2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
4 Copyright (C) 2008-2014 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 king towards the edge of the board
33 // in KX vs K and KQ vs KR endgames.
34 const int PushToEdges[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 king towards a corner square of the
46 // right color in KBN vs K endgames.
47 const int PushToCorners[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 // Tables used to drive a piece towards or away from another piece
59 const int PushClose[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
60 const int PushAway [8] = { 0, 5, 20, 40, 60, 80, 90, 100 };
63 bool verify_material(const Position& pos, Color c, Value npm, int num_pawns) {
64 return pos.non_pawn_material(c) == npm && pos.count<PAWN>(c) == num_pawns;
68 // Map the square as if strongSide is white and strongSide's only pawn
69 // is on the left half of the board.
70 Square normalize(const Position& pos, Color strongSide, Square sq) {
72 assert(pos.count<PAWN>(strongSide) == 1);
74 if (file_of(pos.list<PAWN>(strongSide)[0]) >= FILE_E)
75 sq = Square(sq ^ 7); // Mirror SQ_H1 -> SQ_A1
77 if (strongSide == BLACK)
83 // Get the material key of Position out of the given endgame key code
84 // like "KBPKN". The trick here is to first forge an ad-hoc FEN string
85 // and then let a Position object do the work for us.
86 Key key(const string& code, Color c) {
88 assert(code.length() > 0 && code.length() < 8);
89 assert(code[0] == 'K');
91 string sides[] = { code.substr(code.find('K', 1)), // Weak
92 code.substr(0, code.find('K', 1)) }; // Strong
94 std::transform(sides[c].begin(), sides[c].end(), sides[c].begin(), tolower);
96 string fen = sides[0] + char(8 - sides[0].length() + '0') + "/8/8/8/8/8/8/"
97 + sides[1] + char(8 - sides[1].length() + '0') + " w - - 0 10";
99 return Position(fen, false, NULL).material_key();
103 void delete_endgame(const typename M::value_type& p) { delete p.second; }
108 /// Endgames members definitions
110 Endgames::Endgames() {
127 add<KBPPKB>("KBPPKB");
128 add<KRPPKRP>("KRPPKRP");
131 Endgames::~Endgames() {
133 for_each(m1.begin(), m1.end(), delete_endgame<M1>);
134 for_each(m2.begin(), m2.end(), delete_endgame<M2>);
137 template<EndgameType E>
138 void Endgames::add(const string& code) {
140 map((Endgame<E>*)0)[key(code, WHITE)] = new Endgame<E>(WHITE);
141 map((Endgame<E>*)0)[key(code, BLACK)] = new Endgame<E>(BLACK);
145 /// Mate with KX vs K. This function is used to evaluate positions with
146 /// king and plenty of material vs a lone king. It simply gives the
147 /// attacking side a bonus for driving the defending king towards the edge
148 /// of the board, and for keeping the distance between the two kings small.
150 Value Endgame<KXK>::operator()(const Position& pos) const {
152 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
153 assert(!pos.checkers()); // Eval is never called when in check
155 // Stalemate detection with lone king
156 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
159 Square winnerKSq = pos.king_square(strongSide);
160 Square loserKSq = pos.king_square(weakSide);
162 Value result = pos.non_pawn_material(strongSide)
163 + pos.count<PAWN>(strongSide) * PawnValueEg
164 + PushToEdges[loserKSq]
165 + PushClose[square_distance(winnerKSq, loserKSq)];
167 if ( pos.count<QUEEN>(strongSide)
168 || pos.count<ROOK>(strongSide)
169 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
170 || pos.bishop_pair(strongSide))
171 result += VALUE_KNOWN_WIN;
173 return strongSide == pos.side_to_move() ? result : -result;
177 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
178 /// defending king towards a corner square of the right color.
180 Value Endgame<KBNK>::operator()(const Position& pos) const {
182 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
183 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
185 Square winnerKSq = pos.king_square(strongSide);
186 Square loserKSq = pos.king_square(weakSide);
187 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
189 // kbnk_mate_table() tries to drive toward corners A1 or H8. If we have a
190 // bishop that cannot reach the above squares, we flip the kings in order
191 // to drive the enemy toward corners A8 or H1.
