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) {
131 map<T>()[key(code, WHITE)] = std::unique_ptr<EndgameBase<T>>(new Endgame<E>(WHITE));
132 map<T>()[key(code, BLACK)] = std::unique_ptr<EndgameBase<T>>(new Endgame<E>(BLACK));
136 /// Mate with KX vs K. This function is used to evaluate positions with
137 /// king and plenty of material vs a lone king. It simply gives the
138 /// attacking side a bonus for driving the defending king towards the edge
139 /// of the board, and for keeping the distance between the two kings small.
141 Value Endgame<KXK>::operator()(const Position& pos) const {
143 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
144 assert(!pos.checkers()); // Eval is never called when in check
146 // Stalemate detection with lone king
147 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
150 Square winnerKSq = pos.king_square(strongSide);
151 Square loserKSq = pos.king_square(weakSide);
153 Value result = pos.non_pawn_material(strongSide)
154 + pos.count<PAWN>(strongSide) * PawnValueEg
155 + PushToEdges[loserKSq]
156 + PushClose[distance(winnerKSq, loserKSq)];
158 if ( pos.count<QUEEN>(strongSide)
159 || pos.count<ROOK>(strongSide)
160 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
161 ||(pos.count<BISHOP>(strongSide) > 1 && opposite_colors(pos.list<BISHOP>(strongSide)[0],
162 pos.list<BISHOP>(strongSide)[1])))
163 result += VALUE_KNOWN_WIN;
165 return strongSide == pos.side_to_move() ? result : -result;
169 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
170 /// defending king towards a corner square of the right color.
172 Value Endgame<KBNK>::operator()(const Position& pos) const {
174 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
175 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
177 Square winnerKSq = pos.king_square(strongSide);
178 Square loserKSq = pos.king_square(weakSide);
179 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
181 // kbnk_mate_table() tries to drive toward corners A1 or H8. If we have a
182 // bishop that cannot reach the above squares, we flip the kings in order
183 // to drive the enemy toward corners A8 or H1.
184 if (opposite_colors(bishopSq, SQ_A1))
186 winnerKSq = ~winnerKSq;
187 loserKSq = ~loserKSq;
190 Value result = VALUE_KNOWN_WIN
191 + PushClose[distance(winnerKSq, loserKSq)]
192 + PushToCorners[loserKSq];
194 return strongSide == pos.side_to_move() ? result : -result;
198 /// KP vs K. This endgame is evaluated with the help of a bitbase.
200 Value Endgame<KPK>::operator()(const Position& pos) const {
202 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
203 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
205 // Assume strongSide is white and the pawn is on files A-D
206 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
207 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
208 Square psq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
210 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
212 if (!Bitbases::probe(wksq, psq, bksq, us))
215 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
217 return strongSide == pos.side_to_move() ? result : -result;
221 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
222 /// a bitbase. The function below returns drawish scores when the pawn is
223 /// far advanced with support of the king, while the attacking king is far
226 Value Endgame<KRKP>::operator()(const Position& pos) const {
228 assert(verify_material(pos, strongSide, RookValueMg, 0));
229 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
231 Square wksq = relative_square(strongSide, pos.king_square(strongSide));
232 Square bksq = relative_square(strongSide, pos.king_square(weakSide));
233 Square rsq = relative_square(strongSide, pos.list<ROOK>(strongSide)[0]);
234 Square psq = relative_square(strongSide, pos.list<PAWN>(weakSide)[0]);
236 Square queeningSq = make_square(file_of(psq), RANK_1);
239 // If the stronger side's king is in front of the pawn, it's a win
240 if (wksq < psq && file_of(wksq) == file_of(psq))
241 result = RookValueEg - distance(wksq, psq);
243 // If the weaker side's king is too far from the pawn and the rook,
245 else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
246 && distance(bksq, rsq) >= 3)
247 result = RookValueEg - distance(wksq, psq);
249 // If the pawn is far advanced and supported by the defending king,
250 // the position is drawish
251 else if ( rank_of(bksq) <= RANK_3
252 && distance(bksq, psq) == 1
253 && rank_of(wksq) >= RANK_4
254 && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
255 result = Value(80) - 8 * distance(wksq, psq);
258 result = Value(200) - 8 * ( distance(wksq, psq + DELTA_S)
259 - distance(bksq, psq + DELTA_S)
260 - distance(psq, queeningSq));
262 return strongSide == pos.side_to_move() ? result : -result;
266 /// KR vs KB. This is very simple, and always returns drawish scores. The
267 /// score is slightly bigger when the defending king is close to the edge.
