2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
4 Copyright (C) 2008-2015 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 pawnsCnt) {
64 return pos.non_pawn_material(c) == npm && pos.count<PAWN>(c) == pawnsCnt;
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, nullptr).material_key();
105 /// Endgames members definitions
107 Endgames::Endgames() {
124 add<KBPPKB>("KBPPKB");
125 add<KRPPKRP>("KRPPKRP");
129 template<EndgameType E, typename T>
130 void Endgames::add(const string& code) {
132 map<T>()[key(code, WHITE)] = std::unique_ptr<T>(new Endgame<E>(WHITE));
133 map<T>()[key(code, BLACK)] = std::unique_ptr<T>(new Endgame<E>(BLACK));
137 /// Mate with KX vs K. This function is used to evaluate positions with
138 /// king and plenty of material vs a lone king. It simply gives the
139 /// attacking side a bonus for driving the defending king towards the edge
140 /// of the board, and for keeping the distance between the two kings small.
142 Value Endgame<KXK>::operator()(const Position& pos) const {
144 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
145 assert(!pos.checkers()); // Eval is never called when in check
147 // Stalemate detection with lone king
148 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
151 Square winnerKSq = pos.king_square(strongSide);
152 Square loserKSq = pos.king_square(weakSide);
154 Value result = pos.non_pawn_material(strongSide)
155 + pos.count<PAWN>(strongSide) * PawnValueEg
156 + PushToEdges[loserKSq]
157 + PushClose[distance(winnerKSq, loserKSq)];
159 if ( pos.count<QUEEN>(strongSide)
160 || pos.count<ROOK>(strongSide)
161 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
162 ||(pos.count<BISHOP>(strongSide) > 1 && opposite_colors(pos.list<BISHOP>(strongSide)[0],
163 pos.list<BISHOP>(strongSide)[1])))
164 result += VALUE_KNOWN_WIN;
166 return strongSide == pos.side_to_move() ? result : -result;
170 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
171 /// defending king towards a corner square of the right color.
173 Value Endgame<KBNK>::operator()(const Position& pos) const {
175 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
176 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
178 Square winnerKSq = pos.king_square(strongSide);
179 Square loserKSq = pos.king_square(weakSide);
180 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
182 // kbnk_mate_table() tries to drive toward corners A1 or H8. If we have a
183 // bishop that cannot reach the above squares, we flip the kings in order
184 // to drive the enemy toward corners A8 or H1.
185 if (opposite_colors(bishopSq, SQ_A1))
187 winnerKSq = ~winnerKSq;
188 loserKSq = ~loserKSq;
191 Value result = VALUE_KNOWN_WIN
192 + PushClose[distance(winnerKSq, loserKSq)]
193 + PushToCorners[loserKSq];
195 return strongSide == pos.side_to_move() ? result : -result;
199 /// KP vs K. This endgame is evaluated with the help of a bitbase.
201 Value Endgame<KPK>::operator()(const Position& pos) const {
203 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
204 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
206 // Assume strongSide is white and the pawn is on files A-D
207 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
208 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
209 Square psq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
211 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
213 if (!Bitbases::probe(wksq, psq, bksq, us))
216 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
218 return strongSide == pos.side_to_move() ? result : -result;
222 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
223 /// a bitbase. The function below returns drawish scores when the pawn is
224 /// far advanced with support of the king, while the attacking king is far
227 Value Endgame<KRKP>::operator()(const Position& pos) const {
229 assert(verify_material(pos, strongSide, RookValueMg, 0));
230 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
232 Square wksq = relative_square(strongSide, pos.king_square(strongSide));
233 Square bksq = relative_square(strongSide, pos.king_square(weakSide));
234 Square rsq = relative_square(strongSide, pos.list<ROOK>(strongSide)[0]);
235 Square psq = relative_square(strongSide, pos.list<PAWN>(weakSide)[0]);
237 Square queeningSq = make_square(file_of(psq), RANK_1);
240 // If the stronger side's king is in front of the pawn, it's a win
241 if (wksq < psq && file_of(wksq) == file_of(psq))
242 result = RookValueEg - distance(wksq, psq);
244 // If the weaker side's king is too far from the pawn and the rook,
246 else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
247 && distance(bksq, rsq) >= 3)
248 result = RookValueEg - distance(wksq, psq);
250 // If the pawn is far advanced and supported by the defending king,
251 // the position is drawish
252 else if ( rank_of(bksq) <= RANK_3
253 && distance(bksq, psq) == 1
254 && rank_of(wksq) >= RANK_4
255 && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
256 result = Value(80) - 8 * distance(wksq, psq);
259 result = Value(200) - 8 * ( distance(wksq, psq + DELTA_S)
260 - distance(bksq, psq + DELTA_S)
261 - distance(psq, queeningSq));
263 return strongSide == pos.side_to_move() ? result : -result;
267 /// KR vs KB. This is very simple, and always returns drawish scores. The
268 /// score is slightly bigger when the defending king is close to the edge.
