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 pawnFile = file_of(pos.list<PAWN>(strongSide)[0]);
368 // All pawns are on a single rook file ?
369 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
370 && !(pawns & ~file_bb(pawnFile)))
372 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
373 Square queeningSq = relative_square(strongSide, make_square(pawnFile, RANK_8));
374 Square kingSq = pos.king_square(weakSide);
376 if ( opposite_colors(queeningSq, bishopSq)
377 && square_distance(queeningSq, kingSq) <= 1)
378 return SCALE_FACTOR_DRAW;
381 // If all the pawns are on the same B or G file, then it's potentially a draw
382 if ( (pawnFile == FILE_B || pawnFile == FILE_G)
383 && !(pos.pieces(PAWN) & ~file_bb(pawnFile))
384 && pos.non_pawn_material(weakSide) == 0
385 && pos.count<PAWN>(weakSide) >= 1)
387 // Get weakSide pawn that is closest to the home rank
388 Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
390 Square strongKingSq = pos.king_square(strongSide);
391 Square weakKingSq = pos.king_square(weakSide);
392 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
394 // There's potential for a draw if our pawn is blocked on the 7th rank,
395 // the bishop cannot attack it or they only have one pawn left
396 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
397 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
398 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
400 int strongKingDist = square_distance(weakPawnSq, strongKingSq);
401 int weakKingDist = square_distance(weakPawnSq, weakKingSq);
403 // It's a draw if the weak king is on its back two ranks, within 2
404 // squares of the blocking pawn and the strong king is not
405 // closer. (I think this rule only fails in practically
406 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
407 // and positions where qsearch will immediately correct the
408 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
409 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
411 && weakKingDist <= strongKingDist)
412 return SCALE_FACTOR_DRAW;
416 return SCALE_FACTOR_NONE;
420 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
421 /// the third rank defended by a pawn.
423 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
425 assert(verify_material(pos, strongSide, QueenValueMg, 0));
426 assert(pos.count<ROOK>(weakSide) == 1);
427 assert(pos.count<PAWN>(weakSide) >= 1);
429 Square kingSq = pos.king_square(weakSide);
430 Square rsq = pos.list<ROOK>(weakSide)[0];
432 if ( relative_rank(weakSide, kingSq) <= RANK_2
433 && relative_rank(weakSide, pos.king_square(strongSide)) >= RANK_4
434 && relative_rank(weakSide, rsq) == RANK_3
435 && ( pos.pieces(weakSide, PAWN)
436 & pos.attacks_from<KING>(kingSq)
437 & pos.attacks_from<PAWN>(rsq, strongSide)))
438 return SCALE_FACTOR_DRAW;
440 return SCALE_FACTOR_NONE;
444 /// KRP vs KR. This function knows a handful of the most important classes of
445 /// drawn positions, but is far from perfect. It would probably be a good idea
446 /// to add more knowledge in the future.
448 /// It would also be nice to rewrite the actual code for this function,
449 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
451 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
453 assert(verify_material(pos, strongSide, RookValueMg, 1));
454 assert(verify_material(pos, weakSide, RookValueMg, 0));
456 // Assume strongSide is white and the pawn is on files A-D
457 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
458 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
459 Square wrsq = normalize(pos, strongSide, pos.list<ROOK>(strongSide)[0]);
460 Square wpsq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
461 Square brsq = normalize(pos, strongSide, pos.list<ROOK>(weakSide)[0]);
463 File f = file_of(wpsq);
464 Rank r = rank_of(wpsq);
465 Square queeningSq = make_square(f, RANK_8);
466 int tempo = (pos.side_to_move() == strongSide);
468 // If the pawn is not too far advanced and the defending king defends the
469 // queening square, use the third-rank defence.
471 && square_distance(bksq, queeningSq) <= 1
473 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
474 return SCALE_FACTOR_DRAW;
476 // The defending side saves a draw by checking from behind in case the pawn
477 // has advanced to the 6th rank with the king behind.
