2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
4 Copyright (C) 2008-2010 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/>.
29 extern uint32_t probe_kpk_bitbase(Square wksq, Square wpsq, Square bksq, Color stm);
33 // Table used to drive the defending king towards the edge of the board
34 // in KX vs K and KQ vs KR endgames.
35 const int MateTable[64] = {
36 100, 90, 80, 70, 70, 80, 90, 100,
37 90, 70, 60, 50, 50, 60, 70, 90,
38 80, 60, 40, 30, 30, 40, 60, 80,
39 70, 50, 30, 20, 20, 30, 50, 70,
40 70, 50, 30, 20, 20, 30, 50, 70,
41 80, 60, 40, 30, 30, 40, 60, 80,
42 90, 70, 60, 50, 50, 60, 70, 90,
43 100, 90, 80, 70, 70, 80, 90, 100,
46 // Table used to drive the defending king towards a corner square of the
47 // right color in KBN vs K endgames.
48 const int KBNKMateTable[64] = {
49 200, 190, 180, 170, 160, 150, 140, 130,
50 190, 180, 170, 160, 150, 140, 130, 140,
51 180, 170, 155, 140, 140, 125, 140, 150,
52 170, 160, 140, 120, 110, 140, 150, 160,
53 160, 150, 140, 110, 120, 140, 160, 170,
54 150, 140, 125, 140, 140, 155, 170, 180,
55 140, 130, 140, 150, 160, 170, 180, 190,
56 130, 140, 150, 160, 170, 180, 190, 200
59 // The attacking side is given a descending bonus based on distance between
60 // the two kings in basic endgames.
61 const int DistanceBonus[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
63 // Build corresponding key code for the opposite color: "KBPKN" -> "KNKBP"
64 const string swap_colors(const string& keyCode) {
66 size_t idx = keyCode.find('K', 1);
67 return keyCode.substr(idx) + keyCode.substr(0, idx);
70 // Get the material key of a position out of the given endgame key code
71 // like "KBPKN". The trick here is to first build up a FEN string and then
72 // let a Position object to do the work for us. Note that the FEN string
73 // could correspond to an illegal position.
74 Key mat_key(const string& keyCode) {
76 assert(keyCode.length() > 0 && keyCode.length() < 8);
77 assert(keyCode[0] == 'K');
82 // First add white and then black pieces
83 do fen += keyCode[i]; while (keyCode[++i] != 'K');
84 do fen += char(tolower(keyCode[i])); while (++i < keyCode.length());
86 // Add file padding and remaining empty ranks
87 fen += string(1, '0' + int(8 - keyCode.length())) + "/8/8/8/8/8/8/8 w - - 0 10";
89 // Build a Position out of the fen string and get its material key
90 return Position(fen, false, 0).material_key();
94 void delete_endgame(const typename M::value_type& p) { delete p.second; }
99 /// Endgames member definitions
101 template<> const Endgames::M1& Endgames::map<Endgames::M1>() const { return m1; }
102 template<> const Endgames::M2& Endgames::map<Endgames::M2>() const { return m2; }
104 Endgames::Endgames() {
119 add<KBPPKB>("KBPPKB");
120 add<KRPPKRP>("KRPPKRP");
123 Endgames::~Endgames() {
125 for_each(m1.begin(), m1.end(), delete_endgame<M1>);
126 for_each(m2.begin(), m2.end(), delete_endgame<M2>);
129 template<EndgameType E>
130 void Endgames::add(const string& keyCode) {
132 typedef typename eg_family<E>::type T;
133 typedef typename Map<T>::type M;
135 const_cast<M&>(map<M>()).insert(std::make_pair(mat_key(keyCode), new Endgame<E>(WHITE)));
136 const_cast<M&>(map<M>()).insert(std::make_pair(mat_key(swap_colors(keyCode)), new Endgame<E>(BLACK)));
140 /// Mate with KX vs K. This function is used to evaluate positions with
141 /// King and plenty of material vs a lone king. It simply gives the
142 /// attacking side a bonus for driving the defending king towards the edge
143 /// of the board, and for keeping the distance between the two kings small.
