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. Note that the
86 // FEN string could correspond to an illegal position.
87 Key key(const string& code, Color c) {
89 assert(code.length() > 0 && code.length() < 8);
90 assert(code[0] == 'K');
92 string sides[] = { code.substr(code.find('K', 1)), // Weak
93 code.substr(0, code.find('K', 1)) }; // Strong
95 std::transform(sides[c].begin(), sides[c].end(), sides[c].begin(), tolower);
97 string fen = sides[0] + char('0' + int(8 - code.length()))
98 + sides[1] + "/8/8/8/8/8/8/8 w - - 0 10";
100 return Position(fen, false, NULL).material_key();
104 void delete_endgame(const typename M::value_type& p) { delete p.second; }
109 /// Endgames members definitions
111 Endgames::Endgames() {
129 add<KBPPKB>("KBPPKB");
130 add<KRPPKRP>("KRPPKRP");
133 Endgames::~Endgames() {
135 for_each(m1.begin(), m1.end(), delete_endgame<M1>);
136 for_each(m2.begin(), m2.end(), delete_endgame<M2>);
139 template<EndgameType E>
140 void Endgames::add(const string& code) {
142 map((Endgame<E>*)0)[key(code, WHITE)] = new Endgame<E>(WHITE);
143 map((Endgame<E>*)0)[key(code, BLACK)] = new Endgame<E>(BLACK);
147 /// Mate with KX vs K. This function is used to evaluate positions with
148 /// king and plenty of material vs a lone king. It simply gives the
149 /// attacking side a bonus for driving the defending king towards the edge
150 /// of the board, and for keeping the distance between the two kings small.
152 Value Endgame<KXK>::operator()(const Position& pos) const {
154 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
155 assert(!pos.checkers()); // Eval is never called when in check
157 // Stalemate detection with lone king
158 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
161 Square winnerKSq = pos.king_square(strongSide);
162 Square loserKSq = pos.king_square(weakSide);
164 Value result = pos.non_pawn_material(strongSide)
165 + pos.count<PAWN>(strongSide) * PawnValueEg
166 + PushToEdges[loserKSq]
167 + PushClose[square_distance(winnerKSq, loserKSq)];
169 if ( pos.count<QUEEN>(strongSide)
170 || pos.count<ROOK>(strongSide)
171 || pos.bishop_pair(strongSide))
172 result += VALUE_KNOWN_WIN;
174 return strongSide == pos.side_to_move() ? result : -result;
178 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
179 /// defending king towards a corner square of the right color.
181 Value Endgame<KBNK>::operator()(const Position& pos) const {
183 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
184 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
186 Square winnerKSq = pos.king_square(strongSide);
187 Square loserKSq = pos.king_square(weakSide);
188 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
190 // kbnk_mate_table() tries to drive toward corners A1 or H8. If we have a
191 // bishop that cannot reach the above squares, we flip the kings in order
192 // to drive the enemy toward corners A8 or H1.
193 if (opposite_colors(bishopSq, SQ_A1))
195 winnerKSq = ~winnerKSq;
196 loserKSq = ~loserKSq;
199 Value result = VALUE_KNOWN_WIN
200 + PushClose[square_distance(winnerKSq, loserKSq)]
201 + PushToCorners[loserKSq];
203 return strongSide == pos.side_to_move() ? result : -result;
207 /// KP vs K. This endgame is evaluated with the help of a bitbase.