269 Value Endgame<KRKB>::operator()(const Position& pos) const {
271 assert(verify_material(pos, strongSide, RookValueMg, 0));
272 assert(verify_material(pos, weakSide, BishopValueMg, 0));
274 Value result = Value(PushToEdges[pos.king_square(weakSide)]);
275 return strongSide == pos.side_to_move() ? result : -result;
279 /// KR vs KN. The attacking side has slightly better winning chances than
280 /// in KR vs KB, particularly if the king and the knight are far apart.
282 Value Endgame<KRKN>::operator()(const Position& pos) const {
284 assert(verify_material(pos, strongSide, RookValueMg, 0));
285 assert(verify_material(pos, weakSide, KnightValueMg, 0));
287 Square bksq = pos.king_square(weakSide);
288 Square bnsq = pos.list<KNIGHT>(weakSide)[0];
289 Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
290 return strongSide == pos.side_to_move() ? result : -result;
294 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
295 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
296 /// with a king positioned next to it can be a draw, so in that case, we only
297 /// use the distance between the kings.
299 Value Endgame<KQKP>::operator()(const Position& pos) const {
301 assert(verify_material(pos, strongSide, QueenValueMg, 0));
302 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
304 Square winnerKSq = pos.king_square(strongSide);
305 Square loserKSq = pos.king_square(weakSide);
306 Square pawnSq = pos.list<PAWN>(weakSide)[0];
308 Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
310 if ( relative_rank(weakSide, pawnSq) != RANK_7
311 || distance(loserKSq, pawnSq) != 1
312 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
313 result += QueenValueEg - PawnValueEg;
315 return strongSide == pos.side_to_move() ? result : -result;
319 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
320 /// king a bonus for having the kings close together, and for forcing the
321 /// defending king towards the edge. If we also take care to avoid null move for
322 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
324 Value Endgame<KQKR>::operator()(const Position& pos) const {
326 assert(verify_material(pos, strongSide, QueenValueMg, 0));
327 assert(verify_material(pos, weakSide, RookValueMg, 0));
329 Square winnerKSq = pos.king_square(strongSide);
330 Square loserKSq = pos.king_square(weakSide);
332 Value result = QueenValueEg
334 + PushToEdges[loserKSq]
335 + PushClose[distance(winnerKSq, loserKSq)];
337 return strongSide == pos.side_to_move() ? result : -result;
341 /// Some cases of trivial draws
342 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
345 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
346 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
347 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
350 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
352 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
353 assert(pos.count<PAWN>(strongSide) >= 1);
355 // No assertions about the material of weakSide, because we want draws to
356 // be detected even when the weaker side has some pawns.
358 Bitboard pawns = pos.pieces(strongSide, PAWN);
359 File pawnFile = file_of(pos.list<PAWN>(strongSide)[0]);
361 // All pawns are on a single rook file ?
