2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
4 Copyright (C) 2008-2013 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 defending king towards the edge of the board
33 // in KX vs K and KQ vs KR endgames.
34 const int MateTable[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 defending king towards a corner square of the
46 // right color in KBN vs K endgames.
47 const int KBNKMateTable[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 // The attacking side is given a descending bonus based on distance between
59 // the two kings in basic endgames.
60 const int DistanceBonus[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
62 // Get the material key of a Position out of the given endgame key code
63 // like "KBPKN". The trick here is to first forge an ad-hoc fen string
64 // and then let a Position object to do the work for us. Note that the
65 // fen string could correspond to an illegal position.
66 Key key(const string& code, Color c) {
68 assert(code.length() > 0 && code.length() < 8);
69 assert(code[0] == 'K');
71 string sides[] = { code.substr(code.find('K', 1)), // Weaker
72 code.substr(0, code.find('K', 1)) }; // Stronger
74 std::transform(sides[c].begin(), sides[c].end(), sides[c].begin(), tolower);
76 string fen = sides[0] + char('0' + int(8 - code.length()))
77 + sides[1] + "/8/8/8/8/8/8/8 w - - 0 10";
79 return Position(fen, false, NULL).material_key();
83 void delete_endgame(const typename M::value_type& p) { delete p.second; }
88 /// Endgames members definitions
90 Endgames::Endgames() {
107 add<KBPPKB>("KBPPKB");
108 add<KRPPKRP>("KRPPKRP");
111 Endgames::~Endgames() {
113 for_each(m1.begin(), m1.end(), delete_endgame<M1>);
114 for_each(m2.begin(), m2.end(), delete_endgame<M2>);
117 template<EndgameType E>
118 void Endgames::add(const string& code) {
120 map((Endgame<E>*)0)[key(code, WHITE)] = new Endgame<E>(WHITE);
121 map((Endgame<E>*)0)[key(code, BLACK)] = new Endgame<E>(BLACK);
125 /// Mate with KX vs K. This function is used to evaluate positions with
126 /// King and plenty of material vs a lone king. It simply gives the
127 /// attacking side a bonus for driving the defending king towards the edge
128 /// of the board, and for keeping the distance between the two kings small.
130 Value Endgame<KXK>::operator()(const Position& pos) const {
132 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
133 assert(!pos.count<PAWN>(weakerSide));
134 assert(!pos.checkers()); // Eval is never called when in check
136 // Stalemate detection with lone king
137 if (pos.side_to_move() == weakerSide && !MoveList<LEGAL>(pos).size())
140 Square winnerKSq = pos.king_square(strongerSide);
141 Square loserKSq = pos.king_square(weakerSide);
143 Value result = pos.non_pawn_material(strongerSide)
144 + pos.count<PAWN>(strongerSide) * PawnValueEg
145 + MateTable[loserKSq]
146 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
148 if ( pos.count<QUEEN>(strongerSide)
149 || pos.count<ROOK>(strongerSide)
150 || pos.bishop_pair(strongerSide))
151 result += VALUE_KNOWN_WIN;
153 return strongerSide == pos.side_to_move() ? result : -result;
157 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
158 /// defending king towards a corner square of the right color.
160 Value Endgame<KBNK>::operator()(const Position& pos) const {
162 assert(pos.non_pawn_material(strongerSide) == KnightValueMg + BishopValueMg);
163 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
164 assert(pos.count<BISHOP>(strongerSide) == 1);
165 assert(pos.count<KNIGHT>(strongerSide) == 1);
166 assert(pos.count< PAWN>(strongerSide) == 0);
167 assert(pos.count< PAWN>(weakerSide ) == 0);
169 Square winnerKSq = pos.king_square(strongerSide);
170 Square loserKSq = pos.king_square(weakerSide);
171 Square bishopSq = pos.list<BISHOP>(strongerSide)[0];
173 // kbnk_mate_table() tries to drive toward corners A1 or H8,
174 // if we have a bishop that cannot reach the above squares we
175 // mirror the kings so to drive enemy toward corners A8 or H1.
