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.bishop_pair(strongSide))
170 result += VALUE_KNOWN_WIN;
172 return strongSide == pos.side_to_move() ? result : -result;
176 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
177 /// defending king towards a corner square of the right color.
179 Value Endgame<KBNK>::operator()(const Position& pos) const {
181 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
182 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
184 Square winnerKSq = pos.king_square(strongSide);
185 Square loserKSq = pos.king_square(weakSide);
186 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
188 // kbnk_mate_table() tries to drive toward corners A1 or H8. If we have a
189 // bishop that cannot reach the above squares, we flip the kings in order
190 // to drive the enemy toward corners A8 or H1.
191 if (opposite_colors(bishopSq, SQ_A1))
193 winnerKSq = ~winnerKSq;
194 loserKSq = ~loserKSq;
197 Value result = VALUE_KNOWN_WIN
198 + PushClose[square_distance(winnerKSq, loserKSq)]
199 + PushToCorners[loserKSq];
201 return strongSide == pos.side_to_move() ? result : -result;
205 /// KP vs K. This endgame is evaluated with the help of a bitbase.
207 Value Endgame<KPK>::operator()(const Position& pos) const {
209 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
210 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
212 // Assume strongSide is white and the pawn is on files A-D
213 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
214 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
215 Square psq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
217 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
219 if (!Bitbases::probe_kpk(wksq, psq, bksq, us))
222 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
224 return strongSide == pos.side_to_move() ? result : -result;
228 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
229 /// a bitbase. The function below returns drawish scores when the pawn is
230 /// far advanced with support of the king, while the attacking king is far
233 Value Endgame<KRKP>::operator()(const Position& pos) const {
235 assert(verify_material(pos, strongSide, RookValueMg, 0));
236 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
238 Square wksq = relative_square(strongSide, pos.king_square(strongSide));
239 Square bksq = relative_square(strongSide, pos.king_square(weakSide));
240 Square rsq = relative_square(strongSide, pos.list<ROOK>(strongSide)[0]);
241 Square psq = relative_square(strongSide, pos.list<PAWN>(weakSide)[0]);
243 Square queeningSq = make_square(file_of(psq), RANK_1);
246 // If the stronger side's king is in front of the pawn, it's a win
247 if (wksq < psq && file_of(wksq) == file_of(psq))
248 result = RookValueEg - square_distance(wksq, psq);
250 // If the weaker side's king is too far from the pawn and the rook,
252 else if ( square_distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
253 && square_distance(bksq, rsq) >= 3)
254 result = RookValueEg - square_distance(wksq, psq);
256 // If the pawn is far advanced and supported by the defending king,
257 // the position is drawish
258 else if ( rank_of(bksq) <= RANK_3
259 && square_distance(bksq, psq) == 1
260 && rank_of(wksq) >= RANK_4
261 && square_distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
262 result = Value(80) - 8 * square_distance(wksq, psq);
265 result = Value(200) - 8 * ( square_distance(wksq, psq + DELTA_S)
266 - square_distance(bksq, psq + DELTA_S)
267 - square_distance(psq, queeningSq));
269 return strongSide == pos.side_to_move() ? result : -result;
273 /// KR vs KB. This is very simple, and always returns drawish scores. The
274 /// score is slightly bigger when the defending king is close to the edge.
276 Value Endgame<KRKB>::operator()(const Position& pos) const {
278 assert(verify_material(pos, strongSide, RookValueMg, 0));
279 assert(verify_material(pos, weakSide, BishopValueMg, 0));
281 Value result = Value(PushToEdges[pos.king_square(weakSide)]);
282 return strongSide == pos.side_to_move() ? result : -result;
286 /// KR vs KN. The attacking side has slightly better winning chances than
287 /// in KR vs KB, particularly if the king and the knight are far apart.
289 Value Endgame<KRKN>::operator()(const Position& pos) const {
291 assert(verify_material(pos, strongSide, RookValueMg, 0));
292 assert(verify_material(pos, weakSide, KnightValueMg, 0));
294 Square bksq = pos.king_square(weakSide);
295 Square bnsq = pos.list<KNIGHT>(weakSide)[0];
296 Value result = Value(PushToEdges[bksq] + PushAway[square_distance(bksq, bnsq)]);
297 return strongSide == pos.side_to_move() ? result : -result;
301 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
302 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
303 /// with a king positioned next to it can be a draw, so in that case, we only
304 /// use the distance between the kings.