362 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
363 && !(pawns & ~file_bb(pawnFile)))
365 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
366 Square queeningSq = relative_square(strongSide, make_square(pawnFile, RANK_8));
367 Square kingSq = pos.king_square(weakSide);
369 if ( opposite_colors(queeningSq, bishopSq)
370 && distance(queeningSq, kingSq) <= 1)
371 return SCALE_FACTOR_DRAW;
374 // If all the pawns are on the same B or G file, then it's potentially a draw
375 if ( (pawnFile == FILE_B || pawnFile == FILE_G)
376 && !(pos.pieces(PAWN) & ~file_bb(pawnFile))
377 && pos.non_pawn_material(weakSide) == 0
378 && pos.count<PAWN>(weakSide) >= 1)
380 // Get weakSide pawn that is closest to the home rank
381 Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
383 Square strongKingSq = pos.king_square(strongSide);
384 Square weakKingSq = pos.king_square(weakSide);
385 Square bishopSq = pos.list<BISHOP>(strongSide)[0];
387 // There's potential for a draw if our pawn is blocked on the 7th rank,
388 // the bishop cannot attack it or they only have one pawn left
389 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
390 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
391 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
393 int strongKingDist = distance(weakPawnSq, strongKingSq);
394 int weakKingDist = distance(weakPawnSq, weakKingSq);
396 // It's a draw if the weak king is on its back two ranks, within 2
397 // squares of the blocking pawn and the strong king is not
398 // closer. (I think this rule only fails in practically
399 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
400 // and positions where qsearch will immediately correct the
401 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
402 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
404 && weakKingDist <= strongKingDist)
405 return SCALE_FACTOR_DRAW;
409 return SCALE_FACTOR_NONE;
413 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
414 /// the third rank defended by a pawn.
416 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
418 assert(verify_material(pos, strongSide, QueenValueMg, 0));
419 assert(pos.count<ROOK>(weakSide) == 1);
420 assert(pos.count<PAWN>(weakSide) >= 1);
422 Square kingSq = pos.king_square(weakSide);
423 Square rsq = pos.list<ROOK>(weakSide)[0];
425 if ( relative_rank(weakSide, kingSq) <= RANK_2
426 && relative_rank(weakSide, pos.king_square(strongSide)) >= RANK_4
427 && relative_rank(weakSide, rsq) == RANK_3
428 && ( pos.pieces(weakSide, PAWN)
429 & pos.attacks_from<KING>(kingSq)
430 & pos.attacks_from<PAWN>(rsq, strongSide)))
431 return SCALE_FACTOR_DRAW;
433 return SCALE_FACTOR_NONE;
437 /// KRP vs KR. This function knows a handful of the most important classes of
438 /// drawn positions, but is far from perfect. It would probably be a good idea
439 /// to add more knowledge in the future.
441 /// It would also be nice to rewrite the actual code for this function,
442 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
444 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
446 assert(verify_material(pos, strongSide, RookValueMg, 1));
447 assert(verify_material(pos, weakSide, RookValueMg, 0));
449 // Assume strongSide is white and the pawn is on files A-D
450 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
451 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
452 Square wrsq = normalize(pos, strongSide, pos.list<ROOK>(strongSide)[0]);
453 Square wpsq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
454 Square brsq = normalize(pos, strongSide, pos.list<ROOK>(weakSide)[0]);
456 File f = file_of(wpsq);
457 Rank r = rank_of(wpsq);
458 Square queeningSq = make_square(f, RANK_8);
459 int tempo = (pos.side_to_move() == strongSide);
461 // If the pawn is not too far advanced and the defending king defends the
462 // queening square, use the third-rank defence.
464 && distance(bksq, queeningSq) <= 1
466 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
467 return SCALE_FACTOR_DRAW;
469 // The defending side saves a draw by checking from behind in case the pawn
470 // has advanced to the 6th rank with the king behind.
472 && distance(bksq, queeningSq) <= 1
473 && rank_of(wksq) + tempo <= RANK_6
474 && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
475 return SCALE_FACTOR_DRAW;
478 && bksq == queeningSq
479 && rank_of(brsq) == RANK_1
480 && (!tempo || distance(wksq, wpsq) >= 2))
481 return SCALE_FACTOR_DRAW;
483 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
484 // and the black rook is behind the pawn.