176 if (opposite_colors(bishopSq, SQ_A1))
178 winnerKSq = mirror(winnerKSq);
179 loserKSq = mirror(loserKSq);
182 Value result = VALUE_KNOWN_WIN
183 + DistanceBonus[square_distance(winnerKSq, loserKSq)]
184 + KBNKMateTable[loserKSq];
186 return strongerSide == pos.side_to_move() ? result : -result;
190 /// KP vs K. This endgame is evaluated with the help of a bitbase.
192 Value Endgame<KPK>::operator()(const Position& pos) const {
194 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
195 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
196 assert(pos.count<PAWN>(strongerSide) == 1);
197 assert(pos.count<PAWN>(weakerSide ) == 0);
199 Square wksq, bksq, wpsq;
202 if (strongerSide == WHITE)
204 wksq = pos.king_square(WHITE);
205 bksq = pos.king_square(BLACK);
206 wpsq = pos.list<PAWN>(WHITE)[0];
207 us = pos.side_to_move();
211 wksq = ~pos.king_square(BLACK);
212 bksq = ~pos.king_square(WHITE);
213 wpsq = ~pos.list<PAWN>(BLACK)[0];
214 us = ~pos.side_to_move();
217 if (file_of(wpsq) >= FILE_E)
224 if (!Bitbases::probe_kpk(wksq, wpsq, bksq, us))
227 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(wpsq));
229 return strongerSide == pos.side_to_move() ? result : -result;
233 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
234 /// a bitbase. The function below returns drawish scores when the pawn is
235 /// far advanced with support of the king, while the attacking king is far
238 Value Endgame<KRKP>::operator()(const Position& pos) const {
240 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
241 assert(pos.non_pawn_material(weakerSide) == 0);
242 assert(pos.count<PAWN>(strongerSide) == 0);
243 assert(pos.count<PAWN>(weakerSide ) == 1);
245 Square wksq, wrsq, bksq, bpsq;
246 int tempo = (pos.side_to_move() == strongerSide);
248 wksq = pos.king_square(strongerSide);
249 bksq = pos.king_square(weakerSide);
250 wrsq = pos.list<ROOK>(strongerSide)[0];
251 bpsq = pos.list<PAWN>(weakerSide)[0];
253 if (strongerSide == BLACK)
261 Square queeningSq = file_of(bpsq) | RANK_1;
264 // If the stronger side's king is in front of the pawn, it's a win
265 if (wksq < bpsq && file_of(wksq) == file_of(bpsq))
266 result = RookValueEg - Value(square_distance(wksq, bpsq));
268 // If the weaker side's king is too far from the pawn and the rook,
270 else if ( square_distance(bksq, bpsq) - (tempo ^ 1) >= 3
271 && square_distance(bksq, wrsq) >= 3)
272 result = RookValueEg - Value(square_distance(wksq, bpsq));
274 // If the pawn is far advanced and supported by the defending king,
275 // the position is drawish
276 else if ( rank_of(bksq) <= RANK_3
277 && square_distance(bksq, bpsq) == 1
278 && rank_of(wksq) >= RANK_4
279 && square_distance(wksq, bpsq) - tempo > 2)
280 result = Value(80 - square_distance(wksq, bpsq) * 8);
284 - Value(square_distance(wksq, bpsq + DELTA_S) * 8)
285 + Value(square_distance(bksq, bpsq + DELTA_S) * 8)
286 + Value(square_distance(bpsq, queeningSq) * 8);
288 return strongerSide == pos.side_to_move() ? result : -result;
292 /// KR vs KB. This is very simple, and always returns drawish scores. The
293 /// score is slightly bigger when the defending king is close to the edge.