192 if (opposite_colors(bishopSq, SQ_A1))
194 winnerKSq = ~winnerKSq;
195 loserKSq = ~loserKSq;
198 Value result = VALUE_KNOWN_WIN
199 + PushClose[square_distance(winnerKSq, loserKSq)]
200 + PushToCorners[loserKSq];
202 return strongSide == pos.side_to_move() ? result : -result;
206 /// KP vs K. This endgame is evaluated with the help of a bitbase.
208 Value Endgame<KPK>::operator()(const Position& pos) const {
210 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
211 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
213 // Assume strongSide is white and the pawn is on files A-D
214 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
215 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
216 Square psq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
218 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
220 if (!Bitbases::probe_kpk(wksq, psq, bksq, us))
223 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
225 return strongSide == pos.side_to_move() ? result : -result;
229 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
230 /// a bitbase. The function below returns drawish scores when the pawn is
231 /// far advanced with support of the king, while the attacking king is far
234 Value Endgame<KRKP>::operator()(const Position& pos) const {
236 assert(verify_material(pos, strongSide, RookValueMg, 0));
237 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
239 Square wksq = relative_square(strongSide, pos.king_square(strongSide));
240 Square bksq = relative_square(strongSide, pos.king_square(weakSide));
241 Square rsq = relative_square(strongSide, pos.list<ROOK>(strongSide)[0]);
242 Square psq = relative_square(strongSide, pos.list<PAWN>(weakSide)[0]);
244 Square queeningSq = make_square(file_of(psq), RANK_1);
247 // If the stronger side's king is in front of the pawn, it's a win
248 if (wksq < psq && file_of(wksq) == file_of(psq))
249 result = RookValueEg - square_distance(wksq, psq);
251 // If the weaker side's king is too far from the pawn and the rook,
253 else if ( square_distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
254 && square_distance(bksq, rsq) >= 3)
255 result = RookValueEg - square_distance(wksq, psq);
257 // If the pawn is far advanced and supported by the defending king,
258 // the position is drawish
259 else if ( rank_of(bksq) <= RANK_3
260 && square_distance(bksq, psq) == 1
261 && rank_of(wksq) >= RANK_4
262 && square_distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
263 result = Value(80) - 8 * square_distance(wksq, psq);
266 result = Value(200) - 8 * ( square_distance(wksq, psq + DELTA_S)
267 - square_distance(bksq, psq + DELTA_S)
268 - square_distance(psq, queeningSq));
270 return strongSide == pos.side_to_move() ? result : -result;
274 /// KR vs KB. This is very simple, and always returns drawish scores. The
275 /// score is slightly bigger when the defending king is close to the edge.
277 Value Endgame<KRKB>::operator()(const Position& pos) const {
279 assert(verify_material(pos, strongSide, RookValueMg, 0));
280 assert(verify_material(pos, weakSide, BishopValueMg, 0));
282 Value result = Value(PushToEdges[pos.king_square(weakSide)]);
283 return strongSide == pos.side_to_move() ? result : -result;
287 /// KR vs KN. The attacking side has slightly better winning chances than
288 /// in KR vs KB, particularly if the king and the knight are far apart.
290 Value Endgame<KRKN>::operator()(const Position& pos) const {
292 assert(verify_material(pos, strongSide, RookValueMg, 0));
293 assert(verify_material(pos, weakSide, KnightValueMg, 0));
295 Square bksq = pos.king_square(weakSide);
296 Square bnsq = pos.list<KNIGHT>(weakSide)[0];
297 Value result = Value(PushToEdges[bksq] + PushAway[square_distance(bksq, bnsq)]);
298 return strongSide == pos.side_to_move() ? result : -result;
302 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
303 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
304 /// with a king positioned next to it can be a draw, so in that case, we only
305 /// use the distance between the kings.