487 && (bksq == SQ_H7 || bksq == SQ_G7)
488 && file_of(brsq) == FILE_A
489 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
490 return SCALE_FACTOR_DRAW;
492 // If the defending king blocks the pawn and the attacking king is too far
493 // away, it's a draw.
495 && bksq == wpsq + DELTA_N
496 && distance(wksq, wpsq) - tempo >= 2
497 && distance(wksq, brsq) - tempo >= 2)
498 return SCALE_FACTOR_DRAW;
500 // Pawn on the 7th rank supported by the rook from behind usually wins if the
501 // attacking king is closer to the queening square than the defending king,
502 // and the defending king cannot gain tempi by threatening the attacking rook.
505 && file_of(wrsq) == f
506 && wrsq != queeningSq
507 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
508 && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
509 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
511 // Similar to the above, but with the pawn further back
513 && file_of(wrsq) == f
515 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
516 && (distance(wksq, wpsq + DELTA_N) < distance(bksq, wpsq + DELTA_N) - 2 + tempo)
517 && ( distance(bksq, wrsq) + tempo >= 3
518 || ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
519 && (distance(wksq, wpsq + DELTA_N) < distance(bksq, wrsq) + tempo))))
520 return ScaleFactor( SCALE_FACTOR_MAX
521 - 8 * distance(wpsq, queeningSq)
522 - 2 * distance(wksq, queeningSq));
524 // If the pawn is not far advanced and the defending king is somewhere in
525 // the pawn's path, it's probably a draw.
526 if (r <= RANK_4 && bksq > wpsq)
528 if (file_of(bksq) == file_of(wpsq))
529 return ScaleFactor(10);
530 if ( distance<File>(bksq, wpsq) == 1
531 && distance(wksq, bksq) > 2)
532 return ScaleFactor(24 - 2 * distance(wksq, bksq));
534 return SCALE_FACTOR_NONE;
538 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
540 assert(verify_material(pos, strongSide, RookValueMg, 1));
541 assert(verify_material(pos, weakSide, BishopValueMg, 0));
543 // Test for a rook pawn
544 if (pos.pieces(PAWN) & (FileABB | FileHBB))
546 Square ksq = pos.king_square(weakSide);
547 Square bsq = pos.list<BISHOP>(weakSide)[0];
548 Square psq = pos.list<PAWN>(strongSide)[0];
549 Rank rk = relative_rank(strongSide, psq);
550 Square push = pawn_push(strongSide);
552 // If the pawn is on the 5th rank and the pawn (currently) is on
553 // the same color square as the bishop then there is a chance of
554 // a fortress. Depending on the king position give a moderate
555 // reduction or a stronger one if the defending king is near the
556 // corner but not trapped there.
557 if (rk == RANK_5 && !opposite_colors(bsq, psq))
559 int d = distance(psq + 3 * push, ksq);
561 if (d <= 2 && !(d == 0 && ksq == pos.king_square(strongSide) + 2 * push))
562 return ScaleFactor(24);
564 return ScaleFactor(48);
567 // When the pawn has moved to the 6th rank we can be fairly sure
568 // it's drawn if the bishop attacks the square in front of the
569 // pawn from a reasonable distance and the defending king is near
572 && distance(psq + 2 * push, ksq) <= 1
573 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
574 && distance<File>(bsq, psq) >= 2)
575 return ScaleFactor(8);
578 return SCALE_FACTOR_NONE;
581 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
582 /// pawns and the defending king is actively placed, the position is drawish.
584 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
586 assert(verify_material(pos, strongSide, RookValueMg, 2));
587 assert(verify_material(pos, weakSide, RookValueMg, 1));
589 Square wpsq1 = pos.list<PAWN>(strongSide)[0];
590 Square wpsq2 = pos.list<PAWN>(strongSide)[1];
591 Square bksq = pos.king_square(weakSide);
593 // Does the stronger side have a passed pawn?