209 Value Endgame<KPK>::operator()(const Position& pos) const {
211 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
212 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
214 // Assume strongSide is white and the pawn is on files A-D
215 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
216 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
217 Square psq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
219 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
221 if (!Bitbases::probe_kpk(wksq, psq, bksq, us))
224 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
226 return strongSide == pos.side_to_move() ? result : -result;
230 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
231 /// a bitbase. The function below returns drawish scores when the pawn is
232 /// far advanced with support of the king, while the attacking king is far
235 Value Endgame<KRKP>::operator()(const Position& pos) const {
237 assert(verify_material(pos, strongSide, RookValueMg, 0));
238 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
240 Square wksq = relative_square(strongSide, pos.king_square(strongSide));
241 Square bksq = relative_square(strongSide, pos.king_square(weakSide));
242 Square rsq = relative_square(strongSide, pos.list<ROOK>(strongSide)[0]);
243 Square psq = relative_square(strongSide, pos.list<PAWN>(weakSide)[0]);
245 Square queeningSq = file_of(psq) | RANK_1;
248 // If the stronger side's king is in front of the pawn, it's a win
249 if (wksq < psq && file_of(wksq) == file_of(psq))
250 result = RookValueEg - Value(square_distance(wksq, psq));
252 // If the weaker side's king is too far from the pawn and the rook,
254 else if ( square_distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
255 && square_distance(bksq, rsq) >= 3)
256 result = RookValueEg - Value(square_distance(wksq, psq));
258 // If the pawn is far advanced and supported by the defending king,
259 // the position is drawish
260 else if ( rank_of(bksq) <= RANK_3
261 && square_distance(bksq, psq) == 1
262 && rank_of(wksq) >= RANK_4
263 && square_distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
264 result = Value(80 - square_distance(wksq, psq) * 8);
268 - Value(square_distance(wksq, psq + DELTA_S) * 8)
269 + Value(square_distance(bksq, psq + DELTA_S) * 8)
270 + Value(square_distance(psq, queeningSq) * 8);
272 return strongSide == pos.side_to_move() ? result : -result;
276 /// KR vs KB. This is very simple, and always returns drawish scores. The
277 /// score is slightly bigger when the defending king is close to the edge.
279 Value Endgame<KRKB>::operator()(const Position& pos) const {
281 assert(verify_material(pos, strongSide, RookValueMg, 0));
282 assert(verify_material(pos, weakSide, BishopValueMg, 0));
284 Value result = Value(PushToEdges[pos.king_square(weakSide)]);
285 return strongSide == pos.side_to_move() ? result : -result;
289 /// KR vs KN. The attacking side has slightly better winning chances than
290 /// in KR vs KB, particularly if the king and the knight are far apart.
292 Value Endgame<KRKN>::operator()(const Position& pos) const {
294 assert(verify_material(pos, strongSide, RookValueMg, 0));
295 assert(verify_material(pos, weakSide, KnightValueMg, 0));
297 Square bksq = pos.king_square(weakSide);
298 Square bnsq = pos.list<KNIGHT>(weakSide)[0];
299 Value result = Value(PushToEdges[bksq] + PushAway[square_distance(bksq, bnsq)]);
300 return strongSide == pos.side_to_move() ? result : -result;
304 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
305 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
306 /// with a king positioned next to it can be a draw, so in that case, we only
307 /// use the distance between the kings.
309 Value Endgame<KQKP>::operator()(const Position& pos) const {
311 assert(verify_material(pos, strongSide, QueenValueMg, 0));
312 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
314 Square winnerKSq = pos.king_square(strongSide);
315 Square loserKSq = pos.king_square(weakSide);
316 Square pawnSq = pos.list<PAWN>(weakSide)[0];
318 Value result = Value(PushClose[square_distance(winnerKSq, loserKSq)]);
320 if ( relative_rank(weakSide, pawnSq) != RANK_7
321 || square_distance(loserKSq, pawnSq) != 1
322 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
323 result += QueenValueEg - PawnValueEg;
325 return strongSide == pos.side_to_move() ? result : -result;
329 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
330 /// king a bonus for having the kings close together, and for forcing the
331 /// defending king towards the edge. If we also take care to avoid null move for
332 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
334 Value Endgame<KQKR>::operator()(const Position& pos) const {
336 assert(verify_material(pos, strongSide, QueenValueMg, 0));
337 assert(verify_material(pos, weakSide, RookValueMg, 0));
339 Square winnerKSq = pos.king_square(strongSide);
340 Square loserKSq = pos.king_square(weakSide);
342 Value result = QueenValueEg
344 + PushToEdges[loserKSq]
345 + PushClose[square_distance(winnerKSq, loserKSq)];
347 return strongSide == pos.side_to_move() ? result : -result;
351 /// KBB vs KN. This is almost always a win. We try to push the enemy king to a corner
352 /// and away from his knight. For a reference of this difficult endgame see:
353 /// en.wikipedia.org/wiki/Chess_endgame#Effect_of_tablebases_on_endgame_theory
356 Value Endgame<KBBKN>::operator()(const Position& pos) const {
358 assert(verify_material(pos, strongSide, 2 * BishopValueMg, 0));
359 assert(verify_material(pos, weakSide, KnightValueMg, 0));
361 Square winnerKSq = pos.king_square(strongSide);
362 Square loserKSq = pos.king_square(weakSide);
363 Square knightSq = pos.list<KNIGHT>(weakSide)[0];
365 Value result = VALUE_KNOWN_WIN
366 + PushToCorners[loserKSq]
367 + PushClose[square_distance(winnerKSq, loserKSq)]
368 + PushAway[square_distance(loserKSq, knightSq)];
370 return strongSide == pos.side_to_move() ? result : -result;
374 /// Some cases of trivial draws
375 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
376 template<> Value Endgame<KmmKm>::operator()(const Position&) const { return VALUE_DRAW; }
379 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
380 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
381 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
384 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
386 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
387 assert(pos.count<PAWN>(strongSide) >= 1);
389 // No assertions about the material of weakSide, because we want draws to
390 // be detected even when the weaker side has some pawns.
