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, 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[distance(winnerKSq, loserKSq)];
167 if ( pos.count<QUEEN>(strongSide)
168 || pos.count<ROOK>(strongSide)
169 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
170 ||(pos.count<BISHOP>(strongSide) > 1 && opposite_colors(pos.list<BISHOP>(strongSide)[0],
171 pos.list<BISHOP>(strongSide)[1])))
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[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(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 = make_square(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 - distance(wksq, psq);
252 // If the weaker side's king is too far from the pawn and the rook,
254 else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
255 && distance(bksq, rsq) >= 3)
256 result = RookValueEg - 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 && distance(bksq, psq) == 1
262 && rank_of(wksq) >= RANK_4
263 && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
264 result = Value(80) - 8 * distance(wksq, psq);
267 result = Value(200) - 8 * ( distance(wksq, psq + DELTA_S)
268 - distance(bksq, psq + DELTA_S)
269 - distance(psq, queeningSq));
271 return strongSide == pos.side_to_move() ? result : -result;
275 /// KR vs KB. This is very simple, and always returns drawish scores. The
276 /// score is slightly bigger when the defending king is close to the edge.
278 Value Endgame<KRKB>::operator()(const Position& pos) const {
280 assert(verify_material(pos, strongSide, RookValueMg, 0));
281 assert(verify_material(pos, weakSide, BishopValueMg, 0));
283 Value result = Value(PushToEdges[pos.king_square(weakSide)]);
284 return strongSide == pos.side_to_move() ? result : -result;
288 /// KR vs KN. The attacking side has slightly better winning chances than
289 /// in KR vs KB, particularly if the king and the knight are far apart.
291 Value Endgame<KRKN>::operator()(const Position& pos) const {
293 assert(verify_material(pos, strongSide, RookValueMg, 0));
294 assert(verify_material(pos, weakSide, KnightValueMg, 0));
296 Square bksq = pos.king_square(weakSide);
297 Square bnsq = pos.list<KNIGHT>(weakSide)[0];
298 Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
299 return strongSide == pos.side_to_move() ? result : -result;
303 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
304 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
305 /// with a king positioned next to it can be a draw, so in that case, we only
306 /// use the distance between the kings.
308 Value Endgame<KQKP>::operator()(const Position& pos) const {
310 assert(verify_material(pos, strongSide, QueenValueMg, 0));
311 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
313 Square winnerKSq = pos.king_square(strongSide);
314 Square loserKSq = pos.king_square(weakSide);
315 Square pawnSq = pos.list<PAWN>(weakSide)[0];
317 Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
319 if ( relative_rank(weakSide, pawnSq) != RANK_7
320 || distance(loserKSq, pawnSq) != 1
321 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
322 result += QueenValueEg - PawnValueEg;
324 return strongSide == pos.side_to_move() ? result : -result;
328 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
329 /// king a bonus for having the kings close together, and for forcing the
330 /// defending king towards the edge. If we also take care to avoid null move for
331 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
333 Value Endgame<KQKR>::operator()(const Position& pos) const {
335 assert(verify_material(pos, strongSide, QueenValueMg, 0));
336 assert(verify_material(pos, weakSide, RookValueMg, 0));
338 Square winnerKSq = pos.king_square(strongSide);
339 Square loserKSq = pos.king_square(weakSide);
341 Value result = QueenValueEg
343 + PushToEdges[loserKSq]
344 + PushClose[distance(winnerKSq, loserKSq)];
346 return strongSide == pos.side_to_move() ? result : -result;
350 /// Some cases of trivial draws
351 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
354 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
355 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
356 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
359 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
361 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
362 assert(pos.count<PAWN>(strongSide) >= 1);
364 // No assertions about the material of weakSide, because we want draws to
365 // be detected even when the weaker side has some pawns.
367 Bitboard pawns = pos.pieces(strongSide, PAWN);
368 File pawnFile = file_of(pos.list<PAWN>(strongSide)[0]);
370 // All pawns are on a single rook file ?