594 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
595 return SCALE_FACTOR_NONE;
597 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
599 if ( distance<File>(bksq, wpsq1) <= 1
600 && distance<File>(bksq, wpsq2) <= 1
601 && relative_rank(strongSide, bksq) > r)
604 case RANK_2: return ScaleFactor(10);
605 case RANK_3: return ScaleFactor(10);
606 case RANK_4: return ScaleFactor(15);
607 case RANK_5: return ScaleFactor(20);
608 case RANK_6: return ScaleFactor(40);
609 default: assert(false);
612 return SCALE_FACTOR_NONE;
616 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
617 /// are on the same rook file and are blocked by the defending king, it's a draw.
619 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
621 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
622 assert(pos.count<PAWN>(strongSide) >= 2);
623 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
625 Square ksq = pos.king_square(weakSide);
626 Bitboard pawns = pos.pieces(strongSide, PAWN);
627 Square psq = pos.list<PAWN>(strongSide)[0];
629 // If all pawns are ahead of the king, on a single rook file and
630 // the king is within one file of the pawns, it's a draw.
631 if ( !(pawns & ~in_front_bb(weakSide, rank_of(ksq)))
632 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
633 && distance<File>(ksq, psq) <= 1)
634 return SCALE_FACTOR_DRAW;
636 return SCALE_FACTOR_NONE;
640 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
641 /// path of the pawn, and the square of the king is not of the same color as the
642 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
643 /// it's almost always a draw.
645 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
647 assert(verify_material(pos, strongSide, BishopValueMg, 1));
648 assert(verify_material(pos, weakSide, BishopValueMg, 0));
650 Square pawnSq = pos.list<PAWN>(strongSide)[0];
651 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
652 Square weakBishopSq = pos.list<BISHOP>(weakSide)[0];
653 Square weakKingSq = pos.king_square(weakSide);
655 // Case 1: Defending king blocks the pawn, and cannot be driven away
656 if ( file_of(weakKingSq) == file_of(pawnSq)
657 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
658 && ( opposite_colors(weakKingSq, strongBishopSq)
659 || relative_rank(strongSide, weakKingSq) <= RANK_6))
660 return SCALE_FACTOR_DRAW;
662 // Case 2: Opposite colored bishops
663 if (opposite_colors(strongBishopSq, weakBishopSq))
665 // We assume that the position is drawn in the following three situations:
667 // a. The pawn is on rank 5 or further back.
668 // b. The defending king is somewhere in the pawn's path.
669 // c. The defending bishop attacks some square along the pawn's path,
670 // and is at least three squares away from the pawn.
672 // These rules are probably not perfect, but in practice they work
675 if (relative_rank(strongSide, pawnSq) <= RANK_5)
676 return SCALE_FACTOR_DRAW;
679 Bitboard path = forward_bb(strongSide, pawnSq);
681 if (path & pos.pieces(weakSide, KING))
682 return SCALE_FACTOR_DRAW;
684 if ( (pos.attacks_from<BISHOP>(weakBishopSq) & path)
685 && distance(weakBishopSq, pawnSq) >= 3)
686 return SCALE_FACTOR_DRAW;
689 return SCALE_FACTOR_NONE;
693 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
695 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
697 assert(verify_material(pos, strongSide, BishopValueMg, 2));
698 assert(verify_material(pos, weakSide, BishopValueMg, 0));
700 Square wbsq = pos.list<BISHOP>(strongSide)[0];
701 Square bbsq = pos.list<BISHOP>(weakSide)[0];
703 if (!opposite_colors(wbsq, bbsq))
704 return SCALE_FACTOR_NONE;
706 Square ksq = pos.king_square(weakSide);
707 Square psq1 = pos.list<PAWN>(strongSide)[0];
708 Square psq2 = pos.list<PAWN>(strongSide)[1];
709 Rank r1 = rank_of(psq1);
710 Rank r2 = rank_of(psq2);
711 Square blockSq1, blockSq2;
713 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
715 blockSq1 = psq1 + pawn_push(strongSide);
716 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
720 blockSq1 = psq2 + pawn_push(strongSide);
721 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
724 switch (distance<File>(psq1, psq2))
727 // Both pawns are on the same file. It's an easy draw if the defender firmly
728 // controls some square in the frontmost pawn's path.
