking king is too far
600 // away, it's a draw.
602 && bksq == wpsq + DELTA_N
603 && square_distance(wksq, wpsq) - tempo >= 2
604 && square_distance(wksq, brsq) - tempo >= 2)
605 return SCALE_FACTOR_DRAW;
607 // Pawn on the 7th rank supported by the rook from behind usually wins if the
608 // attacking king is closer to the queening square than the defending king,
609 // and the defending king cannot gain tempi by threatening the attacking rook.
612 && file_of(wrsq) == f
613 && wrsq != queeningSq
614 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
615 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
616 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
618 // Similar to the above, but with the pawn further back
620 && file_of(wrsq) == f
622 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
623 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
624 && ( square_distance(bksq, wrsq) + tempo >= 3
625 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
626 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
627 return ScaleFactor( SCALE_FACTOR_MAX
628 - 8 * square_distance(wpsq, queeningSq)
629 - 2 * square_distance(wksq, queeningSq));
631 // If the pawn is not far advanced, and the defending king is somewhere in
632 // the pawn's path, it's probably a draw.
633 if (r <= RANK_4 && bksq > wpsq)
635 if (file_of(bksq) == file_of(wpsq))
636 return ScaleFactor(10);
637 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
638 && square_distance(wksq, bksq) > 2)
639 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
641 return SCALE_FACTOR_NONE;
645 /// K, rook and two pawns vs K, rook and one pawn. There is only a single
646 /// pattern: If the stronger side has no passed pawns and the defending king
647 /// is actively placed, the position is drawish.
649 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
651 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
652 assert(pos.non_pawn_material(weakerSide) == RookValueMg);
653 assert(pos.count<PAWN>(strongerSide) == 2);
654 assert(pos.count<PAWN>(weakerSide ) == 1);
656 Square wpsq1 = pos.list<PAWN>(strongerSide)[0];
657 Square wpsq2 = pos.list<PAWN>(strongerSide)[1];
658 Square bksq = pos.king_square(weakerSide);
660 // Does the stronger side have a passed pawn?
661 if ( pos.pawn_is_passed(strongerSide, wpsq1)
662 || pos.pawn_is_passed(strongerSide, wpsq2))
663 return SCALE_FACTOR_NONE;
665 Rank r = std::max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
667 if ( file_distance(bksq, wpsq1) <= 1
668 && file_distance(bksq, wpsq2) <= 1
669 && relative_rank(strongerSide, bksq) > r)
672 case RANK_2: return ScaleFactor(10);
673 case RANK_3: return ScaleFactor(10);
674 case RANK_4: return ScaleFactor(15);
675 case RANK_5: return ScaleFactor(20);
676 case RANK_6: return ScaleFactor(40);
677 default: assert(false);
680 return SCALE_FACTOR_NONE;
684 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
685 /// are on the same rook file and are blocked by the defending king, it's a draw.
687 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
689 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
690 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
691 assert(pos.count<PAWN>(strongerSide) >= 2);
692 assert(pos.count<PAWN>(weakerSide ) == 0);
694 Square ksq = pos.king_square(weakerSide);
695 Bitboard pawns = pos.pieces(strongerSide, PAWN);
697 // Are all pawns on the 'a' file?
698 if (!(pawns & ~FileABB))
700 // Does the defending king block the pawns?
701 if ( square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
702 || ( file_of(ksq) == FILE_A
703 && !(in_front_bb(strongerSide, rank_of(ksq)) & pawns)))
704 return SCALE_FACTOR_DRAW;
706 // Are all pawns on the 'h' file?
707 else if (!(pawns & ~FileHBB))
709 // Does the defending king block the pawns?
710 if ( square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
711 || ( file_of(ksq) == FILE_H
712 && !(in_front_bb(strongerSide, rank_of(ksq)) & pawns)))
713 return SCALE_FACTOR_DRAW;
715 return SCALE_FACTOR_NONE;
719 /// K, bishop and a pawn vs K and a bishop. There are two rules: If the defending
720 /// king is somewhere along the path of the pawn, and the square of the king is
721 /// not of the same color as the stronger side's bishop, it's a draw. If the two
722 /// bishops have opposite color, it's almost always a draw.