371 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
372 && !(pawns & ~file_bb(pawnFile)))
374 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
375 Square queeningSq = relative_square(strongSide, make_square(pawnFile, RANK_8));
376 Square kingSq = pos.king_square(weakSide);
378 if ( opposite_colors(queeningSq, bishopSq)
379 && distance(queeningSq, kingSq) <= 1)
380 return SCALE_FACTOR_DRAW;
383 // If all the pawns are on the same B or G file, then it's potentially a draw
384 if ( (pawnFile == FILE_B || pawnFile == FILE_G)
385 && !(pos.pieces(PAWN) & ~file_bb(pawnFile))
386 && pos.non_pawn_material(weakSide) == 0
387 && pos.count<PAWN>(weakSide) >= 1)
389 // Get weakSide pawn that is closest to the home rank
390 Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
392 Square strongKingSq = pos.king_square(strongSide);
393 Square weakKingSq = pos.king_square(weakSide);
394 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
396 // There's potential for a draw if our pawn is blocked on the 7th rank,
397 // the bishop cannot attack it or they only have one pawn left
398 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
399 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
400 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
402 int strongKingDist = distance(weakPawnSq, strongKingSq);
403 int weakKingDist = distance(weakPawnSq, weakKingSq);
405 // It's a draw if the weak king is on its back two ranks, within 2
406 // squares of the blocking pawn and the strong king is not
407 // closer. (I think this rule only fails in practically
408 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
409 // and positions where qsearch will immediately correct the
410 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
411 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
413 && weakKingDist <= strongKingDist)
414 return SCALE_FACTOR_DRAW;
418 return SCALE_FACTOR_NONE;
422 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
423 /// the third rank defended by a pawn.
425 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
427 assert(verify_material(pos, strongSide, QueenValueMg, 0));
428 assert(pos.count<ROOK>(weakSide) == 1);
429 assert(pos.count<PAWN>(weakSide) >= 1);
431 Square kingSq = pos.king_square(weakSide);
432 Square rsq = pos.list<ROOK>(weakSide)[0];
434 if ( relative_rank(weakSide, kingSq) <= RANK_2
435 && relative_rank(weakSide, pos.king_square(strongSide)) >= RANK_4
436 && relative_rank(weakSide, rsq) == RANK_3
437 && ( pos.pieces(weakSide, PAWN)
438 & pos.attacks_from<KING>(kingSq)
439 & pos.attacks_from<PAWN>(rsq, strongSide)))
440 return SCALE_FACTOR_DRAW;
442 return SCALE_FACTOR_NONE;
446 /// KRP vs KR. This function knows a handful of the most important classes of
447 /// drawn positions, but is far from perfect. It would probably be a good idea
448 /// to add more knowledge in the future.
450 /// It would also be nice to rewrite the actual code for this function,
451 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
453 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
455 assert(verify_material(pos, strongSide, RookValueMg, 1));
456 assert(verify_material(pos, weakSide, RookValueMg, 0));
458 // Assume strongSide is white and the pawn is on files A-D
459 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
460 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
461 Square wrsq = normalize(pos, strongSide, pos.list<ROOK>(strongSide)[0]);
462 Square wpsq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
463 Square brsq = normalize(pos, strongSide, pos.list<ROOK>(weakSide)[0]);
465 File f = file_of(wpsq);
466 Rank r = rank_of(wpsq);
467 Square queeningSq = make_square(f, RANK_8);
468 int tempo = (pos.side_to_move() == strongSide);
470 // If the pawn is not too far advanced and the defending king defends the
471 // queening square, use the third-rank defence.
473 && distance(bksq, queeningSq) <= 1
475 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
476 return SCALE_FACTOR_DRAW;
478 // The defending side saves a draw by checking from behind in case the pawn
479 // has advanced to the 6th rank with the king behind.
