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 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 };
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 + PushToEdges[loserKSq]
146 + PushClose[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 + PushClose[square_distance(winnerKSq, loserKSq)]
184 + PushToCorners[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 = pos.king_square(strongerSide);
200 Square bksq = pos.king_square(weakerSide);
201 Square psq = pos.list<PAWN>(strongerSide)[0];
202 Color us = pos.side_to_move();
204 if (strongerSide == BLACK)
212 if (file_of(psq) >= FILE_E)
219 if (!Bitbases::probe_kpk(wksq, psq, bksq, us))
222 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
224 return strongerSide == pos.side_to_move() ? result : -result;
228 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
229 /// a bitbase. The function below returns drawish scores when the pawn is
230 /// far advanced with support of the king, while the attacking king is far
233 Value Endgame<KRKP>::operator()(const Position& pos) const {
235 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
236 assert(pos.non_pawn_material(weakerSide) == 0);
237 assert(pos.count<PAWN>(strongerSide) == 0);
238 assert(pos.count<PAWN>(weakerSide ) == 1);
240 Square wksq = pos.king_square(strongerSide);
241 Square bksq = pos.king_square(weakerSide);
242 Square rsq = pos.list<ROOK>(strongerSide)[0];
243 Square psq = pos.list<PAWN>(weakerSide)[0];
245 if (strongerSide == BLACK)
253 Square queeningSq = file_of(psq) | RANK_1;
256 // If the stronger side's king is in front of the pawn, it's a win
257 if (wksq < psq && file_of(wksq) == file_of(psq))
258 result = RookValueEg - Value(square_distance(wksq, psq));
260 // If the weaker side's king is too far from the pawn and the rook,
262 else if ( square_distance(bksq, psq) >= 3 + (pos.side_to_move() == weakerSide)
263 && square_distance(bksq, rsq) >= 3)
264 result = RookValueEg - Value(square_distance(wksq, psq));
266 // If the pawn is far advanced and supported by the defending king,
267 // the position is drawish
268 else if ( rank_of(bksq) <= RANK_3
269 && square_distance(bksq, psq) == 1
270 && rank_of(wksq) >= RANK_4
271 && square_distance(wksq, psq) > 2 + (pos.side_to_move() == strongerSide))
272 result = Value(80 - square_distance(wksq, psq) * 8);
276 - Value(square_distance(wksq, psq + DELTA_S) * 8)
277 + Value(square_distance(bksq, psq + DELTA_S) * 8)
278 + Value(square_distance(psq, queeningSq) * 8);
280 return strongerSide == pos.side_to_move() ? result : -result;
284 /// KR vs KB. This is very simple, and always returns drawish scores. The
285 /// score is slightly bigger when the defending king is close to the edge.
287 Value Endgame<KRKB>::operator()(const Position& pos) const {
289 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
290 assert(pos.non_pawn_material(weakerSide ) == BishopValueMg);
291 assert(pos.count<BISHOP>(weakerSide ) == 1);
292 assert(pos.count< PAWN>(weakerSide ) == 0);
293 assert(pos.count< PAWN>(strongerSide) == 0);
295 Value result = Value(PushToEdges[pos.king_square(weakerSide)]);
296 return strongerSide == pos.side_to_move() ? result : -result;
300 /// KR vs KN. The attacking side has slightly better winning chances than
301 /// in KR vs KB, particularly if the king and the knight are far apart.
303 Value Endgame<KRKN>::operator()(const Position& pos) const {
305 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
306 assert(pos.non_pawn_material(weakerSide ) == KnightValueMg);
307 assert(pos.count<KNIGHT>(weakerSide ) == 1);
308 assert(pos.count< PAWN>(weakerSide ) == 0);
309 assert(pos.count< PAWN>(strongerSide) == 0);
311 Square bksq = pos.king_square(weakerSide);
312 Square bnsq = pos.list<KNIGHT>(weakerSide)[0];
313 Value result = Value(PushToEdges[bksq] + PushAway[square_distance(bksq, bnsq)]);
314 return strongerSide == pos.side_to_move() ? result : -result;
318 /// KQ vs KP. In general, a win for the stronger side, however, there are a few
319 /// important exceptions. Pawn on 7th rank, A,C,F or H file, with king next can
320 /// be a draw, so we scale down to distance between kings only.