307 Value Endgame<KQKP>::operator()(const Position& pos) const {
309 assert(verify_material(pos, strongSide, QueenValueMg, 0));
310 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
312 Square winnerKSq = pos.king_square(strongSide);
313 Square loserKSq = pos.king_square(weakSide);
314 Square pawnSq = pos.list<PAWN>(weakSide)[0];
316 Value result = Value(PushClose[square_distance(winnerKSq, loserKSq)]);
318 if ( relative_rank(weakSide, pawnSq) != RANK_7
319 || square_distance(loserKSq, pawnSq) != 1
320 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
321 result += QueenValueEg - PawnValueEg;
323 return strongSide == pos.side_to_move() ? result : -result;
327 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
328 /// king a bonus for having the kings close together, and for forcing the
329 /// defending king towards the edge. If we also take care to avoid null move for
330 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
332 Value Endgame<KQKR>::operator()(const Position& pos) const {
334 assert(verify_material(pos, strongSide, QueenValueMg, 0));
335 assert(verify_material(pos, weakSide, RookValueMg, 0));
337 Square winnerKSq = pos.king_square(strongSide);
338 Square loserKSq = pos.king_square(weakSide);
340 Value result = QueenValueEg
342 + PushToEdges[loserKSq]
343 + PushClose[square_distance(winnerKSq, loserKSq)];
345 return strongSide == pos.side_to_move() ? result : -result;
349 /// Some cases of trivial draws
350 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
353 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
354 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
355 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
358 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
360 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
361 assert(pos.count<PAWN>(strongSide) >= 1);
363 // No assertions about the material of weakSide, because we want draws to
364 // be detected even when the weaker side has some pawns.
366 Bitboard pawns = pos.pieces(strongSide, PAWN);
367 File pawnsFile = file_of(lsb(pawns));
369 // All pawns are on a single rook file ?
370 if ( (pawnsFile == FILE_A || pawnsFile == FILE_H)
371 && !(pawns & ~file_bb(pawnsFile)))
373 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
374 Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
375 Square kingSq = pos.king_square(weakSide);
377 // If the bishop has the wrong color, and the defending king is on the file
378 // of the pawn(s) or the neighboring file, then it's potentially a draw.
379 if ( opposite_colors(queeningSq, bishopSq)
380 && file_distance(kingSq, lsb(pawns)) <= 1)
382 // If the defending king has distance <= 1 to the promotion square or
383 // is placed somewhere in front of the frontmost pawn, it's a draw.
384 Rank rank = relative_rank(strongSide, (frontmost_sq(strongSide, pawns)));
386 if ( square_distance(kingSq, queeningSq) <= 1
387 || relative_rank(strongSide, kingSq) >= rank)
388 return SCALE_FACTOR_DRAW;
392 return SCALE_FACTOR_NONE;
396 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
397 /// the third rank defended by a pawn.
399 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
401 assert(verify_material(pos, strongSide, QueenValueMg, 0));
402 assert(pos.count<ROOK>(weakSide) == 1);
403 assert(pos.count<PAWN>(weakSide) >= 1);
405 Square kingSq = pos.king_square(weakSide);
406 Square rsq = pos.list<ROOK>(weakSide)[0];
408 if ( relative_rank(weakSide, kingSq) <= RANK_2
409 && relative_rank(weakSide, pos.king_square(strongSide)) >= RANK_4
410 && relative_rank(weakSide, rsq) == RANK_3
411 && ( pos.pieces(weakSide, PAWN)
412 & pos.attacks_from<KING>(kingSq)
413 & pos.attacks_from<PAWN>(rsq, strongSide)))
414 return SCALE_FACTOR_DRAW;
416 return SCALE_FACTOR_NONE;
420 /// KRP vs KR. This function knows a handful of the most important classes of
421 /// drawn positions, but is far from perfect. It would probably be a good idea
422 /// to add more knowledge in the future.
424 /// It would also be nice to rewrite the actual code for this function,
425 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
427 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
429 assert(verify_material(pos, strongSide, RookValueMg, 1));
430 assert(verify_material(pos, weakSide, RookValueMg, 0));
432 // Assume strongSide is white and the pawn is on files A-D
433 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
434 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
435 Square wrsq = normalize(pos, strongSide, pos.list<ROOK>(strongSide)[0]);
436 Square wpsq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
437 Square brsq = normalize(pos, strongSide, pos.list<ROOK>(weakSide)[0]);
439 File f = file_of(wpsq);
440 Rank r = rank_of(wpsq);
441 Square queeningSq = make_square(f, RANK_8);
442 int tempo = (pos.side_to_move() == strongSide);
444 // If the pawn is not too far advanced and the defending king defends the
445 // queening square, use the third-rank defence.
