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 = 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 - Value(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 - Value(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 - square_distance(wksq, psq) * 8);
266 - Value(square_distance(wksq, psq + DELTA_S) * 8)
267 + Value(square_distance(bksq, psq + DELTA_S) * 8)
268 + Value(square_distance(psq, queeningSq) * 8);
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 pawnFile = file_of(pos.list<PAWN>(strongSide)[0]);
369 // All pawns are on a single rook file ?
370 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
371 && !(pawns & ~file_bb(pawnFile)))
373 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
374 Square queeningSq = relative_square(strongSide, pawnFile | RANK_8);
375 Square kingSq = pos.king_square(weakSide);
377 if ( opposite_colors(queeningSq, bishopSq)
378 && square_distance(queeningSq, kingSq) <= 1)
379 return SCALE_FACTOR_DRAW;
382 // If all the pawns are on the same B or G file, then it's potentially a draw
383 if ( (pawnFile == FILE_B || pawnFile == FILE_G)
384 && !(pos.pieces(PAWN) & ~file_bb(pawnFile))
385 && pos.non_pawn_material(weakSide) == 0
386 && pos.count<PAWN>(weakSide) >= 1)
388 // Get weakSide pawn that is closest to the home rank
389 Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
391 Square strongKingSq = pos.king_square(strongSide);
392 Square weakKingSq = pos.king_square(weakSide);
393 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
395 // There's potential for a draw if our pawn is blocked on the 7th rank,
396 // the bishop cannot attack it or they only have one pawn left
397 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
398 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
399 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
401 int strongKingDist = square_distance(weakPawnSq, strongKingSq);
402 int weakKingDist = square_distance(weakPawnSq, weakKingSq);
404 // It's a draw if the weak king is on its back two ranks, within 2
405 // squares of the blocking pawn and the strong king is not
406 // closer. (I think this rule only fails in practically
407 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
408 // and positions where qsearch will immediately correct the
409 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
410 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
412 && weakKingDist <= strongKingDist)
413 return SCALE_FACTOR_DRAW;
417 return SCALE_FACTOR_NONE;
421 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
422 /// the third rank defended by a pawn.
424 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
426 assert(verify_material(pos, strongSide, QueenValueMg, 0));
427 assert(pos.count<ROOK>(weakSide) == 1);
428 assert(pos.count<PAWN>(weakSide) >= 1);
430 Square kingSq = pos.king_square(weakSide);
431 Square rsq = pos.list<ROOK>(weakSide)[0];
433 if ( relative_rank(weakSide, kingSq) <= RANK_2
434 && relative_rank(weakSide, pos.king_square(strongSide)) >= RANK_4
435 && relative_rank(weakSide, rsq) == RANK_3
436 && ( pos.pieces(weakSide, PAWN)
437 & pos.attacks_from<KING>(kingSq)
438 & pos.attacks_from<PAWN>(rsq, strongSide)))
439 return SCALE_FACTOR_DRAW;
441 return SCALE_FACTOR_NONE;
445 /// KRP vs KR. This function knows a handful of the most important classes of
446 /// drawn positions, but is far from perfect. It would probably be a good idea
447 /// to add more knowledge in the future.
449 /// It would also be nice to rewrite the actual code for this function,
450 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
452 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
454 assert(verify_material(pos, strongSide, RookValueMg, 1));
455 assert(verify_material(pos, weakSide, RookValueMg, 0));
457 // Assume strongSide is white and the pawn is on files A-D
458 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
459 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
460 Square wrsq = normalize(pos, strongSide, pos.list<ROOK>(strongSide)[0]);
461 Square wpsq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
462 Square brsq = normalize(pos, strongSide, pos.list<ROOK>(weakSide)[0]);
464 File f = file_of(wpsq);
465 Rank r = rank_of(wpsq);
466 Square queeningSq = f | RANK_8;
467 int tempo = (pos.side_to_move() == strongSide);
469 // If the pawn is not too far advanced and the defending king defends the
470 // queening square, use the third-rank defence.