481 && distance(bksq, queeningSq) <= 1
482 && rank_of(wksq) + tempo <= RANK_6
483 && (rank_of(brsq) == RANK_1 || (!tempo && distance(file_of(brsq), f) >= 3)))
484 return SCALE_FACTOR_DRAW;
487 && bksq == queeningSq
488 && rank_of(brsq) == RANK_1
489 && (!tempo || distance(wksq, wpsq) >= 2))
490 return SCALE_FACTOR_DRAW;
492 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
493 // and the black rook is behind the pawn.
496 && (bksq == SQ_H7 || bksq == SQ_G7)
497 && file_of(brsq) == FILE_A
498 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
499 return SCALE_FACTOR_DRAW;
501 // If the defending king blocks the pawn and the attacking king is too far
502 // away, it's a draw.
504 && bksq == wpsq + DELTA_N
505 && distance(wksq, wpsq) - tempo >= 2
506 && distance(wksq, brsq) - tempo >= 2)
507 return SCALE_FACTOR_DRAW;
509 // Pawn on the 7th rank supported by the rook from behind usually wins if the
510 // attacking king is closer to the queening square than the defending king,
511 // and the defending king cannot gain tempi by threatening the attacking rook.
514 && file_of(wrsq) == f
515 && wrsq != queeningSq
516 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
517 && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
518 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
520 // Similar to the above, but with the pawn further back
522 && file_of(wrsq) == f
524 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
525 && (distance(wksq, wpsq + DELTA_N) < distance(bksq, wpsq + DELTA_N) - 2 + tempo)
526 && ( distance(bksq, wrsq) + tempo >= 3
527 || ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
528 && (distance(wksq, wpsq + DELTA_N) < distance(bksq, wrsq) + tempo))))
529 return ScaleFactor( SCALE_FACTOR_MAX
530 - 8 * distance(wpsq, queeningSq)
531 - 2 * distance(wksq, queeningSq));
533 // If the pawn is not far advanced and the defending king is somewhere in
534 // the pawn's path, it's probably a draw.
535 if (r <= RANK_4 && bksq > wpsq)
537 if (file_of(bksq) == file_of(wpsq))
538 return ScaleFactor(10);
539 if ( distance<File>(bksq, wpsq) == 1
540 && distance(wksq, bksq) > 2)
541 return ScaleFactor(24 - 2 * distance(wksq, bksq));
543 return SCALE_FACTOR_NONE;
547 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
549 assert(verify_material(pos, strongSide, RookValueMg, 1));
550 assert(verify_material(pos, weakSide, BishopValueMg, 0));
552 // Test for a rook pawn
553 if (pos.pieces(PAWN) & (FileABB | FileHBB))
555 Square ksq = pos.king_square(weakSide);
556 Square bsq = pos.list<BISHOP>(weakSide)[0];
557 Square psq = pos.list<PAWN>(strongSide)[0];
558 Rank rk = relative_rank(strongSide, psq);
559 Square push = pawn_push(strongSide);
561 // If the pawn is on the 5th rank and the pawn (currently) is on
562 // the same color square as the bishop then there is a chance of
563 // a fortress. Depending on the king position give a moderate
564 // reduction or a stronger one if the defending king is near the
565 // corner but not trapped there.
566 if (rk == RANK_5 && !opposite_colors(bsq, psq))
568 int d = distance(psq + 3 * push, ksq);
570 if (d <= 2 && !(d == 0 && ksq == pos.king_square(strongSide) + 2 * push))
571 return ScaleFactor(24);
573 return ScaleFactor(48);
576 // When the pawn has moved to the 6th rank we can be fairly sure
577 // it's drawn if the bishop attacks the square in front of the
578 // pawn from a reasonable distance and the defending king is near
581 && distance(psq + 2 * push, ksq) <= 1
582 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
583 && distance<File>(bsq, psq) >= 2)
584 return ScaleFactor(8);
587 return SCALE_FACTOR_NONE;
590 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
591 /// pawns and the defending king is actively placed, the position is drawish.