724 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
726 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
727 assert(pos.non_pawn_material(weakerSide ) == BishopValueMg);
728 assert(pos.count<BISHOP>(strongerSide) == 1);
729 assert(pos.count<BISHOP>(weakerSide ) == 1);
730 assert(pos.count< PAWN>(strongerSide) == 1);
731 assert(pos.count< PAWN>(weakerSide ) == 0);
733 Square pawnSq = pos.list<PAWN>(strongerSide)[0];
734 Square strongerBishopSq = pos.list<BISHOP>(strongerSide)[0];
735 Square weakerBishopSq = pos.list<BISHOP>(weakerSide)[0];
736 Square weakerKingSq = pos.king_square(weakerSide);
738 // Case 1: Defending king blocks the pawn, and cannot be driven away
739 if ( file_of(weakerKingSq) == file_of(pawnSq)
740 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
741 && ( opposite_colors(weakerKingSq, strongerBishopSq)
742 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
743 return SCALE_FACTOR_DRAW;
745 // Case 2: Opposite colored bishops
746 if (opposite_colors(strongerBishopSq, weakerBishopSq))
748 // We assume that the position is drawn in the following three situations:
750 // a. The pawn is on rank 5 or further back.
751 // b. The defending king is somewhere in the pawn's path.
752 // c. The defending bishop attacks some square along the pawn's path,
753 // and is at least three squares away from the pawn.
755 // These rules are probably not perfect, but in practice they work
758 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
759 return SCALE_FACTOR_DRAW;
762 Bitboard path = forward_bb(strongerSide, pawnSq);
764 if (path & pos.pieces(weakerSide, KING))
765 return SCALE_FACTOR_DRAW;
767 if ( (pos.attacks_from<BISHOP>(weakerBishopSq) & path)
768 && square_distance(weakerBishopSq, pawnSq) >= 3)
769 return SCALE_FACTOR_DRAW;
772 return SCALE_FACTOR_NONE;
776 /// K, bishop and two pawns vs K and bishop. It detects a few basic draws with
777 /// opposite-colored bishops.
779 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
781 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
782 assert(pos.non_pawn_material(weakerSide ) == BishopValueMg);
783 assert(pos.count<BISHOP>(strongerSide) == 1);
784 assert(pos.count<BISHOP>(weakerSide ) == 1);
785 assert(pos.count< PAWN>(strongerSide) == 2);
786 assert(pos.count< PAWN>(weakerSide ) == 0);
788 Square wbsq = pos.list<BISHOP>(strongerSide)[0];
789 Square bbsq = pos.list<BISHOP>(weakerSide)[0];
791 if (!opposite_colors(wbsq, bbsq))
792 return SCALE_FACTOR_NONE;
794 Square ksq = pos.king_square(weakerSide);
795 Square psq1 = pos.list<PAWN>(strongerSide)[0];
796 Square psq2 = pos.list<PAWN>(strongerSide)[1];
797 Rank r1 = rank_of(psq1);
798 Rank r2 = rank_of(psq2);
799 Square blockSq1, blockSq2;
801 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
803 blockSq1 = psq1 + pawn_push(strongerSide);
804 blockSq2 = file_of(psq2) | rank_of(psq1);
808 blockSq1 = psq2 + pawn_push(strongerSide);
809 blockSq2 = file_of(psq1) | rank_of(psq2);
812 switch (file_distance(psq1, psq2))
815 // Both pawns are on the same file. Easy draw if defender firmly controls
816 // some square in the frontmost pawn's path.
817 if ( file_of(ksq) == file_of(blockSq1)
818 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
819 && opposite_colors(ksq, wbsq))
820 return SCALE_FACTOR_DRAW;
822 return SCALE_FACTOR_NONE;
825 // Pawns on adjacent files. Draw if defender firmly controls the square
826 // in front of the frontmost pawn's path, and the square diagonally behind
827 // this square on the file of the other pawn.
829 && opposite_colors(ksq, wbsq)
830 && ( bbsq == blockSq2
831 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakerSide, BISHOP))
832 || abs(r1 - r2) >= 2))
833 return SCALE_FACTOR_DRAW;
835 else if ( ksq == blockSq2
836 && opposite_colors(ksq, wbsq)
837 && ( bbsq == blockSq1
838 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakerSide, BISHOP))))
839 return SCALE_FACTOR_DRAW;
841 return SCALE_FACTOR_NONE;
844 // The pawns are not on the same file or adjacent files. No scaling.