306 Value Endgame<KQKP>::operator()(const Position& pos) const {
308 assert(verify_material(pos, strongSide, QueenValueMg, 0));
309 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
311 Square winnerKSq = pos.king_square(strongSide);
312 Square loserKSq = pos.king_square(weakSide);
313 Square pawnSq = pos.list<PAWN>(weakSide)[0];
315 Value result = Value(PushClose[square_distance(winnerKSq, loserKSq)]);
317 if ( relative_rank(weakSide, pawnSq) != RANK_7
318 || square_distance(loserKSq, pawnSq) != 1
319 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
320 result += QueenValueEg - PawnValueEg;
322 return strongSide == pos.side_to_move() ? result : -result;
326 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
327 /// king a bonus for having the kings close together, and for forcing the
328 /// defending king towards the edge. If we also take care to avoid null move for
329 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
331 Value Endgame<KQKR>::operator()(const Position& pos) const {
333 assert(verify_material(pos, strongSide, QueenValueMg, 0));
334 assert(verify_material(pos, weakSide, RookValueMg, 0));
336 Square winnerKSq = pos.king_square(strongSide);
337 Square loserKSq = pos.king_square(weakSide);
339 Value result = QueenValueEg
341 + PushToEdges[loserKSq]
342 + PushClose[square_distance(winnerKSq, loserKSq)];
344 return strongSide == pos.side_to_move() ? result : -result;
348 /// Some cases of trivial draws
349 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
352 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
353 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
354 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
357 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
359 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
360 assert(pos.count<PAWN>(strongSide) >= 1);
362 // No assertions about the material of weakSide, because we want draws to
363 // be detected even when the weaker side has some pawns.
365 Bitboard pawns = pos.pieces(strongSide, PAWN);
366 File pawnsFile = file_of(lsb(pawns));
368 // All pawns are on a single rook file ?
369 if ( (pawnsFile == FILE_A || pawnsFile == FILE_H)
370 && !(pawns & ~file_bb(pawnsFile)))
372 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
373 Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
374 Square kingSq = pos.king_square(weakSide);
376 // If the bishop has the wrong color, and the defending king is on the file
377 // of the pawn(s) or the neighboring file, then it's potentially a draw.
378 if ( opposite_colors(queeningSq, bishopSq)
379 && file_distance(kingSq, lsb(pawns)) <= 1)
381 // If the defending king has distance <= 1 to the promotion square or
382 // is placed somewhere in front of the frontmost pawn, it's a draw.
383 Rank rank = relative_rank(strongSide, (frontmost_sq(strongSide, pawns)));
385 if ( square_distance(kingSq, queeningSq) <= 1
386 || relative_rank(strongSide, kingSq) >= rank)
387 return SCALE_FACTOR_DRAW;
391 return SCALE_FACTOR_NONE;
395 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
396 /// the third rank defended by a pawn.
398 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
400 assert(verify_material(pos, strongSide, QueenValueMg, 0));
401 assert(pos.count<ROOK>(weakSide) == 1);
402 assert(pos.count<PAWN>(weakSide) >= 1);
404 Square kingSq = pos.king_square(weakSide);
405 Square rsq = pos.list<ROOK>(weakSide)[0];
407 if ( relative_rank(weakSide, kingSq) <= RANK_2
408 && relative_rank(weakSide, pos.king_square(strongSide)) >= RANK_4
409 && relative_rank(weakSide, rsq) == RANK_3
410 && ( pos.pieces(weakSide, PAWN)
411 & pos.attacks_from<KING>(kingSq)
412 & pos.attacks_from<PAWN>(rsq, strongSide)))
413 return SCALE_FACTOR_DRAW;
415 return SCALE_FACTOR_NONE;
419 /// KRP vs KR. This function knows a handful of the most important classes of
420 /// drawn positions, but is far from perfect. It would probably be a good idea
421 /// to add more knowledge in the future.