322 Value Endgame<KQKP>::operator()(const Position& pos) const {
324 assert(pos.non_pawn_material(strongerSide) == QueenValueMg);
325 assert(pos.non_pawn_material(weakerSide ) == VALUE_ZERO);
326 assert(pos.count<PAWN>(strongerSide) == 0);
327 assert(pos.count<PAWN>(weakerSide ) == 1);
329 Square winnerKSq = pos.king_square(strongerSide);
330 Square loserKSq = pos.king_square(weakerSide);
331 Square pawnSq = pos.list<PAWN>(weakerSide)[0];
333 Value result = Value(PushClose[square_distance(winnerKSq, loserKSq)]);
335 if ( relative_rank(weakerSide, pawnSq) != RANK_7
336 || square_distance(loserKSq, pawnSq) != 1
337 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
338 result += QueenValueEg - PawnValueEg;
340 return strongerSide == pos.side_to_move() ? result : -result;
344 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
345 /// king a bonus for having the kings close together, and for forcing the
346 /// defending king towards the edge. If we also take care to avoid null move
347 /// for the defending side in the search, this is usually sufficient to be
348 /// able to win KQ vs KR.
350 Value Endgame<KQKR>::operator()(const Position& pos) const {
352 assert(pos.non_pawn_material(strongerSide) == QueenValueMg);
353 assert(pos.non_pawn_material(weakerSide ) == RookValueMg);
354 assert(pos.count<PAWN>(strongerSide) == 0);
355 assert(pos.count<PAWN>(weakerSide ) == 0);
357 Square winnerKSq = pos.king_square(strongerSide);
358 Square loserKSq = pos.king_square(weakerSide);
360 Value result = QueenValueEg
362 + PushToEdges[loserKSq]
363 + PushClose[square_distance(winnerKSq, loserKSq)];
365 return strongerSide == pos.side_to_move() ? result : -result;
369 /// KBB vs KN. This is almost always a win. We try to push enemy king to a corner
370 /// and away from his knight. For a reference of this difficult endgame see:
371 /// en.wikipedia.org/wiki/Chess_endgame#Effect_of_tablebases_on_endgame_theory
374 Value Endgame<KBBKN>::operator()(const Position& pos) const {
376 assert(pos.non_pawn_material(strongerSide) == 2 * BishopValueMg);
377 assert(pos.non_pawn_material(weakerSide ) == KnightValueMg);
378 assert(pos.count<BISHOP>(strongerSide) == 2);
379 assert(pos.count<KNIGHT>(weakerSide ) == 1);
380 assert(!pos.pieces(PAWN));
382 Square winnerKSq = pos.king_square(strongerSide);
383 Square loserKSq = pos.king_square(weakerSide);
384 Square knightSq = pos.list<KNIGHT>(weakerSide)[0];
386 Value result = VALUE_KNOWN_WIN
387 + PushToCorners[loserKSq]
388 + PushClose[square_distance(winnerKSq, loserKSq)]
389 + PushAway[square_distance(loserKSq, knightSq)];
391 return strongerSide == pos.side_to_move() ? result : -result;
395 /// Some cases of trivial draws
396 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
397 template<> Value Endgame<KmmKm>::operator()(const Position&) const { return VALUE_DRAW; }
400 /// K, bishop and one or more pawns vs K. It checks for draws with rook pawns and
401 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
402 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
405 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
407 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
408 assert(pos.count<BISHOP>(strongerSide) == 1);
409 assert(pos.count< PAWN>(strongerSide) >= 1);
411 // No assertions about the material of weakerSide, because we want draws to
412 // be detected even when the weaker side has some pawns.
414 Bitboard pawns = pos.pieces(strongerSide, PAWN);
415 File pawnFile = file_of(pos.list<PAWN>(strongerSide)[0]);
417 // All pawns are on a single rook file ?