270 Value Endgame<KRKB>::operator()(const Position& pos) const {
272 assert(verify_material(pos, strongSide, RookValueMg, 0));
273 assert(verify_material(pos, weakSide, BishopValueMg, 0));
275 Value result = Value(PushToEdges[pos.king_square(weakSide)]);
276 return strongSide == pos.side_to_move() ? result : -result;
280 /// KR vs KN. The attacking side has slightly better winning chances than
281 /// in KR vs KB, particularly if the king and the knight are far apart.
283 Value Endgame<KRKN>::operator()(const Position& pos) const {
285 assert(verify_material(pos, strongSide, RookValueMg, 0));
286 assert(verify_material(pos, weakSide, KnightValueMg, 0));
288 Square bksq = pos.king_square(weakSide);
289 Square bnsq = pos.list<KNIGHT>(weakSide)[0];
290 Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
291 return strongSide == pos.side_to_move() ? result : -result;
295 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
296 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
297 /// with a king positioned next to it can be a draw, so in that case, we only
298 /// use the distance between the kings.
300 Value Endgame<KQKP>::operator()(const Position& pos) const {
302 assert(verify_material(pos, strongSide, QueenValueMg, 0));
303 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
305 Square winnerKSq = pos.king_square(strongSide);
306 Square loserKSq = pos.king_square(weakSide);
307 Square pawnSq = pos.list<PAWN>(weakSide)[0];
309 Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
311 if ( relative_rank(weakSide, pawnSq) != RANK_7
312 || distance(loserKSq, pawnSq) != 1
313 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
314 result += QueenValueEg - PawnValueEg;
316 return strongSide == pos.side_to_move() ? result : -result;
320 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
321 /// king a bonus for having the kings close together, and for forcing the
322 /// defending king towards the edge. If we also take care to avoid null move for
323 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
325 Value Endgame<KQKR>::operator()(const Position& pos) const {
327 assert(verify_material(pos, strongSide, QueenValueMg, 0));
328 assert(verify_material(pos, weakSide, RookValueMg, 0));
330 Square winnerKSq = pos.king_square(strongSide);
331 Square loserKSq = pos.king_square(weakSide);
333 Value result = QueenValueEg
335 + PushToEdges[loserKSq]
336 + PushClose[distance(winnerKSq, loserKSq)];
338 return strongSide == pos.side_to_move() ? result : -result;
342 /// Some cases of trivial draws
343 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
346 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
347 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
348 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
351 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
353 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
354 assert(pos.count<PAWN>(strongSide) >= 1);
356 // No assertions about the material of weakSide, because we want draws to
357 // be detected even when the weaker side has some pawns.
359 Bitboard pawns = pos.pieces(strongSide, PAWN);
360 File pawnFile = file_of(pos.list<PAWN>(strongSide)[0]);
362 // All pawns are on a single rook file ?