145 Value Endgame<KXK>::operator()(const Position& pos) const {
147 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
148 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
150 Square winnerKSq = pos.king_square(strongerSide);
151 Square loserKSq = pos.king_square(weakerSide);
153 Value result = pos.non_pawn_material(strongerSide)
154 + pos.piece_count(strongerSide, PAWN) * PawnValueEndgame
155 + MateTable[loserKSq]
156 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
158 if ( pos.piece_count(strongerSide, QUEEN)
159 || pos.piece_count(strongerSide, ROOK)
160 || pos.piece_count(strongerSide, BISHOP) > 1)
161 // TODO: check for two equal-colored bishops!
162 result += VALUE_KNOWN_WIN;
164 return strongerSide == pos.side_to_move() ? result : -result;
168 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
169 /// defending king towards a corner square of the right color.
171 Value Endgame<KBNK>::operator()(const Position& pos) const {
173 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
174 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
175 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame + BishopValueMidgame);
176 assert(pos.piece_count(strongerSide, BISHOP) == 1);
177 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
178 assert(pos.piece_count(strongerSide, PAWN) == 0);
180 Square winnerKSq = pos.king_square(strongerSide);
181 Square loserKSq = pos.king_square(weakerSide);
182 Square bishopSquare = pos.piece_list(strongerSide, BISHOP)[0];
184 // kbnk_mate_table() tries to drive toward corners A1 or H8,
185 // if we have a bishop that cannot reach the above squares we
186 // mirror the kings so to drive enemy toward corners A8 or H1.
187 if (opposite_colors(bishopSquare, SQ_A1))
189 winnerKSq = mirror(winnerKSq);
190 loserKSq = mirror(loserKSq);
193 Value result = VALUE_KNOWN_WIN
194 + DistanceBonus[square_distance(winnerKSq, loserKSq)]
195 + KBNKMateTable[loserKSq];
197 return strongerSide == pos.side_to_move() ? result : -result;
201 /// KP vs K. This endgame is evaluated with the help of a bitbase.
203 Value Endgame<KPK>::operator()(const Position& pos) const {
205 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
206 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
207 assert(pos.piece_count(strongerSide, PAWN) == 1);
208 assert(pos.piece_count(weakerSide, PAWN) == 0);
210 Square wksq, bksq, wpsq;
213 if (strongerSide == WHITE)
215 wksq = pos.king_square(WHITE);
216 bksq = pos.king_square(BLACK);
217 wpsq = pos.piece_list(WHITE, PAWN)[0];
218 stm = pos.side_to_move();
222 wksq = flip(pos.king_square(BLACK));
223 bksq = flip(pos.king_square(WHITE));
224 wpsq = flip(pos.piece_list(BLACK, PAWN)[0]);
225 stm = flip(pos.side_to_move());
228 if (file_of(wpsq) >= FILE_E)
235 if (!probe_kpk_bitbase(wksq, wpsq, bksq, stm))
238 Value result = VALUE_KNOWN_WIN
240 + Value(rank_of(wpsq));
242 return strongerSide == pos.side_to_move() ? result : -result;
246 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
247 /// a bitbase. The function below returns drawish scores when the pawn is
248 /// far advanced with support of the king, while the attacking king is far
251 Value Endgame<KRKP>::operator()(const Position& pos) const {
253 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
254 assert(pos.piece_count(strongerSide, PAWN) == 0);
255 assert(pos.non_pawn_material(weakerSide) == 0);
256 assert(pos.piece_count(weakerSide, PAWN) == 1);
258 Square wksq, wrsq, bksq, bpsq;
259 int tempo = (pos.side_to_move() == strongerSide);
261 wksq = pos.king_square(strongerSide);
262 wrsq = pos.piece_list(strongerSide, ROOK)[0];
263 bksq = pos.king_square(weakerSide);
264 bpsq = pos.piece_list(weakerSide, PAWN)[0];
266 if (strongerSide == BLACK)
274 Square queeningSq = make_square(file_of(bpsq), RANK_1);
277 // If the stronger side's king is in front of the pawn, it's a win
278 if (wksq < bpsq && file_of(wksq) == file_of(bpsq))
279 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
281 // If the weaker side's king is too far from the pawn and the rook,
283 else if ( square_distance(bksq, bpsq) - (tempo ^ 1) >= 3
284 && square_distance(bksq, wrsq) >= 3)
285 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
287 // If the pawn is far advanced and supported by the defending king,
288 // the position is drawish
289 else if ( rank_of(bksq) <= RANK_3
290 && square_distance(bksq, bpsq) == 1
291 && rank_of(wksq) >= RANK_4
292 && square_distance(wksq, bpsq) - tempo > 2)
293 result = Value(80 - square_distance(wksq, bpsq) * 8);
297 - Value(square_distance(wksq, bpsq + DELTA_S) * 8)
298 + Value(square_distance(bksq, bpsq + DELTA_S) * 8)
299 + Value(square_distance(bpsq, queeningSq) * 8);
301 return strongerSide == pos.side_to_move() ? result : -result;
305 /// KR vs KB. This is very simple, and always returns drawish scores. The
306 /// score is slightly bigger when the defending king is close to the edge.