423 /// It would also be nice to rewrite the actual code for this function,
424 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
426 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
428 assert(verify_material(pos, strongSide, RookValueMg, 1));
429 assert(verify_material(pos, weakSide, RookValueMg, 0));
431 // Assume strongSide is white and the pawn is on files A-D
432 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
433 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
434 Square wrsq = normalize(pos, strongSide, pos.list<ROOK>(strongSide)[0]);
435 Square wpsq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
436 Square brsq = normalize(pos, strongSide, pos.list<ROOK>(weakSide)[0]);
438 File f = file_of(wpsq);
439 Rank r = rank_of(wpsq);
440 Square queeningSq = make_square(f, RANK_8);
441 int tempo = (pos.side_to_move() == strongSide);
443 // If the pawn is not too far advanced and the defending king defends the
444 // queening square, use the third-rank defence.
446 && square_distance(bksq, queeningSq) <= 1
448 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
449 return SCALE_FACTOR_DRAW;
451 // The defending side saves a draw by checking from behind in case the pawn
452 // has advanced to the 6th rank with the king behind.
454 && square_distance(bksq, queeningSq) <= 1
455 && rank_of(wksq) + tempo <= RANK_6
456 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
457 return SCALE_FACTOR_DRAW;
460 && bksq == queeningSq
461 && rank_of(brsq) == RANK_1
462 && (!tempo || square_distance(wksq, wpsq) >= 2))
463 return SCALE_FACTOR_DRAW;
465 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
466 // and the black rook is behind the pawn.
469 && (bksq == SQ_H7 || bksq == SQ_G7)
470 && file_of(brsq) == FILE_A
471 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
472 return SCALE_FACTOR_DRAW;
474 // If the defending king blocks the pawn and the attacking king is too far
475 // away, it's a draw.
477 && bksq == wpsq + DELTA_N
478 && square_distance(wksq, wpsq) - tempo >= 2
479 && square_distance(wksq, brsq) - tempo >= 2)
480 return SCALE_FACTOR_DRAW;
482 // Pawn on the 7th rank supported by the rook from behind usually wins if the
483 // attacking king is closer to the queening square than the defending king,
484 // and the defending king cannot gain tempi by threatening the attacking rook.
487 && file_of(wrsq) == f
488 && wrsq != queeningSq
489 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
490 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
491 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
493 // Similar to the above, but with the pawn further back
495 && file_of(wrsq) == f
497 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
498 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
499 && ( square_distance(bksq, wrsq) + tempo >= 3
500 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
501 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
502 return ScaleFactor( SCALE_FACTOR_MAX
503 - 8 * square_distance(wpsq, queeningSq)
504 - 2 * square_distance(wksq, queeningSq));
506 // If the pawn is not far advanced and the defending king is somewhere in
507 // the pawn's path, it's probably a draw.
508 if (r <= RANK_4 && bksq > wpsq)
510 if (file_of(bksq) == file_of(wpsq))
511 return ScaleFactor(10);
512 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
513 && square_distance(wksq, bksq) > 2)
514 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
516 return SCALE_FACTOR_NONE;
520 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
522 assert(verify_material(pos, strongSide, RookValueMg, 1));
523 assert(verify_material(pos, weakSide, BishopValueMg, 0));
525 // Test for a rook pawn
526 if (pos.pieces(PAWN) & (FileABB | FileHBB))
528 Square ksq = pos.king_square(weakSide);
529 Square bsq = pos.list<BISHOP>(weakSide)[0];
530 Square psq = pos.list<PAWN>(strongSide)[0];
531 Rank rk = relative_rank(strongSide, psq);
532 Square push = pawn_push(strongSide);
534 // If the pawn is on the 5th rank and the pawn (currently) is on
535 // the same color square as the bishop then there is a chance of
536 // a fortress. Depending on the king position give a moderate
537 // reduction or a stronger one if the defending king is near the
538 // corner but not trapped there.
539 if (rk == RANK_5 && !opposite_colors(bsq, psq))
541 int d = square_distance(psq + 3 * push, ksq);
543 if (d <= 2 && !(d == 0 && ksq == pos.king_square(strongSide) + 2 * push))
544 return ScaleFactor(24);
546 return ScaleFactor(48);
549 // When the pawn has moved to the 6th rank we can be fairly sure
550 // it's drawn if the bishop attacks the square in front of the
551 // pawn from a reasonable distance and the defending king is near
554 && square_distance(psq + 2 * push, ksq) <= 1
555 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
556 && file_distance(bsq, psq) >= 2)
557 return ScaleFactor(8);
560 return SCALE_FACTOR_NONE;
563 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
564 /// pawns and the defending king is actively placed, the position is drawish.