392 Bitboard pawns = pos.pieces(strongSide, PAWN);
393 File pawnFile = file_of(pos.list<PAWN>(strongSide)[0]);
395 // All pawns are on a single rook file ?
396 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
397 && !(pawns & ~file_bb(pawnFile)))
399 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
400 Square queeningSq = relative_square(strongSide, pawnFile | RANK_8);
401 Square kingSq = pos.king_square(weakSide);
403 if ( opposite_colors(queeningSq, bishopSq)
404 && square_distance(queeningSq, kingSq) <= 1)
405 return SCALE_FACTOR_DRAW;
408 // If all the pawns are on the same B or G file, then it's potentially a draw
409 if ( (pawnFile == FILE_B || pawnFile == FILE_G)
410 && !(pos.pieces(PAWN) & ~file_bb(pawnFile))
411 && pos.non_pawn_material(weakSide) == 0
412 && pos.count<PAWN>(weakSide) >= 1)
414 // Get weakSide pawn that is closest to the home rank
415 Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
417 Square strongKingSq = pos.king_square(strongSide);
418 Square weakKingSq = pos.king_square(weakSide);
419 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
421 // There's potential for a draw if our pawn is blocked on the 7th rank,
422 // the bishop cannot attack it or they only have one pawn left
423 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
424 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
425 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
427 int strongKingDist = square_distance(weakPawnSq, strongKingSq);
428 int weakKingDist = square_distance(weakPawnSq, weakKingSq);
430 // It's a draw if the weak king is on its back two ranks, within 2
431 // squares of the blocking pawn and the strong king is not
432 // closer. (I think this rule only fails in practically
433 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
434 // and positions where qsearch will immediately correct the
435 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
436 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
438 && weakKingDist <= strongKingDist)
439 return SCALE_FACTOR_DRAW;
443 return SCALE_FACTOR_NONE;
447 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
448 /// the third rank defended by a pawn.
450 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
452 assert(verify_material(pos, strongSide, QueenValueMg, 0));
453 assert(pos.count<ROOK>(weakSide) == 1);
454 assert(pos.count<PAWN>(weakSide) >= 1);
456 Square kingSq = pos.king_square(weakSide);
457 Square rsq = pos.list<ROOK>(weakSide)[0];
459 if ( relative_rank(weakSide, kingSq) <= RANK_2
460 && relative_rank(weakSide, pos.king_square(strongSide)) >= RANK_4
461 && relative_rank(weakSide, rsq) == RANK_3
462 && ( pos.pieces(weakSide, PAWN)
463 & pos.attacks_from<KING>(kingSq)
464 & pos.attacks_from<PAWN>(rsq, strongSide)))
465 return SCALE_FACTOR_DRAW;
467 return SCALE_FACTOR_NONE;
471 /// KRP vs KR. This function knows a handful of the most important classes of
472 /// drawn positions, but is far from perfect. It would probably be a good idea
473 /// to add more knowledge in the future.