447 && square_distance(bksq, queeningSq) <= 1
449 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
450 return SCALE_FACTOR_DRAW;
452 // The defending side saves a draw by checking from behind in case the pawn
453 // has advanced to the 6th rank with the king behind.
455 && square_distance(bksq, queeningSq) <= 1
456 && rank_of(wksq) + tempo <= RANK_6
457 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
458 return SCALE_FACTOR_DRAW;
461 && bksq == queeningSq
462 && rank_of(brsq) == RANK_1
463 && (!tempo || square_distance(wksq, wpsq) >= 2))
464 return SCALE_FACTOR_DRAW;
466 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
467 // and the black rook is behind the pawn.
470 && (bksq == SQ_H7 || bksq == SQ_G7)
471 && file_of(brsq) == FILE_A
472 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
473 return SCALE_FACTOR_DRAW;
475 // If the defending king blocks the pawn and the attacking king is too far
476 // away, it's a draw.
478 && bksq == wpsq + DELTA_N
479 && square_distance(wksq, wpsq) - tempo >= 2
480 && square_distance(wksq, brsq) - tempo >= 2)
481 return SCALE_FACTOR_DRAW;
483 // Pawn on the 7th rank supported by the rook from behind usually wins if the
484 // attacking king is closer to the queening square than the defending king,
485 // and the defending king cannot gain tempi by threatening the attacking rook.
488 && file_of(wrsq) == f
489 && wrsq != queeningSq
490 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
491 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
492 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
494 // Similar to the above, but with the pawn further back
496 && file_of(wrsq) == f
498 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
499 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
500 && ( square_distance(bksq, wrsq) + tempo >= 3
501 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
502 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
503 return ScaleFactor( SCALE_FACTOR_MAX
504 - 8 * square_distance(wpsq, queeningSq)
505 - 2 * square_distance(wksq, queeningSq));
507 // If the pawn is not far advanced and the defending king is somewhere in
508 // the pawn's path, it's probably a draw.
509 if (r <= RANK_4 && bksq > wpsq)
511 if (file_of(bksq) == file_of(wpsq))
512 return ScaleFactor(10);
513 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
514 && square_distance(wksq, bksq) > 2)
515 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
517 return SCALE_FACTOR_NONE;
521 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
523 assert(verify_material(pos, strongSide, RookValueMg, 1));
524 assert(verify_material(pos, weakSide, BishopValueMg, 0));
526 // Test for a rook pawn
527 if (pos.pieces(PAWN) & (FileABB | FileHBB))
529 Square ksq = pos.king_square(weakSide);
530 Square bsq = pos.list<BISHOP>(weakSide)[0];
531 Square psq = pos.list<PAWN>(strongSide)[0];
532 Rank rk = relative_rank(strongSide, psq);
533 Square push = pawn_push(strongSide);
535 // If the pawn is on the 5th rank and the pawn (currently) is on
536 // the same color square as the bishop then there is a chance of
537 // a fortress. Depending on the king position give a moderate
538 // reduction or a stronger one if the defending king is near the
539 // corner but not trapped there.
540 if (rk == RANK_5 && !opposite_colors(bsq, psq))
542 int d = square_distance(psq + 3 * push, ksq);
544 if (d <= 2 && !(d == 0 && ksq == pos.king_square(strongSide) + 2 * push))
545 return ScaleFactor(24);
547 return ScaleFactor(48);
550 // When the pawn has moved to the 6th rank we can be fairly sure
551 // it's drawn if the bishop attacks the square in front of the
552 // pawn from a reasonable distance and the defending king is near
555 && square_distance(psq + 2 * push, ksq) <= 1
556 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
557 && file_distance(bsq, psq) >= 2)
558 return ScaleFactor(8);
561 return SCALE_FACTOR_NONE;
564 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
565 /// pawns and the defending king is actively placed, the position is drawish.