566 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
568 assert(verify_material(pos, strongSide, RookValueMg, 2));
569 assert(verify_material(pos, weakSide, RookValueMg, 1));
571 Square wpsq1 = pos.list<PAWN>(strongSide)[0];
572 Square wpsq2 = pos.list<PAWN>(strongSide)[1];
573 Square bksq = pos.king_square(weakSide);
575 // Does the stronger side have a passed pawn?
576 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
577 return SCALE_FACTOR_NONE;
579 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
581 if ( file_distance(bksq, wpsq1) <= 1
582 && file_distance(bksq, wpsq2) <= 1
583 && relative_rank(strongSide, bksq) > r)
586 case RANK_2: return ScaleFactor(10);
587 case RANK_3: return ScaleFactor(10);
588 case RANK_4: return ScaleFactor(15);
589 case RANK_5: return ScaleFactor(20);
590 case RANK_6: return ScaleFactor(40);
591 default: assert(false);
594 return SCALE_FACTOR_NONE;
598 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
599 /// are on the same rook file and are blocked by the defending king, it's a draw.
601 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
603 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
604 assert(pos.count<PAWN>(strongSide) >= 2);
605 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
607 Square ksq = pos.king_square(weakSide);
608 Bitboard pawns = pos.pieces(strongSide, PAWN);
609 Square psq = pos.list<PAWN>(strongSide)[0];
611 // If all pawns are ahead of the king, on a single rook file and
612 // the king is within one file of the pawns, it's a draw.
613 if ( !(pawns & ~in_front_bb(weakSide, rank_of(ksq)))
614 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
615 && file_distance(ksq, psq) <= 1)
616 return SCALE_FACTOR_DRAW;
618 return SCALE_FACTOR_NONE;
622 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
623 /// path of the pawn, and the square of the king is not of the same color as the
624 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
625 /// it's almost always a draw.
627 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
629 assert(verify_material(pos, strongSide, BishopValueMg, 1));
630 assert(verify_material(pos, weakSide, BishopValueMg, 0));
632 Square pawnSq = pos.list<PAWN>(strongSide)[0];
633 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
634 Square weakBishopSq = pos.list<BISHOP>(weakSide)[0];
635 Square weakKingSq = pos.king_square(weakSide);
637 // Case 1: Defending king blocks the pawn, and cannot be driven away
638 if ( file_of(weakKingSq) == file_of(pawnSq)
639 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
640 && ( opposite_colors(weakKingSq, strongBishopSq)
641 || relative_rank(strongSide, weakKingSq) <= RANK_6))
642 return SCALE_FACTOR_DRAW;
644 // Case 2: Opposite colored bishops
645 if (opposite_colors(strongBishopSq, weakBishopSq))
647 // We assume that the position is drawn in the following three situations:
649 // a. The pawn is on rank 5 or further back.
650 // b. The defending king is somewhere in the pawn's path.
651 // c. The defending bishop attacks some square along the pawn's path,
652 // and is at least three squares away from the pawn.
654 // These rules are probably not perfect, but in practice they work
657 if (relative_rank(strongSide, pawnSq) <= RANK_5)
658 return SCALE_FACTOR_DRAW;
661 Bitboard path = forward_bb(strongSide, pawnSq);
663 if (path & pos.pieces(weakSide, KING))
664 return SCALE_FACTOR_DRAW;
666 if ( (pos.attacks_from<BISHOP>(weakBishopSq) & path)
667 && square_distance(weakBishopSq, pawnSq) >= 3)
668 return SCALE_FACTOR_DRAW;
671 return SCALE_FACTOR_NONE;
675 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
677 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
679 assert(verify_material(pos, strongSide, BishopValueMg, 2));
680 assert(verify_material(pos, weakSide, BishopValueMg, 0));
682 Square wbsq = pos.list<BISHOP>(strongSide)[0];
683 Square bbsq = pos.list<BISHOP>(weakSide)[0];
685 if (!opposite_colors(wbsq, bbsq))
686 return SCALE_FACTOR_NONE;
688 Square ksq = pos.king_square(weakSide);
689 Square psq1 = pos.list<PAWN>(strongSide)[0];
690 Square psq2 = pos.list<PAWN>(strongSide)[1];
691 Rank r1 = rank_of(psq1);
692 Rank r2 = rank_of(psq2);
693 Square blockSq1, blockSq2;
695 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
697 blockSq1 = psq1 + pawn_push(strongSide);
698 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
702 blockSq1 = psq2 + pawn_push(strongSide);
703 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
706 switch (file_distance(psq1, psq2))
709 // Both pawns are on the same file. It's an easy draw if the defender firmly
710 // controls some square in the frontmost pawn's path.