475 /// It would also be nice to rewrite the actual code for this function,
476 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
478 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
480 assert(verify_material(pos, strongSide, RookValueMg, 1));
481 assert(verify_material(pos, weakSide, RookValueMg, 0));
483 // Assume strongSide is white and the pawn is on files A-D
484 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
485 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
486 Square wrsq = normalize(pos, strongSide, pos.list<ROOK>(strongSide)[0]);
487 Square wpsq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
488 Square brsq = normalize(pos, strongSide, pos.list<ROOK>(weakSide)[0]);
490 File f = file_of(wpsq);
491 Rank r = rank_of(wpsq);
492 Square queeningSq = f | RANK_8;
493 int tempo = (pos.side_to_move() == strongSide);
495 // If the pawn is not too far advanced and the defending king defends the
496 // queening square, use the third-rank defence.
498 && square_distance(bksq, queeningSq) <= 1
500 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
501 return SCALE_FACTOR_DRAW;
503 // The defending side saves a draw by checking from behind in case the pawn
504 // has advanced to the 6th rank with the king behind.
506 && square_distance(bksq, queeningSq) <= 1
507 && rank_of(wksq) + tempo <= RANK_6
508 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
509 return SCALE_FACTOR_DRAW;
512 && bksq == queeningSq
513 && rank_of(brsq) == RANK_1
514 && (!tempo || square_distance(wksq, wpsq) >= 2))
515 return SCALE_FACTOR_DRAW;
517 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
518 // and the black rook is behind the pawn.
521 && (bksq == SQ_H7 || bksq == SQ_G7)
522 && file_of(brsq) == FILE_A
523 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
524 return SCALE_FACTOR_DRAW;
526 // If the defending king blocks the pawn and the attacking king is too far
527 // away, it's a draw.
529 && bksq == wpsq + DELTA_N
530 && square_distance(wksq, wpsq) - tempo >= 2
531 && square_distance(wksq, brsq) - tempo >= 2)
532 return SCALE_FACTOR_DRAW;
534 // Pawn on the 7th rank supported by the rook from behind usually wins if the
535 // attacking king is closer to the queening square than the defending king,
536 // and the defending king cannot gain tempi by threatening the attacking rook.
539 && file_of(wrsq) == f
540 && wrsq != queeningSq
541 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
542 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
543 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
545 // Similar to the above, but with the pawn further back
547 && file_of(wrsq) == f
549 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
550 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
551 && ( square_distance(bksq, wrsq) + tempo >= 3
552 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
553 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
554 return ScaleFactor( SCALE_FACTOR_MAX
555 - 8 * square_distance(wpsq, queeningSq)
556 - 2 * square_distance(wksq, queeningSq));
558 // If the pawn is not far advanced and the defending king is somewhere in
559 // the pawn's path, it's probably a draw.
560 if (r <= RANK_4 && bksq > wpsq)
562 if (file_of(bksq) == file_of(wpsq))
563 return ScaleFactor(10);
564 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
565 && square_distance(wksq, bksq) > 2)
566 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
568 return SCALE_FACTOR_NONE;
572 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
574 assert(verify_material(pos, strongSide, RookValueMg, 1));
575 assert(verify_material(pos, weakSide, BishopValueMg, 0));
577 // Test for a rook pawn
578 if (pos.pieces(PAWN) & (FileABB | FileHBB))
580 Square ksq = pos.king_square(weakSide);
581 Square bsq = pos.list<BISHOP>(weakSide)[0];
582 Square psq = pos.list<PAWN>(strongSide)[0];
583 Rank rk = relative_rank(strongSide, psq);
584 Square push = pawn_push(strongSide);
586 // If the pawn is on the 5th rank and the pawn (currently) is on
587 // the same color square as the bishop then there is a chance of
588 // a fortress. Depending on the king position give a moderate
589 // reduction or a stronger one if the defending king is near the
590 // corner but not trapped there.
591 if (rk == RANK_5 && !opposite_colors(bsq, psq))
593 int d = square_distance(psq + 3 * push, ksq);
595 if (d <= 2 && !(d == 0 && ksq == pos.king_square(strongSide) + 2 * push))
596 return ScaleFactor(24);
598 return ScaleFactor(48);
601 // When the pawn has moved to the 6th rank we can be fairly sure
602 // it's drawn if the bishop attacks the square in front of the
603 // pawn from a reasonable distance and the defending king is near
606 && square_distance(psq + 2 * push, ksq) <= 1
607 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
608 && file_distance(bsq, psq) >= 2)
609 return ScaleFactor(8);
612 return SCALE_FACTOR_NONE;
615 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
616 /// pawns and the defending king is actively placed, the position is drawish.