418 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
419 && !(pawns & ~file_bb(pawnFile)))
421 Square bishopSq = pos.list<BISHOP>(strongerSide)[0];
422 Square queeningSq = relative_square(strongerSide, pawnFile | RANK_8);
423 Square kingSq = pos.king_square(weakerSide);
425 if ( opposite_colors(queeningSq, bishopSq)
426 && abs(file_of(kingSq) - pawnFile) <= 1)
428 // The bishop has the wrong color, and the defending king is on the
429 // file of the pawn(s) or the adjacent file. Find the rank of the
431 Square pawnSq = frontmost_sq(strongerSide, pawns);
433 // If the defending king has distance 1 to the promotion square or
434 // is placed somewhere in front of the pawn, it's a draw.
435 if ( square_distance(kingSq, queeningSq) <= 1
436 || relative_rank(weakerSide, kingSq) <= relative_rank(weakerSide, pawnSq))
437 return SCALE_FACTOR_DRAW;
441 // All pawns on same B or G file? Then potential draw
442 if ( (pawnFile == FILE_B || pawnFile == FILE_G)
443 && !(pos.pieces(PAWN) & ~file_bb(pawnFile))
444 && pos.non_pawn_material(weakerSide) == 0
445 && pos.count<PAWN>(weakerSide) >= 1)
447 // Get weakerSide pawn that is closest to home rank
448 Square weakerPawnSq = backmost_sq(weakerSide, pos.pieces(weakerSide, PAWN));
450 Square strongerKingSq = pos.king_square(strongerSide);
451 Square weakerKingSq = pos.king_square(weakerSide);
452 Square bishopSq = pos.list<BISHOP>(strongerSide)[0];
454 // Potential for a draw if our pawn is blocked on the 7th rank
455 // the bishop cannot attack it or they only have one pawn left
456 if ( relative_rank(strongerSide, weakerPawnSq) == RANK_7
457 && (pos.pieces(strongerSide, PAWN) & (weakerPawnSq + pawn_push(weakerSide)))
458 && (opposite_colors(bishopSq, weakerPawnSq) || pos.count<PAWN>(strongerSide) == 1))
460 int strongerKingDist = square_distance(weakerPawnSq, strongerKingSq);
461 int weakerKingDist = square_distance(weakerPawnSq, weakerKingSq);
463 // Draw if the weak king is on it's back two ranks, within 2
464 // squares of the blocking pawn and the strong king is not
465 // closer. (I think this rule only fails in practically
466 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
467 // and positions where qsearch will immediately correct the
468 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
469 if ( relative_rank(strongerSide, weakerKingSq) >= RANK_7
470 && weakerKingDist <= 2
471 && weakerKingDist <= strongerKingDist)
472 return SCALE_FACTOR_DRAW;
476 return SCALE_FACTOR_NONE;
480 /// K and queen vs K, rook and one or more pawns. It tests for fortress draws with
481 /// a rook on the third rank defended by a pawn.
483 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
485 assert(pos.non_pawn_material(strongerSide) == QueenValueMg);
486 assert(pos.count<QUEEN>(strongerSide) == 1);
487 assert(pos.count< PAWN>(strongerSide) == 0);
488 assert(pos.count< ROOK>(weakerSide ) == 1);
489 assert(pos.count< PAWN>(weakerSide ) >= 1);
491 Square kingSq = pos.king_square(weakerSide);
492 Square rsq = pos.list<ROOK>(weakerSide)[0];
494 if ( relative_rank(weakerSide, kingSq) <= RANK_2
495 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
496 && (pos.pieces(weakerSide, ROOK) & rank_bb(relative_rank(weakerSide, RANK_3)))
497 && (pos.pieces(weakerSide, PAWN) & rank_bb(relative_rank(weakerSide, RANK_2)))
498 && (pos.attacks_from<KING>(kingSq) & pos.pieces(weakerSide, PAWN))
499 && (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(weakerSide, PAWN)))
500 return SCALE_FACTOR_DRAW;
502 return SCALE_FACTOR_NONE;
506 /// K, rook and one pawn vs K and a rook. This function knows a handful of the
507 /// most important classes of drawn positions, but is far from perfect. It would
508 /// probably be a good idea to add more knowledge in the future.