567 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
569 assert(verify_material(pos, strongSide, RookValueMg, 2));
570 assert(verify_material(pos, weakSide, RookValueMg, 1));
572 Square wpsq1 = pos.list<PAWN>(strongSide)[0];
573 Square wpsq2 = pos.list<PAWN>(strongSide)[1];
574 Square bksq = pos.king_square(weakSide);
576 // Does the stronger side have a passed pawn?
577 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
578 return SCALE_FACTOR_NONE;
580 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
582 if ( file_distance(bksq, wpsq1) <= 1
583 && file_distance(bksq, wpsq2) <= 1
584 && relative_rank(strongSide, bksq) > r)
587 case RANK_2: return ScaleFactor(10);
588 case RANK_3: return ScaleFactor(10);
589 case RANK_4: return ScaleFactor(15);
590 case RANK_5: return ScaleFactor(20);
591 case RANK_6: return ScaleFactor(40);
592 default: assert(false);
595 return SCALE_FACTOR_NONE;
599 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
600 /// are on the same rook file and are blocked by the defending king, it's a draw.
602 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
604 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
605 assert(pos.count<PAWN>(strongSide) >= 2);
606 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
608 Square ksq = pos.king_square(weakSide);
609 Bitboard pawns = pos.pieces(strongSide, PAWN);
610 Square psq = pos.list<PAWN>(strongSide)[0];
612 // If all pawns are ahead of the king, on a single rook file and
613 // the king is within one file of the pawns, it's a draw.
614 if ( !(pawns & ~in_front_bb(weakSide, rank_of(ksq)))
615 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
616 && file_distance(ksq, psq) <= 1)
617 return SCALE_FACTOR_DRAW;
619 return SCALE_FACTOR_NONE;
623 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
624 /// path of the pawn, and the square of the king is not of the same color as the
625 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
626 /// it's almost always a draw.
628 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
630 assert(verify_material(pos, strongSide, BishopValueMg, 1));
631 assert(verify_material(pos, weakSide, BishopValueMg, 0));
633 Square pawnSq = pos.list<PAWN>(strongSide)[0];
634 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
635 Square weakBishopSq = pos.list<BISHOP>(weakSide)[0];
636 Square weakKingSq = pos.king_square(weakSide);
638 // Case 1: Defending king blocks the pawn, and cannot be driven away
639 if ( file_of(weakKingSq) == file_of(pawnSq)
640 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
641 && ( opposite_colors(weakKingSq, strongBishopSq)
642 || relative_rank(strongSide, weakKingSq) <= RANK_6))
643 return SCALE_FACTOR_DRAW;
645 // Case 2: Opposite colored bishops
646 if (opposite_colors(strongBishopSq, weakBishopSq))
648 // We assume that the position is drawn in the following three situations:
650 // a. The pawn is on rank 5 or further back.
651 // b. The defending king is somewhere in the pawn's path.
652 // c. The defending bishop attacks some square along the pawn's path,
653 // and is at least three squares away from the pawn.
655 // These rules are probably not perfect, but in practice they work
658 if (relative_rank(strongSide, pawnSq) <= RANK_5)
659 return SCALE_FACTOR_DRAW;
662 Bitboard path = forward_bb(strongSide, pawnSq);
664 if (path & pos.pieces(weakSide, KING))
665 return SCALE_FACTOR_DRAW;
667 if ( (pos.attacks_from<BISHOP>(weakBishopSq) & path)
668 && square_distance(weakBishopSq, pawnSq) >= 3)
669 return SCALE_FACTOR_DRAW;
672 return SCALE_FACTOR_NONE;
676 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
678 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
680 assert(verify_material(pos, strongSide, BishopValueMg, 2));
681 assert(verify_material(pos, weakSide, BishopValueMg, 0));
683 Square wbsq = pos.list<BISHOP>(strongSide)[0];
684 Square bbsq = pos.list<BISHOP>(weakSide)[0];
686 if (!opposite_colors(wbsq, bbsq))
687 return SCALE_FACTOR_NONE;
689 Square ksq = pos.king_square(weakSide);
690 Square psq1 = pos.list<PAWN>(strongSide)[0];
691 Square psq2 = pos.list<PAWN>(strongSide)[1];
692 Rank r1 = rank_of(psq1);
693 Rank r2 = rank_of(psq2);
694 Square blockSq1, blockSq2;
696 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
698 blockSq1 = psq1 + pawn_push(strongSide);
699 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
703 blockSq1 = psq2 + pawn_push(strongSide);
704 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
707 switch (file_distance(psq1, psq2))
710 // Both pawns are on the same file. It's an easy draw if the defender firmly
711 // controls some square in the frontmost pawn's path.