363 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
364 && !(pawns & ~file_bb(pawnFile)))
366 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
367 Square queeningSq = relative_square(strongSide, make_square(pawnFile, RANK_8));
368 Square kingSq = pos.king_square(weakSide);
370 if ( opposite_colors(queeningSq, bishopSq)
371 && distance(queeningSq, kingSq) <= 1)
372 return SCALE_FACTOR_DRAW;
375 // If all the pawns are on the same B or G file, then it's potentially a draw
376 if ( (pawnFile == FILE_B || pawnFile == FILE_G)
377 && !(pos.pieces(PAWN) & ~file_bb(pawnFile))
378 && pos.non_pawn_material(weakSide) == 0
379 && pos.count<PAWN>(weakSide) >= 1)
381 // Get weakSide pawn that is closest to the home rank
382 Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
384 Square strongKingSq = pos.king_square(strongSide);
385 Square weakKingSq = pos.king_square(weakSide);
386 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
388 // There's potential for a draw if our pawn is blocked on the 7th rank,
389 // the bishop cannot attack it or they only have one pawn left
390 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
391 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
392 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
394 int strongKingDist = distance(weakPawnSq, strongKingSq);
395 int weakKingDist = distance(weakPawnSq, weakKingSq);
397 // It's a draw if the weak king is on its back two ranks, within 2
398 // squares of the blocking pawn and the strong king is not
399 // closer. (I think this rule only fails in practically
400 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
401 // and positions where qsearch will immediately correct the
402 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
403 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
405 && weakKingDist <= strongKingDist)
406 return SCALE_FACTOR_DRAW;
410 return SCALE_FACTOR_NONE;
414 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
415 /// the third rank defended by a pawn.
417 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
419 assert(verify_material(pos, strongSide, QueenValueMg, 0));
420 assert(pos.count<ROOK>(weakSide) == 1);
421 assert(pos.count<PAWN>(weakSide) >= 1);
423 Square kingSq = pos.king_square(weakSide);
424 Square rsq = pos.list<ROOK>(weakSide)[0];
426 if ( relative_rank(weakSide, kingSq) <= RANK_2
427 && relative_rank(weakSide, pos.king_square(strongSide)) >= RANK_4
428 && relative_rank(weakSide, rsq) == RANK_3
429 && ( pos.pieces(weakSide, PAWN)
430 & pos.attacks_from<KING>(kingSq)
431 & pos.attacks_from<PAWN>(rsq, strongSide)))
432 return SCALE_FACTOR_DRAW;
434 return SCALE_FACTOR_NONE;
438 /// KRP vs KR. This function knows a handful of the most important classes of
439 /// drawn positions, but is far from perfect. It would probably be a good idea
440 /// to add more knowledge in the future.
442 /// It would also be nice to rewrite the actual code for this function,
443 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
445 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
447 assert(verify_material(pos, strongSide, RookValueMg, 1));
448 assert(verify_material(pos, weakSide, RookValueMg, 0));
450 // Assume strongSide is white and the pawn is on files A-D
451 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
452 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
453 Square wrsq = normalize(pos, strongSide, pos.list<ROOK>(strongSide)[0]);
454 Square wpsq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
455 Square brsq = normalize(pos, strongSide, pos.list<ROOK>(weakSide)[0]);
457 File f = file_of(wpsq);
458 Rank r = rank_of(wpsq);
459 Square queeningSq = make_square(f, RANK_8);
460 int tempo = (pos.side_to_move() == strongSide);
462 // If the pawn is not too far advanced and the defending king defends the
463 // queening square, use the third-rank defence.
465 && distance(bksq, queeningSq) <= 1
467 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
468 return SCALE_FACTOR_DRAW;
470 // The defending side saves a draw by checking from behind in case the pawn
471 // has advanced to the 6th rank with the king behind.