618 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
620 assert(verify_material(pos, strongSide, RookValueMg, 2));
621 assert(verify_material(pos, weakSide, RookValueMg, 1));
623 Square wpsq1 = pos.list<PAWN>(strongSide)[0];
624 Square wpsq2 = pos.list<PAWN>(strongSide)[1];
625 Square bksq = pos.king_square(weakSide);
627 // Does the stronger side have a passed pawn?
628 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
629 return SCALE_FACTOR_NONE;
631 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
633 if ( file_distance(bksq, wpsq1) <= 1
634 && file_distance(bksq, wpsq2) <= 1
635 && relative_rank(strongSide, bksq) > r)
638 case RANK_2: return ScaleFactor(10);
639 case RANK_3: return ScaleFactor(10);
640 case RANK_4: return ScaleFactor(15);
641 case RANK_5: return ScaleFactor(20);
642 case RANK_6: return ScaleFactor(40);
643 default: assert(false);
646 return SCALE_FACTOR_NONE;
650 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
651 /// are on the same rook file and are blocked by the defending king, it's a draw.
653 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
655 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
656 assert(pos.count<PAWN>(strongSide) >= 2);
657 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
659 Square ksq = pos.king_square(weakSide);
660 Bitboard pawns = pos.pieces(strongSide, PAWN);
661 Square psq = pos.list<PAWN>(strongSide)[0];
663 // If all pawns are ahead of the king, on a single rook file and
664 // the king is within one file of the pawns, it's a draw.
665 if ( !(pawns & ~in_front_bb(weakSide, rank_of(ksq)))
666 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
667 && file_distance(ksq, psq) <= 1)
668 return SCALE_FACTOR_DRAW;
670 return SCALE_FACTOR_NONE;
674 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
675 /// path of the pawn, and the square of the king is not of the same color as the
676 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
677 /// it's almost always a draw.
679 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
681 assert(verify_material(pos, strongSide, BishopValueMg, 1));
682 assert(verify_material(pos, weakSide, BishopValueMg, 0));
684 Square pawnSq = pos.list<PAWN>(strongSide)[0];
685 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
686 Square weakBishopSq = pos.list<BISHOP>(weakSide)[0];
687 Square weakKingSq = pos.king_square(weakSide);
689 // Case 1: Defending king blocks the pawn, and cannot be driven away
690 if ( file_of(weakKingSq) == file_of(pawnSq)
691 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
692 && ( opposite_colors(weakKingSq, strongBishopSq)
693 || relative_rank(strongSide, weakKingSq) <= RANK_6))
694 return SCALE_FACTOR_DRAW;
696 // Case 2: Opposite colored bishops
697 if (opposite_colors(strongBishopSq, weakBishopSq))
699 // We assume that the position is drawn in the following three situations:
701 // a. The pawn is on rank 5 or further back.
702 // b. The defending king is somewhere in the pawn's path.
703 // c. The defending bishop attacks some square along the pawn's path,
704 // and is at least three squares away from the pawn.
706 // These rules are probably not perfect, but in practice they work
709 if (relative_rank(strongSide, pawnSq) <= RANK_5)
710 return SCALE_FACTOR_DRAW;
713 Bitboard path = forward_bb(strongSide, pawnSq);
715 if (path & pos.pieces(weakSide, KING))
716 return SCALE_FACTOR_DRAW;
718 if ( (pos.attacks_from<BISHOP>(weakBishopSq) & path)
719 && square_distance(weakBishopSq, pawnSq) >= 3)
720 return SCALE_FACTOR_DRAW;
723 return SCALE_FACTOR_NONE;
727 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
729 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
731 assert(verify_material(pos, strongSide, BishopValueMg, 2));
732 assert(verify_material(pos, weakSide, BishopValueMg, 0));
734 Square wbsq = pos.list<BISHOP>(strongSide)[0];
735 Square bbsq = pos.list<BISHOP>(weakSide)[0];
737 if (!opposite_colors(wbsq, bbsq))
738 return SCALE_FACTOR_NONE;
740 Square ksq = pos.king_square(weakSide);
741 Square psq1 = pos.list<PAWN>(strongSide)[0];
742 Square psq2 = pos.list<PAWN>(strongSide)[1];
743 Rank r1 = rank_of(psq1);
744 Rank r2 = rank_of(psq2);
745 Square blockSq1, blockSq2;
747 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
749 blockSq1 = psq1 + pawn_push(strongSide);
750 blockSq2 = file_of(psq2) | rank_of(psq1);
754 blockSq1 = psq2 + pawn_push(strongSide);
755 blockSq2 = file_of(psq1) | rank_of(psq2);
758 switch (file_distance(psq1, psq2))
761 // Both pawns are on the same file. It's an easy draw if the defender firmly
762 // controls some square in the frontmost pawn's path.