295 Value Endgame<KRKB>::operator()(const Position& pos) const {
297 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
298 assert(pos.non_pawn_material(weakerSide ) == BishopValueMg);
299 assert(pos.count<BISHOP>(weakerSide ) == 1);
300 assert(pos.count< PAWN>(weakerSide ) == 0);
301 assert(pos.count< PAWN>(strongerSide) == 0);
303 Value result = Value(MateTable[pos.king_square(weakerSide)]);
304 return strongerSide == pos.side_to_move() ? result : -result;
308 /// KR vs KN. The attacking side has slightly better winning chances than
309 /// in KR vs KB, particularly if the king and the knight are far apart.
311 Value Endgame<KRKN>::operator()(const Position& pos) const {
313 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
314 assert(pos.non_pawn_material(weakerSide ) == KnightValueMg);
315 assert(pos.count<KNIGHT>(weakerSide ) == 1);
316 assert(pos.count< PAWN>(weakerSide ) == 0);
317 assert(pos.count< PAWN>(strongerSide) == 0);
319 const int penalty[8] = { 0, 10, 14, 20, 30, 42, 58, 80 };
321 Square bksq = pos.king_square(weakerSide);
322 Square bnsq = pos.list<KNIGHT>(weakerSide)[0];
323 Value result = Value(MateTable[bksq] + penalty[square_distance(bksq, bnsq)]);
324 return strongerSide == pos.side_to_move() ? result : -result;
328 /// KQ vs KP. In general, a win for the stronger side, however, there are a few
329 /// important exceptions. Pawn on 7th rank, A,C,F or H file, with king next can
330 /// be a draw, so we scale down to distance between kings only.
332 Value Endgame<KQKP>::operator()(const Position& pos) const {
334 assert(pos.non_pawn_material(strongerSide) == QueenValueMg);
335 assert(pos.non_pawn_material(weakerSide ) == VALUE_ZERO);
336 assert(pos.count<PAWN>(strongerSide) == 0);
337 assert(pos.count<PAWN>(weakerSide ) == 1);
339 Square winnerKSq = pos.king_square(strongerSide);
340 Square loserKSq = pos.king_square(weakerSide);
341 Square pawnSq = pos.list<PAWN>(weakerSide)[0];
343 Value result = QueenValueEg
345 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
347 if ( square_distance(loserKSq, pawnSq) == 1
348 && relative_rank(weakerSide, pawnSq) == RANK_7)
350 File f = file_of(pawnSq);
352 if (f == FILE_A || f == FILE_C || f == FILE_F || f == FILE_H)
353 result = Value(DistanceBonus[square_distance(winnerKSq, loserKSq)]);
355 return strongerSide == pos.side_to_move() ? result : -result;
359 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
360 /// king a bonus for having the kings close together, and for forcing the
361 /// defending king towards the edge. If we also take care to avoid null move
362 /// for the defending side in the search, this is usually sufficient to be
363 /// able to win KQ vs KR.
365 Value Endgame<KQKR>::operator()(const Position& pos) const {
367 assert(pos.non_pawn_material(strongerSide) == QueenValueMg);
368 assert(pos.non_pawn_material(weakerSide ) == RookValueMg);
369 assert(pos.count<PAWN>(strongerSide) == 0);
370 assert(pos.count<PAWN>(weakerSide ) == 0);
372 Square winnerKSq = pos.king_square(strongerSide);
373 Square loserKSq = pos.king_square(weakerSide);
375 Value result = QueenValueEg
377 + MateTable[loserKSq]
378 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
380 return strongerSide == pos.side_to_move() ? result : -result;
384 Value Endgame<KBBKN>::operator()(const Position& pos) const {
386 assert(pos.non_pawn_material(strongerSide) == 2 * BishopValueMg);
387 assert(pos.non_pawn_material(weakerSide ) == KnightValueMg);
388 assert(pos.count<BISHOP>(strongerSide) == 2);
389 assert(pos.count<KNIGHT>(weakerSide ) == 1);
390 assert(!pos.pieces(PAWN));
392 Value result = BishopValueEg;
393 Square wksq = pos.king_square(strongerSide);
394 Square bksq = pos.king_square(weakerSide);
395 Square nsq = pos.list<KNIGHT>(weakerSide)[0];
397 // Bonus for attacking king close to defending king
398 result += Value(DistanceBonus[square_distance(wksq, bksq)]);
400 // Bonus for driving the defending king and knight apart
401 result += Value(square_distance(bksq, nsq) * 32);
403 // Bonus for restricting the knight's mobility
404 result += Value((8 - popcount<Max15>(pos.attacks_from<KNIGHT>(nsq))) * 8);
406 return strongerSide == pos.side_to_move() ? result : -result;
410 /// Some cases of trivial draws
411 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
412 template<> Value Endgame<KmmKm>::operator()(const Position&) const { return VALUE_DRAW; }
415 /// K, bishop and one or more pawns vs K. It checks for draws with rook pawns and
416 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
417 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
420 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
422 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
423 assert(pos.count<BISHOP>(strongerSide) == 1);
424 assert(pos.count< PAWN>(strongerSide) >= 1);
426 // No assertions about the material of weakerSide, because we want draws to
427 // be detected even when the weaker side has some pawns.