712 if ( file_of(ksq) == file_of(blockSq1)
713 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
714 && opposite_colors(ksq, wbsq))
715 return SCALE_FACTOR_DRAW;
717 return SCALE_FACTOR_NONE;
720 // Pawns on adjacent files. It's a draw if the defender firmly controls the
721 // square in front of the frontmost pawn's path, and the square diagonally
722 // behind this square on the file of the other pawn.
724 && opposite_colors(ksq, wbsq)
725 && ( bbsq == blockSq2
726 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
727 || abs(r1 - r2) >= 2))
728 return SCALE_FACTOR_DRAW;
730 else if ( ksq == blockSq2
731 && opposite_colors(ksq, wbsq)
732 && ( bbsq == blockSq1
733 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
734 return SCALE_FACTOR_DRAW;
736 return SCALE_FACTOR_NONE;
739 // The pawns are not on the same file or adjacent files. No scaling.
740 return SCALE_FACTOR_NONE;
745 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
746 /// the path of the pawn, and the square of the king is not of the same color as
747 /// the stronger side's bishop, it's a draw.
749 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
751 assert(verify_material(pos, strongSide, BishopValueMg, 1));
752 assert(verify_material(pos, weakSide, KnightValueMg, 0));
754 Square pawnSq = pos.list<PAWN>(strongSide)[0];
755 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
756 Square weakKingSq = pos.king_square(weakSide);
758 if ( file_of(weakKingSq) == file_of(pawnSq)
759 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
760 && ( opposite_colors(weakKingSq, strongBishopSq)
761 || relative_rank(strongSide, weakKingSq) <= RANK_6))
762 return SCALE_FACTOR_DRAW;
764 return SCALE_FACTOR_NONE;
768 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
769 /// and the defending king prevents the pawn from advancing, the position is drawn.
771 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
773 assert(verify_material(pos, strongSide, KnightValueMg, 1));
774 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
776 // Assume strongSide is white and the pawn is on files A-D
777 Square pawnSq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
778 Square weakKingSq = normalize(pos, strongSide, pos.king_square(weakSide));
780 if (pawnSq == SQ_A7 && square_distance(SQ_A8, weakKingSq) <= 1)
781 return SCALE_FACTOR_DRAW;
783 return SCALE_FACTOR_NONE;
787 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
788 /// Otherwise the position is drawn.
790 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
792 Square pawnSq = pos.list<PAWN>(strongSide)[0];
793 Square bishopSq = pos.list<BISHOP>(weakSide)[0];
794 Square weakKingSq = pos.king_square(weakSide);
796 // King needs to get close to promoting pawn to prevent knight from blocking.
797 // Rules for this are very tricky, so just approximate.
798 if (forward_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
799 return ScaleFactor(square_distance(weakKingSq, pawnSq));
801 return SCALE_FACTOR_NONE;
805 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
806 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
807 /// has at least a draw with the pawn as well. The exception is when the stronger
808 /// side's pawn is far advanced and not on a rook file; in this case it is often
809 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
811 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
813 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
814 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
816 // Assume strongSide is white and the pawn is on files A-D
817 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
818 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
819 Square psq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
821 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
823 // If the pawn has advanced to the fifth rank or further, and is not a
824 // rook pawn, it's too dangerous to assume that it's at least a draw.
825 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
826 return SCALE_FACTOR_NONE;
828 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
829 // it's probably at least a draw even with the pawn.
830 return Bitbases::probe_kpk(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;