472 && square_distance(bksq, queeningSq) <= 1
474 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
475 return SCALE_FACTOR_DRAW;
477 // The defending side saves a draw by checking from behind in case the pawn
478 // has advanced to the 6th rank with the king behind.
480 && square_distance(bksq, queeningSq) <= 1
481 && rank_of(wksq) + tempo <= RANK_6
482 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
483 return SCALE_FACTOR_DRAW;
486 && bksq == queeningSq
487 && rank_of(brsq) == RANK_1
488 && (!tempo || square_distance(wksq, wpsq) >= 2))
489 return SCALE_FACTOR_DRAW;
491 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
492 // and the black rook is behind the pawn.
495 && (bksq == SQ_H7 || bksq == SQ_G7)
496 && file_of(brsq) == FILE_A
497 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
498 return SCALE_FACTOR_DRAW;
500 // If the defending king blocks the pawn and the attacking king is too far
501 // away, it's a draw.
503 && bksq == wpsq + DELTA_N
504 && square_distance(wksq, wpsq) - tempo >= 2
505 && square_distance(wksq, brsq) - tempo >= 2)
506 return SCALE_FACTOR_DRAW;
508 // Pawn on the 7th rank supported by the rook from behind usually wins if the
509 // attacking king is closer to the queening square than the defending king,
510 // and the defending king cannot gain tempi by threatening the attacking rook.
513 && file_of(wrsq) == f
514 && wrsq != queeningSq
515 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
516 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
517 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
519 // Similar to the above, but with the pawn further back
521 && file_of(wrsq) == f
523 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
524 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
525 && ( square_distance(bksq, wrsq) + tempo >= 3
526 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
527 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
528 return ScaleFactor( SCALE_FACTOR_MAX
529 - 8 * square_distance(wpsq, queeningSq)
530 - 2 * square_distance(wksq, queeningSq));
532 // If the pawn is not far advanced and the defending king is somewhere in
533 // the pawn's path, it's probably a draw.
534 if (r <= RANK_4 && bksq > wpsq)
536 if (file_of(bksq) == file_of(wpsq))
537 return ScaleFactor(10);
538 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
539 && square_distance(wksq, bksq) > 2)
540 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
542 return SCALE_FACTOR_NONE;
546 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
548 assert(verify_material(pos, strongSide, RookValueMg, 1));
549 assert(verify_material(pos, weakSide, BishopValueMg, 0));
551 // Test for a rook pawn
552 if (pos.pieces(PAWN) & (FileABB | FileHBB))
554 Square ksq = pos.king_square(weakSide);
555 Square bsq = pos.list<BISHOP>(weakSide)[0];
556 Square psq = pos.list<PAWN>(strongSide)[0];
557 Rank rk = relative_rank(strongSide, psq);
558 Square push = pawn_push(strongSide);
560 // If the pawn is on the 5th rank and the pawn (currently) is on
561 // the same color square as the bishop then there is a chance of
562 // a fortress. Depending on the king position give a moderate
563 // reduction or a stronger one if the defending king is near the
564 // corner but not trapped there.
565 if (rk == RANK_5 && !opposite_colors(bsq, psq))
567 int d = square_distance(psq + 3 * push, ksq);
569 if (d <= 2 && !(d == 0 && ksq == pos.king_square(strongSide) + 2 * push))
570 return ScaleFactor(24);
572 return ScaleFactor(48);
575 // When the pawn has moved to the 6th rank we can be fairly sure
576 // it's drawn if the bishop attacks the square in front of the
577 // pawn from a reasonable distance and the defending king is near
580 && square_distance(psq + 2 * push, ksq) <= 1
581 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
582 && file_distance(bsq, psq) >= 2)
583 return ScaleFactor(8);
586 return SCALE_FACTOR_NONE;
589 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
590 /// pawns and the defending king is actively placed, the position is drawish.