593 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
595 assert(verify_material(pos, strongSide, RookValueMg, 2));
596 assert(verify_material(pos, weakSide, RookValueMg, 1));
598 Square wpsq1 = pos.list<PAWN>(strongSide)[0];
599 Square wpsq2 = pos.list<PAWN>(strongSide)[1];
600 Square bksq = pos.king_square(weakSide);
602 // Does the stronger side have a passed pawn?
603 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
604 return SCALE_FACTOR_NONE;
606 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
608 if ( distance<File>(bksq, wpsq1) <= 1
609 && distance<File>(bksq, wpsq2) <= 1
610 && relative_rank(strongSide, bksq) > r)
613 case RANK_2: return ScaleFactor(10);
614 case RANK_3: return ScaleFactor(10);
615 case RANK_4: return ScaleFactor(15);
616 case RANK_5: return ScaleFactor(20);
617 case RANK_6: return ScaleFactor(40);
618 default: assert(false);
621 return SCALE_FACTOR_NONE;
625 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
626 /// are on the same rook file and are blocked by the defending king, it's a draw.
628 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
630 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
631 assert(pos.count<PAWN>(strongSide) >= 2);
632 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
634 Square ksq = pos.king_square(weakSide);
635 Bitboard pawns = pos.pieces(strongSide, PAWN);
636 Square psq = pos.list<PAWN>(strongSide)[0];
638 // If all pawns are ahead of the king, on a single rook file and
639 // the king is within one file of the pawns, it's a draw.
640 if ( !(pawns & ~in_front_bb(weakSide, rank_of(ksq)))
641 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
642 && distance<File>(ksq, psq) <= 1)
643 return SCALE_FACTOR_DRAW;
645 return SCALE_FACTOR_NONE;
649 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
650 /// path of the pawn, and the square of the king is not of the same color as the
651 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
652 /// it's almost always a draw.
654 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
656 assert(verify_material(pos, strongSide, BishopValueMg, 1));
657 assert(verify_material(pos, weakSide, BishopValueMg, 0));
659 Square pawnSq = pos.list<PAWN>(strongSide)[0];
660 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
661 Square weakBishopSq = pos.list<BISHOP>(weakSide)[0];
662 Square weakKingSq = pos.king_square(weakSide);
664 // Case 1: Defending king blocks the pawn, and cannot be driven away
665 if ( file_of(weakKingSq) == file_of(pawnSq)
666 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
667 && ( opposite_colors(weakKingSq, strongBishopSq)
668 || relative_rank(strongSide, weakKingSq) <= RANK_6))
669 return SCALE_FACTOR_DRAW;
671 // Case 2: Opposite colored bishops
672 if (opposite_colors(strongBishopSq, weakBishopSq))
674 // We assume that the position is drawn in the following three situations:
676 // a. The pawn is on rank 5 or further back.
677 // b. The defending king is somewhere in the pawn's path.
678 // c. The defending bishop attacks some square along the pawn's path,
679 // and is at least three squares away from the pawn.
681 // These rules are probably not perfect, but in practice they work
684 if (relative_rank(strongSide, pawnSq) <= RANK_5)
685 return SCALE_FACTOR_DRAW;
688 Bitboard path = forward_bb(strongSide, pawnSq);
690 if (path & pos.pieces(weakSide, KING))
691 return SCALE_FACTOR_DRAW;
693 if ( (pos.attacks_from<BISHOP>(weakBishopSq) & path)
694 && distance(weakBishopSq, pawnSq) >= 3)
695 return SCALE_FACTOR_DRAW;
698 return SCALE_FACTOR_NONE;
702 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
704 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
706 assert(verify_material(pos, strongSide, BishopValueMg, 2));
707 assert(verify_material(pos, weakSide, BishopValueMg, 0));
709 Square wbsq = pos.list<BISHOP>(strongSide)[0];
710 Square bbsq = pos.list<BISHOP>(weakSide)[0];
712 if (!opposite_colors(wbsq, bbsq))
713 return SCALE_FACTOR_NONE;
715 Square ksq = pos.king_square(weakSide);
716 Square psq1 = pos.list<PAWN>(strongSide)[0];
717 Square psq2 = pos.list<PAWN>(strongSide)[1];
718 Rank r1 = rank_of(psq1);
719 Rank r2 = rank_of(psq2);
720 Square blockSq1, blockSq2;
722 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
724 blockSq1 = psq1 + pawn_push(strongSide);
725 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
729 blockSq1 = psq2 + pawn_push(strongSide);
730 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
733 switch (distance<File>(psq1, psq2))
736 // Both pawns are on the same file. It's an easy draw if the defender firmly
737 // controls some square in the frontmost pawn's path.