429 Bitboard pawns = pos.pieces(strongerSide, PAWN);
430 File pawnFile = file_of(pos.list<PAWN>(strongerSide)[0]);
432 // All pawns are on a single rook file ?
433 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
434 && !(pawns & ~file_bb(pawnFile)))
436 Square bishopSq = pos.list<BISHOP>(strongerSide)[0];
437 Square queeningSq = relative_square(strongerSide, pawnFile | RANK_8);
438 Square kingSq = pos.king_square(weakerSide);
440 if ( opposite_colors(queeningSq, bishopSq)
441 && abs(file_of(kingSq) - pawnFile) <= 1)
443 // The bishop has the wrong color, and the defending king is on the
444 // file of the pawn(s) or the adjacent file. Find the rank of the
447 if (strongerSide == WHITE)
449 for (rank = RANK_7; !(rank_bb(rank) & pawns); rank--) {}
450 assert(rank >= RANK_2 && rank <= RANK_7);
454 for (rank = RANK_2; !(rank_bb(rank) & pawns); rank++) {}
455 rank = Rank(rank ^ 7); // HACK to get the relative rank
456 assert(rank >= RANK_2 && rank <= RANK_7);
458 // If the defending king has distance 1 to the promotion square or
459 // is placed somewhere in front of the pawn, it's a draw.
460 if ( square_distance(kingSq, queeningSq) <= 1
461 || relative_rank(strongerSide, kingSq) >= rank)
462 return SCALE_FACTOR_DRAW;
466 // All pawns on same B or G file? Then potential draw
467 if ( (pawnFile == FILE_B || pawnFile == FILE_G)
468 && !(pos.pieces(PAWN) & ~file_bb(pawnFile))
469 && pos.non_pawn_material(weakerSide) == 0
470 && pos.count<PAWN>(weakerSide) >= 1)
472 // Get weaker pawn closest to opponent's queening square
473 Bitboard wkPawns = pos.pieces(weakerSide, PAWN);
474 Square weakerPawnSq = strongerSide == WHITE ? msb(wkPawns) : lsb(wkPawns);
476 Square strongerKingSq = pos.king_square(strongerSide);
477 Square weakerKingSq = pos.king_square(weakerSide);
478 Square bishopSq = pos.list<BISHOP>(strongerSide)[0];
480 // Draw if weaker pawn is on rank 7, bishop can't attack the pawn, and
481 // weaker king can stop opposing opponent's king from penetrating.
482 if ( relative_rank(strongerSide, weakerPawnSq) == RANK_7
483 && opposite_colors(bishopSq, weakerPawnSq)
484 && square_distance(weakerPawnSq, weakerKingSq) <= square_distance(weakerPawnSq, strongerKingSq))
485 return SCALE_FACTOR_DRAW;
488 return SCALE_FACTOR_NONE;
492 /// K and queen vs K, rook and one or more pawns. It tests for fortress draws with
493 /// a rook on the third rank defended by a pawn.