473 && distance(bksq, queeningSq) <= 1
474 && rank_of(wksq) + tempo <= RANK_6
475 && (rank_of(brsq) == RANK_1 || (!tempo && distance(file_of(brsq), f) >= 3)))
476 return SCALE_FACTOR_DRAW;
479 && bksq == queeningSq
480 && rank_of(brsq) == RANK_1
481 && (!tempo || distance(wksq, wpsq) >= 2))
482 return SCALE_FACTOR_DRAW;
484 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
485 // and the black rook is behind the pawn.
488 && (bksq == SQ_H7 || bksq == SQ_G7)
489 && file_of(brsq) == FILE_A
490 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
491 return SCALE_FACTOR_DRAW;
493 // If the defending king blocks the pawn and the attacking king is too far
494 // away, it's a draw.
496 && bksq == wpsq + DELTA_N
497 && distance(wksq, wpsq) - tempo >= 2
498 && distance(wksq, brsq) - tempo >= 2)
499 return SCALE_FACTOR_DRAW;
501 // Pawn on the 7th rank supported by the rook from behind usually wins if the
502 // attacking king is closer to the queening square than the defending king,
503 // and the defending king cannot gain tempi by threatening the attacking rook.
506 && file_of(wrsq) == f
507 && wrsq != queeningSq
508 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
509 && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
510 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
512 // Similar to the above, but with the pawn further back
514 && file_of(wrsq) == f
516 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
517 && (distance(wksq, wpsq + DELTA_N) < distance(bksq, wpsq + DELTA_N) - 2 + tempo)
518 && ( distance(bksq, wrsq) + tempo >= 3
519 || ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
520 && (distance(wksq, wpsq + DELTA_N) < distance(bksq, wrsq) + tempo))))
521 return ScaleFactor( SCALE_FACTOR_MAX
522 - 8 * distance(wpsq, queeningSq)
523 - 2 * distance(wksq, queeningSq));
525 // If the pawn is not far advanced and the defending king is somewhere in
526 // the pawn's path, it's probably a draw.
527 if (r <= RANK_4 && bksq > wpsq)
529 if (file_of(bksq) == file_of(wpsq))
530 return ScaleFactor(10);
531 if ( distance<File>(bksq, wpsq) == 1
532 && distance(wksq, bksq) > 2)
533 return ScaleFactor(24 - 2 * distance(wksq, bksq));
535 return SCALE_FACTOR_NONE;
539 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
541 assert(verify_material(pos, strongSide, RookValueMg, 1));
542 assert(verify_material(pos, weakSide, BishopValueMg, 0));
544 // Test for a rook pawn
545 if (pos.pieces(PAWN) & (FileABB | FileHBB))
547 Square ksq = pos.king_square(weakSide);
548 Square bsq = pos.list<BISHOP>(weakSide)[0];
549 Square psq = pos.list<PAWN>(strongSide)[0];
550 Rank rk = relative_rank(strongSide, psq);
551 Square push = pawn_push(strongSide);
553 // If the pawn is on the 5th rank and the pawn (currently) is on
554 // the same color square as the bishop then there is a chance of
555 // a fortress. Depending on the king position give a moderate
556 // reduction or a stronger one if the defending king is near the
557 // corner but not trapped there.
558 if (rk == RANK_5 && !opposite_colors(bsq, psq))
560 int d = distance(psq + 3 * push, ksq);
562 if (d <= 2 && !(d == 0 && ksq == pos.king_square(strongSide) + 2 * push))
563 return ScaleFactor(24);
565 return ScaleFactor(48);
568 // When the pawn has moved to the 6th rank we can be fairly sure
569 // it's drawn if the bishop attacks the square in front of the
570 // pawn from a reasonable distance and the defending king is near
573 && distance(psq + 2 * push, ksq) <= 1
574 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
575 && distance<File>(bsq, psq) >= 2)
576 return ScaleFactor(8);
579 return SCALE_FACTOR_NONE;
582 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
583 /// pawns and the defending king is actively placed, the position is drawish.