738 if ( file_of(ksq) == file_of(blockSq1)
739 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
740 && opposite_colors(ksq, wbsq))
741 return SCALE_FACTOR_DRAW;
743 return SCALE_FACTOR_NONE;
746 // Pawns on adjacent files. It's a draw if the defender firmly controls the
747 // square in front of the frontmost pawn's path, and the square diagonally
748 // behind this square on the file of the other pawn.
750 && opposite_colors(ksq, wbsq)
751 && ( bbsq == blockSq2
752 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
753 || distance(r1, r2) >= 2))
754 return SCALE_FACTOR_DRAW;
756 else if ( ksq == blockSq2
757 && opposite_colors(ksq, wbsq)
758 && ( bbsq == blockSq1
759 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
760 return SCALE_FACTOR_DRAW;
762 return SCALE_FACTOR_NONE;
765 // The pawns are not on the same file or adjacent files. No scaling.
766 return SCALE_FACTOR_NONE;
771 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
772 /// the path of the pawn, and the square of the king is not of the same color as
773 /// the stronger side's bishop, it's a draw.
775 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
777 assert(verify_material(pos, strongSide, BishopValueMg, 1));
778 assert(verify_material(pos, weakSide, KnightValueMg, 0));
780 Square pawnSq = pos.list<PAWN>(strongSide)[0];
781 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
782 Square weakKingSq = pos.king_square(weakSide);
784 if ( file_of(weakKingSq) == file_of(pawnSq)
785 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
786 && ( opposite_colors(weakKingSq, strongBishopSq)
787 || relative_rank(strongSide, weakKingSq) <= RANK_6))
788 return SCALE_FACTOR_DRAW;
790 return SCALE_FACTOR_NONE;
794 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
795 /// and the defending king prevents the pawn from advancing, the position is drawn.
797 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
799 assert(verify_material(pos, strongSide, KnightValueMg, 1));
800 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
802 // Assume strongSide is white and the pawn is on files A-D
803 Square pawnSq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
804 Square weakKingSq = normalize(pos, strongSide, pos.king_square(weakSide));
806 if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
807 return SCALE_FACTOR_DRAW;
809 return SCALE_FACTOR_NONE;
813 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
814 /// Otherwise the position is drawn.
816 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
818 Square pawnSq = pos.list<PAWN>(strongSide)[0];
819 Square bishopSq = pos.list<BISHOP>(weakSide)[0];
820 Square weakKingSq = pos.king_square(weakSide);
822 // King needs to get close to promoting pawn to prevent knight from blocking.
823 // Rules for this are very tricky, so just approximate.
824 if (forward_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
825 return ScaleFactor(distance(weakKingSq, pawnSq));
827 return SCALE_FACTOR_NONE;
831 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
832 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
833 /// has at least a draw with the pawn as well. The exception is when the stronger
834 /// side's pawn is far advanced and not on a rook file; in this case it is often
835 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
837 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
839 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
840 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
842 // Assume strongSide is white and the pawn is on files A-D
843 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
844 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
845 Square psq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
847 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
849 // If the pawn has advanced to the fifth rank or further, and is not a
850 // rook pawn, it's too dangerous to assume that it's at least a draw.
851 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
852 return SCALE_FACTOR_NONE;
854 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
855 // it's probably at least a draw even with the pawn.
856 return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;