495 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
497 assert(pos.non_pawn_material(strongerSide) == QueenValueMg);
498 assert(pos.count<QUEEN>(strongerSide) == 1);
499 assert(pos.count< PAWN>(strongerSide) == 0);
500 assert(pos.count< ROOK>(weakerSide ) == 1);
501 assert(pos.count< PAWN>(weakerSide ) >= 1);
503 Square kingSq = pos.king_square(weakerSide);
504 if ( relative_rank(weakerSide, kingSq) <= RANK_2
505 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
506 && (pos.pieces(weakerSide, ROOK) & rank_bb(relative_rank(weakerSide, RANK_3)))
507 && (pos.pieces(weakerSide, PAWN) & rank_bb(relative_rank(weakerSide, RANK_2)))
508 && (pos.attacks_from<KING>(kingSq) & pos.pieces(weakerSide, PAWN)))
510 Square rsq = pos.list<ROOK>(weakerSide)[0];
511 if (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(weakerSide, PAWN))
512 return SCALE_FACTOR_DRAW;
514 return SCALE_FACTOR_NONE;
518 /// K, rook and one pawn vs K and a rook. This function knows a handful of the
519 /// most important classes of drawn positions, but is far from perfect. It would
520 /// probably be a good idea to add more knowledge in the future.
522 /// It would also be nice to rewrite the actual code for this function,
523 /// which is mostly copied from Glaurung 1.x, and not very pretty.
525 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
527 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
528 assert(pos.non_pawn_material(weakerSide) == RookValueMg);
529 assert(pos.count<PAWN>(strongerSide) == 1);
530 assert(pos.count<PAWN>(weakerSide ) == 0);
532 Square wksq = pos.king_square(strongerSide);
533 Square bksq = pos.king_square(weakerSide);
534 Square wrsq = pos.list<ROOK>(strongerSide)[0];
535 Square wpsq = pos.list<PAWN>(strongerSide)[0];
536 Square brsq = pos.list<ROOK>(weakerSide)[0];
538 // Orient the board in such a way that the stronger side is white, and the
539 // pawn is on the left half of the board.
540 if (strongerSide == BLACK)
548 if (file_of(wpsq) > FILE_D)
557 File f = file_of(wpsq);
558 Rank r = rank_of(wpsq);
559 Square queeningSq = f | RANK_8;
560 int tempo = (pos.side_to_move() == strongerSide);
562 // If the pawn is not too far advanced and the defending king defends the
563 // queening square, use the third-rank defence.
565 && square_distance(bksq, queeningSq) <= 1
567 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
568 return SCALE_FACTOR_DRAW;
570 // The defending side saves a draw by checking from behind in case the pawn
571 // has advanced to the 6th rank with the king behind.
573 && square_distance(bksq, queeningSq) <= 1
574 && rank_of(wksq) + tempo <= RANK_6
575 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
576 return SCALE_FACTOR_DRAW;
579 && bksq == queeningSq
580 && rank_of(brsq) == RANK_1
581 && (!tempo || square_distance(wksq, wpsq) >= 2))
582 return SCALE_FACTOR_DRAW;
584 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
585 // and the black rook is behind the pawn.
588 && (bksq == SQ_H7 || bksq == SQ_G7)
589 && file_of(brsq) == FILE_A
590 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
591 return SCALE_FACTOR_DRAW;
593 // If the defending king blocks the pawn and the attacking king is too far
594 // away, it's a draw.
596 && bksq == wpsq + DELTA_N
597 && square_distance(wksq, wpsq) - tempo >= 2
598 && square_distance(wksq, brsq) - tempo >= 2)
599 return SCALE_FACTOR_DRAW;
601 // Pawn on the 7th rank supported by the rook from behind usually wins if the
602 // attacking king is closer to the queening square than the defending king,
603 // and the defending king cannot gain tempi by threatening the attacking rook.
606 && file_of(wrsq) == f
607 && wrsq != queeningSq
608 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
609 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
610 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
612 // Similar to the above, but with the pawn further back
614 && file_of(wrsq) == f
616 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
617 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
618 && ( square_distance(bksq, wrsq) + tempo >= 3
619 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
620 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
621 return ScaleFactor( SCALE_FACTOR_MAX
622 - 8 * square_distance(wpsq, queeningSq)
623 - 2 * square_distance(wksq, queeningSq));
625 // If the pawn is not far advanced, and the defending king is somewhere in
626 // the pawn's path, it's probably a draw.