308 Value Endgame<KRKB>::operator()(const Position& pos) const {
310 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
311 assert(pos.piece_count(strongerSide, PAWN) == 0);
312 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
313 assert(pos.piece_count(weakerSide, PAWN) == 0);
314 assert(pos.piece_count(weakerSide, BISHOP) == 1);
316 Value result = Value(MateTable[pos.king_square(weakerSide)]);
317 return strongerSide == pos.side_to_move() ? result : -result;
321 /// KR vs KN. The attacking side has slightly better winning chances than
322 /// in KR vs KB, particularly if the king and the knight are far apart.
324 Value Endgame<KRKN>::operator()(const Position& pos) const {
326 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
327 assert(pos.piece_count(strongerSide, PAWN) == 0);
328 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
329 assert(pos.piece_count(weakerSide, PAWN) == 0);
330 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
332 const int penalty[8] = { 0, 10, 14, 20, 30, 42, 58, 80 };
334 Square bksq = pos.king_square(weakerSide);
335 Square bnsq = pos.piece_list(weakerSide, KNIGHT)[0];
336 Value result = Value(MateTable[bksq] + penalty[square_distance(bksq, bnsq)]);
337 return strongerSide == pos.side_to_move() ? result : -result;
341 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
342 /// king a bonus for having the kings close together, and for forcing the
343 /// defending king towards the edge. If we also take care to avoid null move
344 /// for the defending side in the search, this is usually sufficient to be
345 /// able to win KQ vs KR.
347 Value Endgame<KQKR>::operator()(const Position& pos) const {
349 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
350 assert(pos.piece_count(strongerSide, PAWN) == 0);
351 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
352 assert(pos.piece_count(weakerSide, PAWN) == 0);
354 Square winnerKSq = pos.king_square(strongerSide);
355 Square loserKSq = pos.king_square(weakerSide);
357 Value result = QueenValueEndgame
359 + MateTable[loserKSq]
360 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
362 return strongerSide == pos.side_to_move() ? result : -result;
366 Value Endgame<KBBKN>::operator()(const Position& pos) const {
368 assert(pos.piece_count(strongerSide, BISHOP) == 2);
369 assert(pos.non_pawn_material(strongerSide) == 2*BishopValueMidgame);
370 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
371 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
372 assert(!pos.pieces(PAWN));
374 Value result = BishopValueEndgame;
375 Square wksq = pos.king_square(strongerSide);
376 Square bksq = pos.king_square(weakerSide);
377 Square nsq = pos.piece_list(weakerSide, KNIGHT)[0];
379 // Bonus for attacking king close to defending king
380 result += Value(DistanceBonus[square_distance(wksq, bksq)]);
382 // Bonus for driving the defending king and knight apart
383 result += Value(square_distance(bksq, nsq) * 32);
385 // Bonus for restricting the knight's mobility
386 result += Value((8 - count_1s<CNT32_MAX15>(pos.attacks_from<KNIGHT>(nsq))) * 8);
388 return strongerSide == pos.side_to_move() ? result : -result;
392 /// K and two minors vs K and one or two minors or K and two knights against
393 /// king alone are always draw.