479 && square_distance(bksq, queeningSq) <= 1
480 && rank_of(wksq) + tempo <= RANK_6
481 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
482 return SCALE_FACTOR_DRAW;
485 && bksq == queeningSq
486 && rank_of(brsq) == RANK_1
487 && (!tempo || square_distance(wksq, wpsq) >= 2))
488 return SCALE_FACTOR_DRAW;
490 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
491 // and the black rook is behind the pawn.
494 && (bksq == SQ_H7 || bksq == SQ_G7)
495 && file_of(brsq) == FILE_A
496 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
497 return SCALE_FACTOR_DRAW;
499 // If the defending king blocks the pawn and the attacking king is too far
500 // away, it's a draw.
502 && bksq == wpsq + DELTA_N
503 && square_distance(wksq, wpsq) - tempo >= 2
504 && square_distance(wksq, brsq) - tempo >= 2)
505 return SCALE_FACTOR_DRAW;
507 // Pawn on the 7th rank supported by the rook from behind usually wins if the
508 // attacking king is closer to the queening square than the defending king,
509 // and the defending king cannot gain tempi by threatening the attacking rook.
512 && file_of(wrsq) == f
513 && wrsq != queeningSq
514 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
515 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
516 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
518 // Similar to the above, but with the pawn further back
520 && file_of(wrsq) == f
522 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
523 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
524 && ( square_distance(bksq, wrsq) + tempo >= 3
525 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
526 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
527 return ScaleFactor( SCALE_FACTOR_MAX
528 - 8 * square_distance(wpsq, queeningSq)
529 - 2 * square_distance(wksq, queeningSq));
531 // If the pawn is not far advanced and the defending king is somewhere in
532 // the pawn's path, it's probably a draw.
533 if (r <= RANK_4 && bksq > wpsq)
535 if (file_of(bksq) == file_of(wpsq))
536 return ScaleFactor(10);
537 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
538 && square_distance(wksq, bksq) > 2)
539 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
541 return SCALE_FACTOR_NONE;
545 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
547 assert(verify_material(pos, strongSide, RookValueMg, 1));
548 assert(verify_material(pos, weakSide, BishopValueMg, 0));
550 // Test for a rook pawn
551 if (pos.pieces(PAWN) & (FileABB | FileHBB))
553 Square ksq = pos.king_square(weakSide);
554 Square bsq = pos.list<BISHOP>(weakSide)[0];
555 Square psq = pos.list<PAWN>(strongSide)[0];
556 Rank rk = relative_rank(strongSide, psq);
557 Square push = pawn_push(strongSide);
559 // If the pawn is on the 5th rank and the pawn (currently) is on
560 // the same color square as the bishop then there is a chance of
561 // a fortress. Depending on the king position give a moderate
562 // reduction or a stronger one if the defending king is near the
563 // corner but not trapped there.
564 if (rk == RANK_5 && !opposite_colors(bsq, psq))
566 int d = square_distance(psq + 3 * push, ksq);
568 if (d <= 2 && !(d == 0 && ksq == pos.king_square(strongSide) + 2 * push))
569 return ScaleFactor(24);
571 return ScaleFactor(48);
574 // When the pawn has moved to the 6th rank we can be fairly sure
575 // it's drawn if the bishop attacks the square in front of the
576 // pawn from a reasonable distance and the defending king is near
579 && square_distance(psq + 2 * push, ksq) <= 1
580 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
581 && file_distance(bsq, psq) >= 2)
582 return ScaleFactor(8);
585 return SCALE_FACTOR_NONE;
588 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
589 /// pawns and the defending king is actively placed, the position is drawish.
591 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
593 assert(verify_material(pos, strongSide, RookValueMg, 2));
594 assert(verify_material(pos, weakSide, RookValueMg, 1));
596 Square wpsq1 = pos.list<PAWN>(strongSide)[0];
597 Square wpsq2 = pos.list<PAWN>(strongSide)[1];
598 Square bksq = pos.king_square(weakSide);
600 // Does the stronger side have a passed pawn?