627 if (r <= RANK_4 && bksq > wpsq)
629 if (file_of(bksq) == file_of(wpsq))
630 return ScaleFactor(10);
631 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
632 && square_distance(wksq, bksq) > 2)
633 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
635 return SCALE_FACTOR_NONE;
639 /// K, rook and two pawns vs K, rook and one pawn. There is only a single
640 /// pattern: If the stronger side has no passed pawns and the defending king
641 /// is actively placed, the position is drawish.
643 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
645 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
646 assert(pos.non_pawn_material(weakerSide) == RookValueMg);
647 assert(pos.count<PAWN>(strongerSide) == 2);
648 assert(pos.count<PAWN>(weakerSide ) == 1);
650 Square wpsq1 = pos.list<PAWN>(strongerSide)[0];
651 Square wpsq2 = pos.list<PAWN>(strongerSide)[1];
652 Square bksq = pos.king_square(weakerSide);
654 // Does the stronger side have a passed pawn?
655 if ( pos.pawn_is_passed(strongerSide, wpsq1)
656 || pos.pawn_is_passed(strongerSide, wpsq2))
657 return SCALE_FACTOR_NONE;
659 Rank r = std::max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
661 if ( file_distance(bksq, wpsq1) <= 1
662 && file_distance(bksq, wpsq2) <= 1
663 && relative_rank(strongerSide, bksq) > r)
666 case RANK_2: return ScaleFactor(10);
667 case RANK_3: return ScaleFactor(10);
668 case RANK_4: return ScaleFactor(15);
669 case RANK_5: return ScaleFactor(20);
670 case RANK_6: return ScaleFactor(40);
671 default: assert(false);
674 return SCALE_FACTOR_NONE;
678 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
679 /// are on the same rook file and are blocked by the defending king, it's a draw.
681 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
683 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
684 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
685 assert(pos.count<PAWN>(strongerSide) >= 2);
686 assert(pos.count<PAWN>(weakerSide ) == 0);
688 Square ksq = pos.king_square(weakerSide);
689 Bitboard pawns = pos.pieces(strongerSide, PAWN);
691 // Are all pawns on the 'a' file?
692 if (!(pawns & ~FileABB))
694 // Does the defending king block the pawns?
695 if ( square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
696 || ( file_of(ksq) == FILE_A
697 && !(in_front_bb(strongerSide, rank_of(ksq)) & pawns)))
698 return SCALE_FACTOR_DRAW;
700 // Are all pawns on the 'h' file?
701 else if (!(pawns & ~FileHBB))
703 // Does the defending king block the pawns?
704 if ( square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
705 || ( file_of(ksq) == FILE_H
706 && !(in_front_bb(strongerSide, rank_of(ksq)) & pawns)))
707 return SCALE_FACTOR_DRAW;
709 return SCALE_FACTOR_NONE;
713 /// K, bishop and a pawn vs K and a bishop. There are two rules: If the defending
714 /// king is somewhere along the path of the pawn, and the square of the king is
715 /// not of the same color as the stronger side's bishop, it's a draw. If the two
716 /// bishops have opposite color, it's almost always a draw.
718 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
720 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
721 assert(pos.non_pawn_material(weakerSide ) == BishopValueMg);
722 assert(pos.count<BISHOP>(strongerSide) == 1);
723 assert(pos.count<BISHOP>(weakerSide ) == 1);
724 assert(pos.count< PAWN>(strongerSide) == 1);
725 assert(pos.count< PAWN>(weakerSide ) == 0);
727 Square pawnSq = pos.list<PAWN>(strongerSide)[0];
728 Square strongerBishopSq = pos.list<BISHOP>(strongerSide)[0];
729 Square weakerBishopSq = pos.list<BISHOP>(weakerSide)[0];
730 Square weakerKingSq = pos.king_square(weakerSide);
732 // Case 1: Defending king blocks the pawn, and cannot be driven away
733 if ( file_of(weakerKingSq) == file_of(pawnSq)
734 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
735 && ( opposite_colors(weakerKingSq, strongerBishopSq)
736 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
737 return SCALE_FACTOR_DRAW;
739 // Case 2: Opposite colored bishops
740 if (opposite_colors(strongerBishopSq, weakerBishopSq))
742 // We assume that the position is drawn in the following three situations:
744 // a. The pawn is on rank 5 or further back.