395 Value Endgame<KmmKm>::operator()(const Position&) const {
400 Value Endgame<KNNK>::operator()(const Position&) const {
404 /// K, bishop and one or more pawns vs K. It checks for draws with rook pawns and
405 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
406 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
409 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
411 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
412 assert(pos.piece_count(strongerSide, BISHOP) == 1);
413 assert(pos.piece_count(strongerSide, PAWN) >= 1);
415 // No assertions about the material of weakerSide, because we want draws to
416 // be detected even when the weaker side has some pawns.
418 Bitboard pawns = pos.pieces(PAWN, strongerSide);
419 File pawnFile = file_of(pos.piece_list(strongerSide, PAWN)[0]);
421 // All pawns are on a single rook file ?
422 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
423 && !(pawns & ~file_bb(pawnFile)))
425 Square bishopSq = pos.piece_list(strongerSide, BISHOP)[0];
426 Square queeningSq = relative_square(strongerSide, make_square(pawnFile, RANK_8));
427 Square kingSq = pos.king_square(weakerSide);
429 if ( opposite_colors(queeningSq, bishopSq)
430 && abs(file_of(kingSq) - pawnFile) <= 1)
432 // The bishop has the wrong color, and the defending king is on the
433 // file of the pawn(s) or the neighboring file. Find the rank of the
436 if (strongerSide == WHITE)
438 for (rank = RANK_7; !(rank_bb(rank) & pawns); rank--) {}
439 assert(rank >= RANK_2 && rank <= RANK_7);
443 for (rank = RANK_2; !(rank_bb(rank) & pawns); rank++) {}
444 rank = Rank(rank ^ 7); // HACK to get the relative rank
445 assert(rank >= RANK_2 && rank <= RANK_7);
447 // If the defending king has distance 1 to the promotion square or
448 // is placed somewhere in front of the pawn, it's a draw.
449 if ( square_distance(kingSq, queeningSq) <= 1
450 || relative_rank(strongerSide, kingSq) >= rank)
451 return SCALE_FACTOR_DRAW;
454 return SCALE_FACTOR_NONE;
458 /// K and queen vs K, rook and one or more pawns. It tests for fortress draws with
459 /// a rook on the third rank defended by a pawn.
461 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
463 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
464 assert(pos.piece_count(strongerSide, QUEEN) == 1);
465 assert(pos.piece_count(strongerSide, PAWN) == 0);
466 assert(pos.piece_count(weakerSide, ROOK) == 1);
467 assert(pos.piece_count(weakerSide, PAWN) >= 1);
469 Square kingSq = pos.king_square(weakerSide);
470 if ( relative_rank(weakerSide, kingSq) <= RANK_2
471 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
472 && (pos.pieces(ROOK, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_3)))
473 && (pos.pieces(PAWN, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_2)))
474 && (pos.attacks_from<KING>(kingSq) & pos.pieces(PAWN, weakerSide)))
476 Square rsq = pos.piece_list(weakerSide, ROOK)[0];
477 if (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(PAWN, weakerSide))
478 return SCALE_FACTOR_DRAW;
480 return SCALE_FACTOR_NONE;
484 /// K, rook and one pawn vs K and a rook. This function knows a handful of the
485 /// most important classes of drawn positions, but is far from perfect. It would
486 /// probably be a good idea to add more knowledge in the future.
488 /// It would also be nice to rewrite the actual code for this function,
489 /// which is mostly copied from Glaurung 1.x, and not very pretty.
491 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
493 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
494 assert(pos.piece_count(strongerSide, PAWN) == 1);
495 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
496 assert(pos.piece_count(weakerSide, PAWN) == 0);
498 Square wksq = pos.king_square(strongerSide);
499 Square wrsq = pos.piece_list(strongerSide, ROOK)[0];
500 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
501 Square bksq = pos.king_square(weakerSide);
502 Square brsq = pos.piece_list(weakerSide, ROOK)[0];
504 // Orient the board in such a way that the stronger side is white, and the
505 // pawn is on the left half of the board.