585 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
587 assert(verify_material(pos, strongSide, RookValueMg, 2));
588 assert(verify_material(pos, weakSide, RookValueMg, 1));
590 Square wpsq1 = pos.list<PAWN>(strongSide)[0];
591 Square wpsq2 = pos.list<PAWN>(strongSide)[1];
592 Square bksq = pos.king_square(weakSide);
594 // Does the stronger side have a passed pawn?
595 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
596 return SCALE_FACTOR_NONE;
598 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
600 if ( distance<File>(bksq, wpsq1) <= 1
601 && distance<File>(bksq, wpsq2) <= 1
602 && relative_rank(strongSide, bksq) > r)
605 case RANK_2: return ScaleFactor(10);
606 case RANK_3: return ScaleFactor(10);
607 case RANK_4: return ScaleFactor(15);
608 case RANK_5: return ScaleFactor(20);
609 case RANK_6: return ScaleFactor(40);
610 default: assert(false);
613 return SCALE_FACTOR_NONE;
617 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
618 /// are on the same rook file and are blocked by the defending king, it's a draw.
620 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
622 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
623 assert(pos.count<PAWN>(strongSide) >= 2);
624 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
626 Square ksq = pos.king_square(weakSide);
627 Bitboard pawns = pos.pieces(strongSide, PAWN);
628 Square psq = pos.list<PAWN>(strongSide)[0];
630 // If all pawns are ahead of the king, on a single rook file and
631 // the king is within one file of the pawns, it's a draw.
632 if ( !(pawns & ~in_front_bb(weakSide, rank_of(ksq)))
633 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
634 && distance<File>(ksq, psq) <= 1)
635 return SCALE_FACTOR_DRAW;
637 return SCALE_FACTOR_NONE;
641 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
642 /// path of the pawn, and the square of the king is not of the same color as the
643 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
644 /// it's almost always a draw.
646 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
648 assert(verify_material(pos, strongSide, BishopValueMg, 1));
649 assert(verify_material(pos, weakSide, BishopValueMg, 0));
651 Square pawnSq = pos.list<PAWN>(strongSide)[0];
652 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
653 Square weakBishopSq = pos.list<BISHOP>(weakSide)[0];
654 Square weakKingSq = pos.king_square(weakSide);
656 // Case 1: Defending king blocks the pawn, and cannot be driven away
657 if ( file_of(weakKingSq) == file_of(pawnSq)
658 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
659 && ( opposite_colors(weakKingSq, strongBishopSq)
660 || relative_rank(strongSide, weakKingSq) <= RANK_6))
661 return SCALE_FACTOR_DRAW;
663 // Case 2: Opposite colored bishops
664 if (opposite_colors(strongBishopSq, weakBishopSq))
666 // We assume that the position is drawn in the following three situations:
668 // a. The pawn is on rank 5 or further back.
669 // b. The defending king is somewhere in the pawn's path.
670 // c. The defending bishop attacks some square along the pawn's path,
671 // and is at least three squares away from the pawn.
673 // These rules are probably not perfect, but in practice they work
676 if (relative_rank(strongSide, pawnSq) <= RANK_5)
677 return SCALE_FACTOR_DRAW;
680 Bitboard path = forward_bb(strongSide, pawnSq);
682 if (path & pos.pieces(weakSide, KING))
683 return SCALE_FACTOR_DRAW;
685 if ( (pos.attacks_from<BISHOP>(weakBishopSq) & path)
686 && distance(weakBishopSq, pawnSq) >= 3)
687 return SCALE_FACTOR_DRAW;
690 return SCALE_FACTOR_NONE;
694 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
696 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
698 assert(verify_material(pos, strongSide, BishopValueMg, 2));
699 assert(verify_material(pos, weakSide, BishopValueMg, 0));
701 Square wbsq = pos.list<BISHOP>(strongSide)[0];
702 Square bbsq = pos.list<BISHOP>(weakSide)[0];
704 if (!opposite_colors(wbsq, bbsq))
705 return SCALE_FACTOR_NONE;
707 Square ksq = pos.king_square(weakSide);
708 Square psq1 = pos.list<PAWN>(strongSide)[0];
709 Square psq2 = pos.list<PAWN>(strongSide)[1];
710 Rank r1 = rank_of(psq1);
711 Rank r2 = rank_of(psq2);
712 Square blockSq1, blockSq2;
714 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
716 blockSq1 = psq1 + pawn_push(strongSide);
717 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
721 blockSq1 = psq2 + pawn_push(strongSide);
722 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
725 switch (distance<File>(psq1, psq2))
728 // Both pawns are on the same file. It's an easy draw if the defender firmly
729 // controls some square in the frontmost pawn's path.