711 if ( file_of(ksq) == file_of(blockSq1)
712 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
713 && opposite_colors(ksq, wbsq))
714 return SCALE_FACTOR_DRAW;
716 return SCALE_FACTOR_NONE;
719 // Pawns on adjacent files. It's a draw if the defender firmly controls the
720 // square in front of the frontmost pawn's path, and the square diagonally
721 // behind this square on the file of the other pawn.
723 && opposite_colors(ksq, wbsq)
724 && ( bbsq == blockSq2
725 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
726 || abs(r1 - r2) >= 2))
727 return SCALE_FACTOR_DRAW;
729 else if ( ksq == blockSq2
730 && opposite_colors(ksq, wbsq)
731 && ( bbsq == blockSq1
732 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
733 return SCALE_FACTOR_DRAW;
735 return SCALE_FACTOR_NONE;
738 // The pawns are not on the same file or adjacent files. No scaling.
739 return SCALE_FACTOR_NONE;
744 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
745 /// the path of the pawn, and the square of the king is not of the same color as
746 /// the stronger side's bishop, it's a draw.
748 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
750 assert(verify_material(pos, strongSide, BishopValueMg, 1));
751 assert(verify_material(pos, weakSide, KnightValueMg, 0));
753 Square pawnSq = pos.list<PAWN>(strongSide)[0];
754 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
755 Square weakKingSq = pos.king_square(weakSide);
757 if ( file_of(weakKingSq) == file_of(pawnSq)
758 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
759 && ( opposite_colors(weakKingSq, strongBishopSq)
760 || relative_rank(strongSide, weakKingSq) <= RANK_6))
761 return SCALE_FACTOR_DRAW;
763 return SCALE_FACTOR_NONE;
767 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
768 /// and the defending king prevents the pawn from advancing, the position is drawn.
770 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
772 assert(verify_material(pos, strongSide, KnightValueMg, 1));
773 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
775 // Assume strongSide is white and the pawn is on files A-D
776 Square pawnSq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
777 Square weakKingSq = normalize(pos, strongSide, pos.king_square(weakSide));
779 if (pawnSq == SQ_A7 && square_distance(SQ_A8, weakKingSq) <= 1)
780 return SCALE_FACTOR_DRAW;
782 return SCALE_FACTOR_NONE;
786 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
787 /// Otherwise the position is drawn.
789 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
791 Square pawnSq = pos.list<PAWN>(strongSide)[0];
792 Square bishopSq = pos.list<BISHOP>(weakSide)[0];
793 Square weakKingSq = pos.king_square(weakSide);
795 // King needs to get close to promoting pawn to prevent knight from blocking.
796 // Rules for this are very tricky, so just approximate.
797 if (forward_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
798 return ScaleFactor(square_distance(weakKingSq, pawnSq));
800 return SCALE_FACTOR_NONE;
804 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
805 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
806 /// has at least a draw with the pawn as well. The exception is when the stronger
807 /// side's pawn is far advanced and not on a rook file; in this case it is often
808 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
810 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
812 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
813 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
815 // Assume strongSide is white and the pawn is on files A-D
816 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
817 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
818 Square psq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
820 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
822 // If the pawn has advanced to the fifth rank or further, and is not a
823 // rook pawn, it's too dangerous to assume that it's at least a draw.
824 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
825 return SCALE_FACTOR_NONE;
827 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
828 // it's probably at least a draw even with the pawn.
829 return Bitbases::probe_kpk(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;