506 if (strongerSide == BLACK)
514 if (file_of(wpsq) > FILE_D)
523 File f = file_of(wpsq);
524 Rank r = rank_of(wpsq);
525 Square queeningSq = make_square(f, RANK_8);
526 int tempo = (pos.side_to_move() == strongerSide);
528 // If the pawn is not too far advanced and the defending king defends the
529 // queening square, use the third-rank defence.
531 && square_distance(bksq, queeningSq) <= 1
533 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
534 return SCALE_FACTOR_DRAW;
536 // The defending side saves a draw by checking from behind in case the pawn
537 // has advanced to the 6th rank with the king behind.
539 && square_distance(bksq, queeningSq) <= 1
540 && rank_of(wksq) + tempo <= RANK_6
541 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
542 return SCALE_FACTOR_DRAW;
545 && bksq == queeningSq
546 && rank_of(brsq) == RANK_1
547 && (!tempo || square_distance(wksq, wpsq) >= 2))
548 return SCALE_FACTOR_DRAW;
550 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
551 // and the black rook is behind the pawn.
554 && (bksq == SQ_H7 || bksq == SQ_G7)
555 && file_of(brsq) == FILE_A
556 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
557 return SCALE_FACTOR_DRAW;
559 // If the defending king blocks the pawn and the attacking king is too far
560 // away, it's a draw.
562 && bksq == wpsq + DELTA_N
563 && square_distance(wksq, wpsq) - tempo >= 2
564 && square_distance(wksq, brsq) - tempo >= 2)
565 return SCALE_FACTOR_DRAW;
567 // Pawn on the 7th rank supported by the rook from behind usually wins if the
568 // attacking king is closer to the queening square than the defending king,
569 // and the defending king cannot gain tempi by threatening the attacking rook.
572 && file_of(wrsq) == f
573 && wrsq != queeningSq
574 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
575 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
576 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
578 // Similar to the above, but with the pawn further back
580 && file_of(wrsq) == f
582 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
583 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
584 && ( square_distance(bksq, wrsq) + tempo >= 3
585 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
586 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
587 return ScaleFactor( SCALE_FACTOR_MAX
588 - 8 * square_distance(wpsq, queeningSq)
589 - 2 * square_distance(wksq, queeningSq));
591 // If the pawn is not far advanced, and the defending king is somewhere in
592 // the pawn's path, it's probably a draw.
593 if (r <= RANK_4 && bksq > wpsq)
595 if (file_of(bksq) == file_of(wpsq))
596 return ScaleFactor(10);
597 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
598 && square_distance(wksq, bksq) > 2)
599 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
601 return SCALE_FACTOR_NONE;
605 /// K, rook and two pawns vs K, rook and one pawn. There is only a single
606 /// pattern: If the stronger side has no passed pawns and the defending king
607 /// is actively placed, the position is drawish.
609 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
611 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
612 assert(pos.piece_count(strongerSide, PAWN) == 2);
613 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
614 assert(pos.piece_count(weakerSide, PAWN) == 1);
616 Square wpsq1 = pos.piece_list(strongerSide, PAWN)[0];
617 Square wpsq2 = pos.piece_list(strongerSide, PAWN)[1];
618 Square bksq = pos.king_square(weakerSide);
620 // Does the stronger side have a passed pawn?
621 if ( pos.pawn_is_passed(strongerSide, wpsq1)
622 || pos.pawn_is_passed(strongerSide, wpsq2))
623 return SCALE_FACTOR_NONE;
625 Rank r = std::max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
627 if ( file_distance(bksq, wpsq1) <= 1
628 && file_distance(bksq, wpsq2) <= 1
629 && relative_rank(strongerSide, bksq) > r)
632 case RANK_2: return ScaleFactor(10);
633 case RANK_3: return ScaleFactor(10);
634 case RANK_4: return ScaleFactor(15);
635 case RANK_5: return ScaleFactor(20);
636 case RANK_6: return ScaleFactor(40);
637 default: assert(false);
640 return SCALE_FACTOR_NONE;
644 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
645 /// are on the same rook file and are blocked by the defending king, it's a draw.