592 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
594 assert(verify_material(pos, strongSide, RookValueMg, 2));
595 assert(verify_material(pos, weakSide, RookValueMg, 1));
597 Square wpsq1 = pos.list<PAWN>(strongSide)[0];
598 Square wpsq2 = pos.list<PAWN>(strongSide)[1];
599 Square bksq = pos.king_square(weakSide);
601 // Does the stronger side have a passed pawn?
602 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
603 return SCALE_FACTOR_NONE;
605 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
607 if ( file_distance(bksq, wpsq1) <= 1
608 && file_distance(bksq, wpsq2) <= 1
609 && relative_rank(strongSide, bksq) > r)
612 case RANK_2: return ScaleFactor(10);
613 case RANK_3: return ScaleFactor(10);
614 case RANK_4: return ScaleFactor(15);
615 case RANK_5: return ScaleFactor(20);
616 case RANK_6: return ScaleFactor(40);
617 default: assert(false);
620 return SCALE_FACTOR_NONE;
624 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
625 /// are on the same rook file and are blocked by the defending king, it's a draw.
627 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
629 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
630 assert(pos.count<PAWN>(strongSide) >= 2);
631 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
633 Square ksq = pos.king_square(weakSide);
634 Bitboard pawns = pos.pieces(strongSide, PAWN);
635 Square psq = pos.list<PAWN>(strongSide)[0];
637 // If all pawns are ahead of the king, on a single rook file and
638 // the king is within one file of the pawns, it's a draw.
639 if ( !(pawns & ~in_front_bb(weakSide, rank_of(ksq)))
640 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
641 && file_distance(ksq, psq) <= 1)
642 return SCALE_FACTOR_DRAW;
644 return SCALE_FACTOR_NONE;
648 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
649 /// path of the pawn, and the square of the king is not of the same color as the
650 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
651 /// it's almost always a draw.
653 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
655 assert(verify_material(pos, strongSide, BishopValueMg, 1));
656 assert(verify_material(pos, weakSide, BishopValueMg, 0));
658 Square pawnSq = pos.list<PAWN>(strongSide)[0];
659 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
660 Square weakBishopSq = pos.list<BISHOP>(weakSide)[0];
661 Square weakKingSq = pos.king_square(weakSide);
663 // Case 1: Defending king blocks the pawn, and cannot be driven away
664 if ( file_of(weakKingSq) == file_of(pawnSq)
665 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
666 && ( opposite_colors(weakKingSq, strongBishopSq)
667 || relative_rank(strongSide, weakKingSq) <= RANK_6))
668 return SCALE_FACTOR_DRAW;
670 // Case 2: Opposite colored bishops
671 if (opposite_colors(strongBishopSq, weakBishopSq))
673 // We assume that the position is drawn in the following three situations:
675 // a. The pawn is on rank 5 or further back.
676 // b. The defending king is somewhere in the pawn's path.
677 // c. The defending bishop attacks some square along the pawn's path,
678 // and is at least three squares away from the pawn.
680 // These rules are probably not perfect, but in practice they work
683 if (relative_rank(strongSide, pawnSq) <= RANK_5)
684 return SCALE_FACTOR_DRAW;
687 Bitboard path = forward_bb(strongSide, pawnSq);
689 if (path & pos.pieces(weakSide, KING))
690 return SCALE_FACTOR_DRAW;
692 if ( (pos.attacks_from<BISHOP>(weakBishopSq) & path)
693 && square_distance(weakBishopSq, pawnSq) >= 3)
694 return SCALE_FACTOR_DRAW;
697 return SCALE_FACTOR_NONE;
701 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
703 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
705 assert(verify_material(pos, strongSide, BishopValueMg, 2));
706 assert(verify_material(pos, weakSide, BishopValueMg, 0));
708 Square wbsq = pos.list<BISHOP>(strongSide)[0];
709 Square bbsq = pos.list<BISHOP>(weakSide)[0];
711 if (!opposite_colors(wbsq, bbsq))
712 return SCALE_FACTOR_NONE;
714 Square ksq = pos.king_square(weakSide);
715 Square psq1 = pos.list<PAWN>(strongSide)[0];
716 Square psq2 = pos.list<PAWN>(strongSide)[1];
717 Rank r1 = rank_of(psq1);
718 Rank r2 = rank_of(psq2);
719 Square blockSq1, blockSq2;
721 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
723 blockSq1 = psq1 + pawn_push(strongSide);
724 blockSq2 = file_of(psq2) | rank_of(psq1);
728 blockSq1 = psq2 + pawn_push(strongSide);
729 blockSq2 = file_of(psq1) | rank_of(psq2);
732 switch (file_distance(psq1, psq2))
735 // Both pawns are on the same file. It's an easy draw if the defender firmly
736 // controls some square in the frontmost pawn's path.