745 // b. The defending king is somewhere in the pawn's path.
746 // c. The defending bishop attacks some square along the pawn's path,
747 // and is at least three squares away from the pawn.
749 // These rules are probably not perfect, but in practice they work
752 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
753 return SCALE_FACTOR_DRAW;
756 Bitboard path = forward_bb(strongerSide, pawnSq);
758 if (path & pos.pieces(weakerSide, KING))
759 return SCALE_FACTOR_DRAW;
761 if ( (pos.attacks_from<BISHOP>(weakerBishopSq) & path)
762 && square_distance(weakerBishopSq, pawnSq) >= 3)
763 return SCALE_FACTOR_DRAW;
766 return SCALE_FACTOR_NONE;
770 /// K, bishop and two pawns vs K and bishop. It detects a few basic draws with
771 /// opposite-colored bishops.
773 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
775 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
776 assert(pos.non_pawn_material(weakerSide ) == BishopValueMg);
777 assert(pos.count<BISHOP>(strongerSide) == 1);
778 assert(pos.count<BISHOP>(weakerSide ) == 1);
779 assert(pos.count< PAWN>(strongerSide) == 2);
780 assert(pos.count< PAWN>(weakerSide ) == 0);
782 Square wbsq = pos.list<BISHOP>(strongerSide)[0];
783 Square bbsq = pos.list<BISHOP>(weakerSide)[0];
785 if (!opposite_colors(wbsq, bbsq))
786 return SCALE_FACTOR_NONE;
788 Square ksq = pos.king_square(weakerSide);
789 Square psq1 = pos.list<PAWN>(strongerSide)[0];
790 Square psq2 = pos.list<PAWN>(strongerSide)[1];
791 Rank r1 = rank_of(psq1);
792 Rank r2 = rank_of(psq2);
793 Square blockSq1, blockSq2;
795 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
797 blockSq1 = psq1 + pawn_push(strongerSide);
798 blockSq2 = file_of(psq2) | rank_of(psq1);
802 blockSq1 = psq2 + pawn_push(strongerSide);
803 blockSq2 = file_of(psq1) | rank_of(psq2);
806 switch (file_distance(psq1, psq2))
809 // Both pawns are on the same file. Easy draw if defender firmly controls
810 // some square in the frontmost pawn's path.
811 if ( file_of(ksq) == file_of(blockSq1)
812 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
813 && opposite_colors(ksq, wbsq))
814 return SCALE_FACTOR_DRAW;
816 return SCALE_FACTOR_NONE;
819 // Pawns on adjacent files. Draw if defender firmly controls the square
820 // in front of the frontmost pawn's path, and the square diagonally behind
821 // this square on the file of the other pawn.
823 && opposite_colors(ksq, wbsq)
824 && ( bbsq == blockSq2
825 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakerSide, BISHOP))
826 || abs(r1 - r2) >= 2))
827 return SCALE_FACTOR_DRAW;
829 else if ( ksq == blockSq2
830 && opposite_colors(ksq, wbsq)
831 && ( bbsq == blockSq1
832 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakerSide, BISHOP))))
833 return SCALE_FACTOR_DRAW;
835 return SCALE_FACTOR_NONE;
838 // The pawns are not on the same file or adjacent files. No scaling.
839 return SCALE_FACTOR_NONE;
844 /// K, bisop and a pawn vs K and knight. There is a single rule: If the defending
845 /// king is somewhere along the path of the pawn, and the square of the king is
846 /// not of the same color as the stronger side's bishop, it's a draw.