647 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
649 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
650 assert(pos.piece_count(strongerSide, PAWN) >= 2);
651 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
652 assert(pos.piece_count(weakerSide, PAWN) == 0);
654 Square ksq = pos.king_square(weakerSide);
655 Bitboard pawns = pos.pieces(PAWN, strongerSide);
657 // Are all pawns on the 'a' file?
658 if (!(pawns & ~FileABB))
660 // Does the defending king block the pawns?
661 if ( square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
662 || ( file_of(ksq) == FILE_A
663 && !in_front_bb(strongerSide, ksq) & pawns))
664 return SCALE_FACTOR_DRAW;
666 // Are all pawns on the 'h' file?
667 else if (!(pawns & ~FileHBB))
669 // Does the defending king block the pawns?
670 if ( square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
671 || ( file_of(ksq) == FILE_H
672 && !in_front_bb(strongerSide, ksq) & pawns))
673 return SCALE_FACTOR_DRAW;
675 return SCALE_FACTOR_NONE;
679 /// K, bishop and a pawn vs K and a bishop. There are two rules: If the defending
680 /// king is somewhere along the path of the pawn, and the square of the king is
681 /// not of the same color as the stronger side's bishop, it's a draw. If the two
682 /// bishops have opposite color, it's almost always a draw.
684 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
686 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
687 assert(pos.piece_count(strongerSide, BISHOP) == 1);
688 assert(pos.piece_count(strongerSide, PAWN) == 1);
689 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
690 assert(pos.piece_count(weakerSide, BISHOP) == 1);
691 assert(pos.piece_count(weakerSide, PAWN) == 0);
693 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
694 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
695 Square weakerBishopSq = pos.piece_list(weakerSide, BISHOP)[0];
696 Square weakerKingSq = pos.king_square(weakerSide);
698 // Case 1: Defending king blocks the pawn, and cannot be driven away
699 if ( file_of(weakerKingSq) == file_of(pawnSq)
700 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
701 && ( opposite_colors(weakerKingSq, strongerBishopSq)
702 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
703 return SCALE_FACTOR_DRAW;
705 // Case 2: Opposite colored bishops
706 if (opposite_colors(strongerBishopSq, weakerBishopSq))
708 // We assume that the position is drawn in the following three situations:
710 // a. The pawn is on rank 5 or further back.
711 // b. The defending king is somewhere in the pawn's path.
712 // c. The defending bishop attacks some square along the pawn's path,
713 // and is at least three squares away from the pawn.
715 // These rules are probably not perfect, but in practice they work
718 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
719 return SCALE_FACTOR_DRAW;
722 Bitboard path = squares_in_front_of(strongerSide, pawnSq);
724 if (path & pos.pieces(KING, weakerSide))
725 return SCALE_FACTOR_DRAW;
727 if ( (pos.attacks_from<BISHOP>(weakerBishopSq) & path)
728 && square_distance(weakerBishopSq, pawnSq) >= 3)
729 return SCALE_FACTOR_DRAW;
732 return SCALE_FACTOR_NONE;
736 /// K, bishop and two pawns vs K and bishop. It detects a few basic draws with
737 /// opposite-colored bishops.
739 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
741 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
742 assert(pos.piece_count(strongerSide, BISHOP) == 1);
743 assert(pos.piece_count(strongerSide, PAWN) == 2);
744 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
745 assert(pos.piece_count(weakerSide, BISHOP) == 1);
746 assert(pos.piece_count(weakerSide, PAWN) == 0);
748 Square wbsq = pos.piece_list(strongerSide, BISHOP)[0];
749 Square bbsq = pos.piece_list(weakerSide, BISHOP)[0];
751 if (!opposite_colors(wbsq, bbsq))
752 return SCALE_FACTOR_NONE;
754 Square ksq = pos.king_square(weakerSide);
755 Square psq1 = pos.piece_list(strongerSide, PAWN)[0];
756 Square psq2 = pos.piece_list(strongerSide, PAWN)[1];
757 Rank r1 = rank_of(psq1);
758 Rank r2 = rank_of(psq2);
759 Square blockSq1, blockSq2;
761 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
763 blockSq1 = psq1 + pawn_push(strongerSide);
764 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
768 blockSq1 = psq2 + pawn_push(strongerSide);
769 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
772 switch (file_distance(psq1, psq2))
775 // Both pawns are on the same file. Easy draw if defender firmly controls
776 // some square in the frontmost pawn's path.