763 if ( file_of(ksq) == file_of(blockSq1)
764 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
765 && opposite_colors(ksq, wbsq))
766 return SCALE_FACTOR_DRAW;
768 return SCALE_FACTOR_NONE;
771 // Pawns on adjacent files. It's a draw if the defender firmly controls the
772 // square in front of the frontmost pawn's path, and the square diagonally
773 // behind this square on the file of the other pawn.
775 && opposite_colors(ksq, wbsq)
776 && ( bbsq == blockSq2
777 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
778 || abs(r1 - r2) >= 2))
779 return SCALE_FACTOR_DRAW;
781 else if ( ksq == blockSq2
782 && opposite_colors(ksq, wbsq)
783 && ( bbsq == blockSq1
784 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
785 return SCALE_FACTOR_DRAW;
787 return SCALE_FACTOR_NONE;
790 // The pawns are not on the same file or adjacent files. No scaling.
791 return SCALE_FACTOR_NONE;
796 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
797 /// the path of the pawn, and the square of the king is not of the same color as
798 /// the stronger side's bishop, it's a draw.
800 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
802 assert(verify_material(pos, strongSide, BishopValueMg, 1));
803 assert(verify_material(pos, weakSide, KnightValueMg, 0));
805 Square pawnSq = pos.list<PAWN>(strongSide)[0];
806 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
807 Square weakKingSq = pos.king_square(weakSide);
809 if ( file_of(weakKingSq) == file_of(pawnSq)
810 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
811 && ( opposite_colors(weakKingSq, strongBishopSq)
812 || relative_rank(strongSide, weakKingSq) <= RANK_6))
813 return SCALE_FACTOR_DRAW;
815 return SCALE_FACTOR_NONE;
819 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
820 /// and the defending king prevents the pawn from advancing, the position is drawn.
822 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
824 assert(verify_material(pos, strongSide, KnightValueMg, 1));
825 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
827 // Assume strongSide is white and the pawn is on files A-D
828 Square pawnSq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
829 Square weakKingSq = normalize(pos, strongSide, pos.king_square(weakSide));
831 if (pawnSq == SQ_A7 && square_distance(SQ_A8, weakKingSq) <= 1)
832 return SCALE_FACTOR_DRAW;
834 return SCALE_FACTOR_NONE;
838 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
839 /// Otherwise the position is drawn.
841 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
843 Square pawnSq = pos.list<PAWN>(strongSide)[0];
844 Square bishopSq = pos.list<BISHOP>(weakSide)[0];
845 Square weakKingSq = pos.king_square(weakSide);
847 // King needs to get close to promoting pawn to prevent knight from blocking.
848 // Rules for this are very tricky, so just approximate.
849 if (forward_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
850 return ScaleFactor(square_distance(weakKingSq, pawnSq));
852 return SCALE_FACTOR_NONE;
856 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
857 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
858 /// has at least a draw with the pawn as well. The exception is when the stronger
859 /// side's pawn is far advanced and not on a rook file; in this case it is often
860 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
862 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
864 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
865 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
867 // Assume strongSide is white and the pawn is on files A-D
868 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
869 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
870 Square psq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
872 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
874 // If the pawn has advanced to the fifth rank or further, and is not a
875 // rook pawn, it's too dangerous to assume that it's at least a draw.
876 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
877 return SCALE_FACTOR_NONE;
879 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
880 // it's probably at least a draw even with the pawn.
881 return Bitbases::probe_kpk(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;