848 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
850 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
851 assert(pos.non_pawn_material(weakerSide ) == KnightValueMg);
852 assert(pos.count<BISHOP>(strongerSide) == 1);
853 assert(pos.count<KNIGHT>(weakerSide ) == 1);
854 assert(pos.count< PAWN>(strongerSide) == 1);
855 assert(pos.count< PAWN>(weakerSide ) == 0);
857 Square pawnSq = pos.list<PAWN>(strongerSide)[0];
858 Square strongerBishopSq = pos.list<BISHOP>(strongerSide)[0];
859 Square weakerKingSq = pos.king_square(weakerSide);
861 if ( file_of(weakerKingSq) == file_of(pawnSq)
862 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
863 && ( opposite_colors(weakerKingSq, strongerBishopSq)
864 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
865 return SCALE_FACTOR_DRAW;
867 return SCALE_FACTOR_NONE;
871 /// K, knight and a pawn vs K. There is a single rule: If the pawn is a rook pawn
872 /// on the 7th rank and the defending king prevents the pawn from advancing, the
873 /// position is drawn.
875 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
877 assert(pos.non_pawn_material(strongerSide) == KnightValueMg);
878 assert(pos.non_pawn_material(weakerSide ) == VALUE_ZERO);
879 assert(pos.count<KNIGHT>(strongerSide) == 1);
880 assert(pos.count< PAWN>(strongerSide) == 1);
881 assert(pos.count< PAWN>(weakerSide ) == 0);
883 Square pawnSq = pos.list<PAWN>(strongerSide)[0];
884 Square weakerKingSq = pos.king_square(weakerSide);
886 if ( pawnSq == relative_square(strongerSide, SQ_A7)
887 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
888 return SCALE_FACTOR_DRAW;
890 if ( pawnSq == relative_square(strongerSide, SQ_H7)
891 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
892 return SCALE_FACTOR_DRAW;
894 return SCALE_FACTOR_NONE;
898 /// K, knight and a pawn vs K and bishop. If knight can block bishop from taking
899 /// pawn, it's a win. Otherwise, drawn.
901 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
903 Square pawnSq = pos.list<PAWN>(strongerSide)[0];
904 Square bishopSq = pos.list<BISHOP>(weakerSide)[0];
905 Square weakerKingSq = pos.king_square(weakerSide);
907 // King needs to get close to promoting pawn to prevent knight from blocking.
908 // Rules for this are very tricky, so just approximate.
909 if (forward_bb(strongerSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
910 return ScaleFactor(square_distance(weakerKingSq, pawnSq));
912 return SCALE_FACTOR_NONE;
916 /// K and a pawn vs K and a pawn. This is done by removing the weakest side's
917 /// pawn and probing the KP vs K bitbase: If the weakest side has a draw without
918 /// the pawn, she probably has at least a draw with the pawn as well. The exception
919 /// is when the stronger side's pawn is far advanced and not on a rook file; in
920 /// this case it is often possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
922 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
924 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
925 assert(pos.non_pawn_material(weakerSide ) == VALUE_ZERO);
926 assert(pos.count<PAWN>(WHITE) == 1);
927 assert(pos.count<PAWN>(BLACK) == 1);
929 Square wksq = pos.king_square(strongerSide);
930 Square bksq = pos.king_square(weakerSide);
931 Square wpsq = pos.list<PAWN>(strongerSide)[0];
932 Color us = pos.side_to_move();
934 if (strongerSide == BLACK)
942 if (file_of(wpsq) >= FILE_E)
949 // If the pawn has advanced to the fifth rank or further, and is not a
950 // rook pawn, it's too dangerous to assume that it's at least a draw.
951 if ( rank_of(wpsq) >= RANK_5
952 && file_of(wpsq) != FILE_A)
953 return SCALE_FACTOR_NONE;
955 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
956 // it's probably at least a draw even with the pawn.
957 return Bitbases::probe_kpk(wksq, wpsq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;