777 if ( file_of(ksq) == file_of(blockSq1)
778 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
779 && opposite_colors(ksq, wbsq))
780 return SCALE_FACTOR_DRAW;
782 return SCALE_FACTOR_NONE;
785 // Pawns on neighboring files. Draw if defender firmly controls the square
786 // in front of the frontmost pawn's path, and the square diagonally behind
787 // this square on the file of the other pawn.
789 && opposite_colors(ksq, wbsq)
790 && ( bbsq == blockSq2
791 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(BISHOP, weakerSide))
792 || abs(r1 - r2) >= 2))
793 return SCALE_FACTOR_DRAW;
795 else if ( ksq == blockSq2
796 && opposite_colors(ksq, wbsq)
797 && ( bbsq == blockSq1
798 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(BISHOP, weakerSide))))
799 return SCALE_FACTOR_DRAW;
801 return SCALE_FACTOR_NONE;
804 // The pawns are not on the same file or adjacent files. No scaling.
805 return SCALE_FACTOR_NONE;
810 /// K, bisop and a pawn vs K and knight. There is a single rule: If the defending
811 /// king is somewhere along the path of the pawn, and the square of the king is
812 /// not of the same color as the stronger side's bishop, it's a draw.
814 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
816 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
817 assert(pos.piece_count(strongerSide, BISHOP) == 1);
818 assert(pos.piece_count(strongerSide, PAWN) == 1);
819 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
820 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
821 assert(pos.piece_count(weakerSide, PAWN) == 0);
823 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
824 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
825 Square weakerKingSq = pos.king_square(weakerSide);
827 if ( file_of(weakerKingSq) == file_of(pawnSq)
828 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
829 && ( opposite_colors(weakerKingSq, strongerBishopSq)
830 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
831 return SCALE_FACTOR_DRAW;
833 return SCALE_FACTOR_NONE;
837 /// K, knight and a pawn vs K. There is a single rule: If the pawn is a rook pawn
838 /// on the 7th rank and the defending king prevents the pawn from advancing, the
839 /// position is drawn.
841 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
843 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame);
844 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
845 assert(pos.piece_count(strongerSide, PAWN) == 1);
846 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
847 assert(pos.piece_count(weakerSide, PAWN) == 0);
849 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
850 Square weakerKingSq = pos.king_square(weakerSide);
852 if ( pawnSq == relative_square(strongerSide, SQ_A7)
853 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
854 return SCALE_FACTOR_DRAW;
856 if ( pawnSq == relative_square(strongerSide, SQ_H7)
857 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
858 return SCALE_FACTOR_DRAW;
860 return SCALE_FACTOR_NONE;
864 /// K and a pawn vs K and a pawn. This is done by removing the weakest side's
865 /// pawn and probing the KP vs K bitbase: If the weakest side has a draw without
866 /// the pawn, she probably has at least a draw with the pawn as well. The exception
867 /// is when the stronger side's pawn is far advanced and not on a rook file; in
868 /// this case it is often possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
870 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
872 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
873 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
874 assert(pos.piece_count(WHITE, PAWN) == 1);
875 assert(pos.piece_count(BLACK, PAWN) == 1);
877 Square wksq = pos.king_square(strongerSide);
878 Square bksq = pos.king_square(weakerSide);
879 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
880 Color stm = pos.side_to_move();
882 if (strongerSide == BLACK)
890 if (file_of(wpsq) >= FILE_E)
897 // If the pawn has advanced to the fifth rank or further, and is not a
898 // rook pawn, it's too dangerous to assume that it's at least a draw.
899 if ( rank_of(wpsq) >= RANK_5
900 && file_of(wpsq) != FILE_A)
901 return SCALE_FACTOR_NONE;
903 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
904 // it's probably at least a draw even with the pawn.
905 return probe_kpk_bitbase(wksq, wpsq, bksq, stm) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;