737 if ( file_of(ksq) == file_of(blockSq1)
738 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
739 && opposite_colors(ksq, wbsq))
740 return SCALE_FACTOR_DRAW;
742 return SCALE_FACTOR_NONE;
745 // Pawns on adjacent files. It's a draw if the defender firmly controls the
746 // square in front of the frontmost pawn's path, and the square diagonally
747 // behind this square on the file of the other pawn.
749 && opposite_colors(ksq, wbsq)
750 && ( bbsq == blockSq2
751 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
752 || abs(r1 - r2) >= 2))
753 return SCALE_FACTOR_DRAW;
755 else if ( ksq == blockSq2
756 && opposite_colors(ksq, wbsq)
757 && ( bbsq == blockSq1
758 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
759 return SCALE_FACTOR_DRAW;
761 return SCALE_FACTOR_NONE;
764 // The pawns are not on the same file or adjacent files. No scaling.
765 return SCALE_FACTOR_NONE;
770 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
771 /// the path of the pawn, and the square of the king is not of the same color as
772 /// the stronger side's bishop, it's a draw.
774 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
776 assert(verify_material(pos, strongSide, BishopValueMg, 1));
777 assert(verify_material(pos, weakSide, KnightValueMg, 0));
779 Square pawnSq = pos.list<PAWN>(strongSide)[0];
780 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
781 Square weakKingSq = pos.king_square(weakSide);
783 if ( file_of(weakKingSq) == file_of(pawnSq)
784 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
785 && ( opposite_colors(weakKingSq, strongBishopSq)
786 || relative_rank(strongSide, weakKingSq) <= RANK_6))
787 return SCALE_FACTOR_DRAW;
789 return SCALE_FACTOR_NONE;
793 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
794 /// and the defending king prevents the pawn from advancing, the position is drawn.
796 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
798 assert(verify_material(pos, strongSide, KnightValueMg, 1));
799 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
801 // Assume strongSide is white and the pawn is on files A-D
802 Square pawnSq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
803 Square weakKingSq = normalize(pos, strongSide, pos.king_square(weakSide));
805 if (pawnSq == SQ_A7 && square_distance(SQ_A8, weakKingSq) <= 1)
806 return SCALE_FACTOR_DRAW;
808 return SCALE_FACTOR_NONE;
812 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
813 /// Otherwise the position is drawn.
815 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
817 Square pawnSq = pos.list<PAWN>(strongSide)[0];
818 Square bishopSq = pos.list<BISHOP>(weakSide)[0];
819 Square weakKingSq = pos.king_square(weakSide);
821 // King needs to get close to promoting pawn to prevent knight from blocking.
822 // Rules for this are very tricky, so just approximate.
823 if (forward_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
824 return ScaleFactor(square_distance(weakKingSq, pawnSq));
826 return SCALE_FACTOR_NONE;
830 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
831 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
832 /// has at least a draw with the pawn as well. The exception is when the stronger
833 /// side's pawn is far advanced and not on a rook file; in this case it is often
834 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
836 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
838 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
839 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
841 // Assume strongSide is white and the pawn is on files A-D
842 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
843 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
844 Square psq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
846 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
848 // If the pawn has advanced to the fifth rank or further, and is not a
849 // rook pawn, it's too dangerous to assume that it's at least a draw.
850 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
851 return SCALE_FACTOR_NONE;
853 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
854 // it's probably at least a draw even with the pawn.
855 return Bitbases::probe_kpk(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;