730 if ( file_of(ksq) == file_of(blockSq1)
731 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
732 && opposite_colors(ksq, wbsq))
733 return SCALE_FACTOR_DRAW;
735 return SCALE_FACTOR_NONE;
738 // Pawns on adjacent files. It's a draw if the defender firmly controls the
739 // square in front of the frontmost pawn's path, and the square diagonally
740 // behind this square on the file of the other pawn.
742 && opposite_colors(ksq, wbsq)
743 && ( bbsq == blockSq2
744 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
745 || distance(r1, r2) >= 2))
746 return SCALE_FACTOR_DRAW;
748 else if ( ksq == blockSq2
749 && opposite_colors(ksq, wbsq)
750 && ( bbsq == blockSq1
751 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
752 return SCALE_FACTOR_DRAW;
754 return SCALE_FACTOR_NONE;
757 // The pawns are not on the same file or adjacent files. No scaling.
758 return SCALE_FACTOR_NONE;
763 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
764 /// the path of the pawn, and the square of the king is not of the same color as
765 /// the stronger side's bishop, it's a draw.
767 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
769 assert(verify_material(pos, strongSide, BishopValueMg, 1));
770 assert(verify_material(pos, weakSide, KnightValueMg, 0));
772 Square pawnSq = pos.list<PAWN>(strongSide)[0];
773 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
774 Square weakKingSq = pos.king_square(weakSide);
776 if ( file_of(weakKingSq) == file_of(pawnSq)
777 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
778 && ( opposite_colors(weakKingSq, strongBishopSq)
779 || relative_rank(strongSide, weakKingSq) <= RANK_6))
780 return SCALE_FACTOR_DRAW;
782 return SCALE_FACTOR_NONE;
786 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
787 /// and the defending king prevents the pawn from advancing, the position is drawn.
789 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
791 assert(verify_material(pos, strongSide, KnightValueMg, 1));
792 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
794 // Assume strongSide is white and the pawn is on files A-D
795 Square pawnSq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
796 Square weakKingSq = normalize(pos, strongSide, pos.king_square(weakSide));
798 if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
799 return SCALE_FACTOR_DRAW;
801 return SCALE_FACTOR_NONE;
805 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
806 /// Otherwise the position is drawn.
808 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
810 Square pawnSq = pos.list<PAWN>(strongSide)[0];
811 Square bishopSq = pos.list<BISHOP>(weakSide)[0];
812 Square weakKingSq = pos.king_square(weakSide);
814 // King needs to get close to promoting pawn to prevent knight from blocking.
815 // Rules for this are very tricky, so just approximate.
816 if (forward_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
817 return ScaleFactor(distance(weakKingSq, pawnSq));
819 return SCALE_FACTOR_NONE;
823 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
824 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
825 /// has at least a draw with the pawn as well. The exception is when the stronger
826 /// side's pawn is far advanced and not on a rook file; in this case it is often
827 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
829 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
831 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
832 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
834 // Assume strongSide is white and the pawn is on files A-D
835 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
836 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
837 Square psq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
839 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
841 // If the pawn has advanced to the fifth rank or further, and is not a
842 // rook pawn, it's too dangerous to assume that it's at least a draw.
843 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
844 return SCALE_FACTOR_NONE;
846 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
847 // it's probably at least a draw even with the pawn.
848 return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;