601 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
602 return SCALE_FACTOR_NONE;
604 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
606 if ( file_distance(bksq, wpsq1) <= 1
607 && file_distance(bksq, wpsq2) <= 1
608 && relative_rank(strongSide, bksq) > r)
611 case RANK_2: return ScaleFactor(10);
612 case RANK_3: return ScaleFactor(10);
613 case RANK_4: return ScaleFactor(15);
614 case RANK_5: return ScaleFactor(20);
615 case RANK_6: return ScaleFactor(40);
616 default: assert(false);
619 return SCALE_FACTOR_NONE;
623 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
624 /// are on the same rook file and are blocked by the defending king, it's a draw.
626 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
628 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
629 assert(pos.count<PAWN>(strongSide) >= 2);
630 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
632 Square ksq = pos.king_square(weakSide);
633 Bitboard pawns = pos.pieces(strongSide, PAWN);
634 Square psq = pos.list<PAWN>(strongSide)[0];
636 // If all pawns are ahead of the king, on a single rook file and
637 // the king is within one file of the pawns, it's a draw.
638 if ( !(pawns & ~in_front_bb(weakSide, rank_of(ksq)))
639 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
640 && file_distance(ksq, psq) <= 1)
641 return SCALE_FACTOR_DRAW;
643 return SCALE_FACTOR_NONE;
647 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
648 /// path of the pawn, and the square of the king is not of the same color as the
649 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
650 /// it's almost always a draw.
652 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
654 assert(verify_material(pos, strongSide, BishopValueMg, 1));
655 assert(verify_material(pos, weakSide, BishopValueMg, 0));
657 Square pawnSq = pos.list<PAWN>(strongSide)[0];
658 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
659 Square weakBishopSq = pos.list<BISHOP>(weakSide)[0];
660 Square weakKingSq = pos.king_square(weakSide);
662 // Case 1: Defending king blocks the pawn, and cannot be driven away
663 if ( file_of(weakKingSq) == file_of(pawnSq)
664 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
665 && ( opposite_colors(weakKingSq, strongBishopSq)
666 || relative_rank(strongSide, weakKingSq) <= RANK_6))
667 return SCALE_FACTOR_DRAW;
669 // Case 2: Opposite colored bishops
670 if (opposite_colors(strongBishopSq, weakBishopSq))
672 // We assume that the position is drawn in the following three situations:
674 // a. The pawn is on rank 5 or further back.
675 // b. The defending king is somewhere in the pawn's path.
676 // c. The defending bishop attacks some square along the pawn's path,
677 // and is at least three squares away from the pawn.
679 // These rules are probably not perfect, but in practice they work
682 if (relative_rank(strongSide, pawnSq) <= RANK_5)
683 return SCALE_FACTOR_DRAW;
686 Bitboard path = forward_bb(strongSide, pawnSq);
688 if (path & pos.pieces(weakSide, KING))
689 return SCALE_FACTOR_DRAW;
691 if ( (pos.attacks_from<BISHOP>(weakBishopSq) & path)
692 && square_distance(weakBishopSq, pawnSq) >= 3)
693 return SCALE_FACTOR_DRAW;
696 return SCALE_FACTOR_NONE;
700 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
702 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
704 assert(verify_material(pos, strongSide, BishopValueMg, 2));
705 assert(verify_material(pos, weakSide, BishopValueMg, 0));
707 Square wbsq = pos.list<BISHOP>(strongSide)[0];
708 Square bbsq = pos.list<BISHOP>(weakSide)[0];
710 if (!opposite_colors(wbsq, bbsq))
711 return SCALE_FACTOR_NONE;
713 Square ksq = pos.king_square(weakSide);
714 Square psq1 = pos.list<PAWN>(strongSide)[0];
715 Square psq2 = pos.list<PAWN>(strongSide)[1];
716 Rank r1 = rank_of(psq1);
717 Rank r2 = rank_of(psq2);
718 Square blockSq1, blockSq2;
720 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
722 blockSq1 = psq1 + pawn_push(strongSide);
723 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
727 blockSq1 = psq2 + pawn_push(strongSide);
728 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
731 switch (file_distance(psq1, psq2))
734 // Both pawns are on the same file. It's an easy draw if the defender firmly
735 // controls some square in the frontmost pawn's path.