729 if ( file_of(ksq) == file_of(blockSq1)
730 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
731 && opposite_colors(ksq, wbsq))
732 return SCALE_FACTOR_DRAW;
734 return SCALE_FACTOR_NONE;
737 // Pawns on adjacent files. It's a draw if the defender firmly controls the
738 // square in front of the frontmost pawn's path, and the square diagonally
739 // behind this square on the file of the other pawn.
741 && opposite_colors(ksq, wbsq)
742 && ( bbsq == blockSq2
743 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
744 || distance(r1, r2) >= 2))
745 return SCALE_FACTOR_DRAW;
747 else if ( ksq == blockSq2
748 && opposite_colors(ksq, wbsq)
749 && ( bbsq == blockSq1
750 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
751 return SCALE_FACTOR_DRAW;
753 return SCALE_FACTOR_NONE;
756 // The pawns are not on the same file or adjacent files. No scaling.
757 return SCALE_FACTOR_NONE;
762 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
763 /// the path of the pawn, and the square of the king is not of the same color as
764 /// the stronger side's bishop, it's a draw.
766 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
768 assert(verify_material(pos, strongSide, BishopValueMg, 1));
769 assert(verify_material(pos, weakSide, KnightValueMg, 0));
771 Square pawnSq = pos.list<PAWN>(strongSide)[0];
772 Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
773 Square weakKingSq = pos.king_square(weakSide);
775 if ( file_of(weakKingSq) == file_of(pawnSq)
776 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
777 && ( opposite_colors(weakKingSq, strongBishopSq)
778 || relative_rank(strongSide, weakKingSq) <= RANK_6))
779 return SCALE_FACTOR_DRAW;
781 return SCALE_FACTOR_NONE;
785 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
786 /// and the defending king prevents the pawn from advancing, the position is drawn.
788 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
790 assert(verify_material(pos, strongSide, KnightValueMg, 1));
791 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
793 // Assume strongSide is white and the pawn is on files A-D
794 Square pawnSq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
795 Square weakKingSq = normalize(pos, strongSide, pos.king_square(weakSide));
797 if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
798 return SCALE_FACTOR_DRAW;
800 return SCALE_FACTOR_NONE;
804 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
805 /// Otherwise the position is drawn.
807 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
809 Square pawnSq = pos.list<PAWN>(strongSide)[0];
810 Square bishopSq = pos.list<BISHOP>(weakSide)[0];
811 Square weakKingSq = pos.king_square(weakSide);
813 // King needs to get close to promoting pawn to prevent knight from blocking.
814 // Rules for this are very tricky, so just approximate.
815 if (forward_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
816 return ScaleFactor(distance(weakKingSq, pawnSq));
818 return SCALE_FACTOR_NONE;
822 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
823 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
824 /// has at least a draw with the pawn as well. The exception is when the stronger
825 /// side's pawn is far advanced and not on a rook file; in this case it is often
826 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
828 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
830 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
831 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
833 // Assume strongSide is white and the pawn is on files A-D
834 Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
835 Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
836 Square psq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
838 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
840 // If the pawn has advanced to the fifth rank or further, and is not a
841 // rook pawn, it's too dangerous to assume that it's at least a draw.
842 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
843 return SCALE_FACTOR_NONE;
845 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
846 // it's probably at least a draw even with the pawn.
847 return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;