845 return SCALE_FACTOR_NONE;
850 /// K, bisop and a pawn vs K and knight. There is a single rule: If the defending
851 /// king is somewhere along the path of the pawn, and the square of the king is
852 /// not of the same color as the stronger side's bishop, it's a draw.
854 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
856 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
857 assert(pos.non_pawn_material(weakerSide ) == KnightValueMg);
858 assert(pos.count<BISHOP>(strongerSide) == 1);
859 assert(pos.count<KNIGHT>(weakerSide ) == 1);
860 assert(pos.count< PAWN>(strongerSide) == 1);
861 assert(pos.count< PAWN>(weakerSide ) == 0);
863 Square pawnSq = pos.list<PAWN>(strongerSide)[0];
864 Square strongerBishopSq = pos.list<BISHOP>(strongerSide)[0];
865 Square weakerKingSq = pos.king_square(weakerSide);
867 if ( file_of(weakerKingSq) == file_of(pawnSq)
868 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
869 && ( opposite_colors(weakerKingSq, strongerBishopSq)
870 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
871 return SCALE_FACTOR_DRAW;
873 return SCALE_FACTOR_NONE;
877 /// K, knight and a pawn vs K. There is a single rule: If the pawn is a rook pawn
878 /// on the 7th rank and the defending king prevents the pawn from advancing, the
879 /// position is drawn.
881 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
883 assert(pos.non_pawn_material(strongerSide) == KnightValueMg);
884 assert(pos.non_pawn_material(weakerSide ) == VALUE_ZERO);
885 assert(pos.count<KNIGHT>(strongerSide) == 1);
886 assert(pos.count< PAWN>(strongerSide) == 1);
887 assert(pos.count< PAWN>(weakerSide ) == 0);
889 Square pawnSq = pos.list<PAWN>(strongerSide)[0];
890 Square weakerKingSq = pos.king_square(weakerSide);
892 if ( pawnSq == relative_square(strongerSide, SQ_A7)
893 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
894 return SCALE_FACTOR_DRAW;
896 if ( pawnSq == relative_square(strongerSide, SQ_H7)
897 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
898 return SCALE_FACTOR_DRAW;
900 return SCALE_FACTOR_NONE;
904 /// K, knight and a pawn vs K and bishop. If knight can block bishop from taking
905 /// pawn, it's a win. Otherwise, drawn.
907 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
909 Square pawnSq = pos.list<PAWN>(strongerSide)[0];
910 Square bishopSq = pos.list<BISHOP>(weakerSide)[0];
911 Square weakerKingSq = pos.king_square(weakerSide);
913 // King needs to get close to promoting pawn to prevent knight from blocking.
914 // Rules for this are very tricky, so just approximate.
915 if (forward_bb(strongerSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
916 return ScaleFactor(square_distance(weakerKingSq, pawnSq));
918 return SCALE_FACTOR_NONE;
922 /// K and a pawn vs K and a pawn. This is done by removing the weakest side's
923 /// pawn and probing the KP vs K bitbase: If the weakest side has a draw without
924 /// the pawn, she probably has at least a draw with the pawn as well. The exception
925 /// is when the stronger side's pawn is far advanced and not on a rook file; in
926 /// this case it is often possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
928 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
930 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
931 assert(pos.non_pawn_material(weakerSide ) == VALUE_ZERO);
932 assert(pos.count<PAWN>(WHITE) == 1);
933 assert(pos.count<PAWN>(BLACK) == 1);
935 Square wksq = pos.king_square(strongerSide);
936 Square bksq = pos.king_square(weakerSide);
937 Square wpsq = pos.list<PAWN>(strongerSide)[0];
938 Color us = pos.side_to_move();
940 if (strongerSide == BLACK)
948 if (file_of(wpsq) >= FILE_E)
955 // If the pawn has advanced to the fifth rank or further, and is not a
956 // rook pawn, it's too dangerous to assume that it's at least a draw.
957 if ( rank_of(wpsq) >= RANK_5
958 && file_of(wpsq) != FILE_A)
959 return SCALE_FACTOR_NONE;
961 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
962 // it's probably at least a draw even with the pawn.
963 return Bitbases::probe_kpk(wksq, wpsq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;