736 if ( file_of(ksq) == file_of(blockSq1)
737 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
738 && opposite_colors(ksq, wbsq))
739 return SCALE_FACTOR_DRAW;
741 return SCALE_FACTOR_NONE;
744 // Pawns on adjacent files. It's a draw if the defender firmly controls the
745 // square in front of the frontmost pawn's path, and the square diagonally
746 // behind this square on the file of the other pawn.
748 && opposite_colors(ksq, wbsq)
749 && ( bbsq == blockSq2
750 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
751 || abs(r1 - r2) >= 2))
752 return SCALE_FACTOR_DRAW;
754 else if ( ksq == blockSq2
755 && opposite_colors(ksq, wbsq)
756 && ( bbsq == blockSq1
757 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
758 return SCALE_FACTOR_DRAW;
760 return SCALE_FACTOR_NONE;
763 // The pawns are not on the same file or adjacent files. No scaling.
764 return SCALE_FACTOR_NONE;
769 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
770 /// the path of the pawn, and the square of the king is not of the same color as
771 /// the stronger side's bishop, it's a draw.
773 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
775 assert(verify_material(pos, strongSide, BishopValueMg, 1));
776 assert(verify_material(pos, weakSide, KnightValueMg, 0));
778 Square pawnSq = pos.list<PAWN>(strongSide)[0];
779 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
780 Square weakKingSq = pos.king_square(weakSide);
782 if ( file_of(weakKingSq) == file_of(pawnSq)
783 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
784 && ( opposite_colors(weakKingSq, strongBishopSq)
785 || relative_rank(strongSide, weakKingSq) <= RANK_6))
786 return SCALE_FACTOR_DRAW;
788 return SCALE_FACTOR_NONE;
792 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
793 /// and the defending king prevents the pawn from advancing, the position is drawn.
795 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
797 assert(verify_material(pos, strongSide, KnightValueMg, 1));
798 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
800 // Assume strongSide is white and the pawn is on files A-D
801 Square pawnSq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
802 Square weakKingSq = normalize(pos, strongSide, pos.king_square(weakSide));
804 if (pawnSq == SQ_A7 && square_distance(SQ_A8, weakKingSq) <= 1)
805 return SCALE_FACTOR_DRAW;
807 return SCALE_FACTOR_NONE;
811 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
812 /// Otherwise the position is drawn.
814 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
816 Square pawnSq = pos.list<PAWN>(strongSide)[0];
817 Square bishopSq = pos.list<BISHOP>(weakSide)[0];
818 Square weakKingSq = pos.king_square(weakSide);
820 // King needs to get close to promoting pawn to prevent knight from blocking.
821 // Rules for this are very tricky, so just approximate.
822 if (forward_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
823 return ScaleFactor(square_distance(weakKingSq, pawnSq));
825 return SCALE_FACTOR_NONE;
829 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
830 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
831 /// has at least a draw with the pawn as well. The exception is when the stronger
832 /// side's pawn is far advanced and not on a rook file; in this case it is often
833 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
835 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
837 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
838 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
840 // Assume strongSide is white and the pawn is on files A-D
841 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
842 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
843 Square psq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
845 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
847 // If the pawn has advanced to the fifth rank or further, and is not a
848 // rook pawn, it's too dangerous to assume that it's at least a draw.
849 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
850 return SCALE_FACTOR_NONE;
852 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
853 // it's probably at least a draw even with the pawn.
854 return Bitbases::probe_kpk(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;