510 /// It would also be nice to rewrite the actual code for this function,
511 /// which is mostly copied from Glaurung 1.x, and not very pretty.
513 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
515 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
516 assert(pos.non_pawn_material(weakerSide) == RookValueMg);
517 assert(pos.count<PAWN>(strongerSide) == 1);
518 assert(pos.count<PAWN>(weakerSide ) == 0);
520 Square wksq = pos.king_square(strongerSide);
521 Square bksq = pos.king_square(weakerSide);
522 Square wrsq = pos.list<ROOK>(strongerSide)[0];
523 Square wpsq = pos.list<PAWN>(strongerSide)[0];
524 Square brsq = pos.list<ROOK>(weakerSide)[0];
526 // Orient the board in such a way that the stronger side is white, and the
527 // pawn is on the left half of the board.
528 if (strongerSide == BLACK)
537 if (file_of(wpsq) > FILE_D)
546 File f = file_of(wpsq);
547 Rank r = rank_of(wpsq);
548 Square queeningSq = f | RANK_8;
549 int tempo = (pos.side_to_move() == strongerSide);
551 // If the pawn is not too far advanced and the defending king defends the
552 // queening square, use the third-rank defence.
554 && square_distance(bksq, queeningSq) <= 1
556 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
557 return SCALE_FACTOR_DRAW;
559 // The defending side saves a draw by checking from behind in case the pawn
560 // has advanced to the 6th rank with the king behind.
562 && square_distance(bksq, queeningSq) <= 1
563 && rank_of(wksq) + tempo <= RANK_6
564 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
565 return SCALE_FACTOR_DRAW;
568 && bksq == queeningSq
569 && rank_of(brsq) == RANK_1
570 && (!tempo || square_distance(wksq, wpsq) >= 2))
571 return SCALE_FACTOR_DRAW;
573 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
574 // and the black rook is behind the pawn.
577 && (bksq == SQ_H7 || bksq == SQ_G7)
578 && file_of(brsq) == FILE_A
579 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
580 return SCALE_FACTOR_DRAW;
582 // If the defending king blocks the pawn and the attacking king is too far
583 // away, it's a draw.
585 && bksq == wpsq + DELTA_N
586 && square_distance(wksq, wpsq) - tempo >= 2
587 && square_distance(wksq, brsq) - tempo >= 2)
588 return SCALE_FACTOR_DRAW;
590 // Pawn on the 7th rank supported by the rook from behind usually wins if the
591 // attacking king is closer to the queening square than the defending king,
592 // and the defending king cannot gain tempi by threatening the attacking rook.
595 && file_of(wrsq) == f
596 && wrsq != queeningSq
597 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
598 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
599 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
601 // Similar to the above, but with the pawn further back
603 && file_of(wrsq) == f
605 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
606 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
607 && ( square_distance(bksq, wrsq) + tempo >= 3
608 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
609 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
610 return ScaleFactor( SCALE_FACTOR_MAX
611 - 8 * square_distance(wpsq, queeningSq)
612 - 2 * square_distance(wksq, queeningSq));
614 // If the pawn is not far advanced, and the defending king is somewhere in
615 // the pawn's path, it's probably a draw.
616 if (r <= RANK_4 && bksq > wpsq)
618 if (file_of(bksq) == file_of(wpsq))
619 return ScaleFactor(10);
620 if ( abs(file_of(bksq) - file_of(wpsq)) == 1
621 && square_distance(wksq, bksq) > 2)
622 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
624 return SCALE_FACTOR_NONE;
628 /// K, rook and two pawns vs K, rook and one pawn. There is only a single
629 /// pattern: If the stronger side has no passed pawns and the defending king
630 /// is actively placed, the position is drawish.
632 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
634 assert(pos.non_pawn_material(strongerSide) == RookValueMg);
635 assert(pos.non_pawn_material(weakerSide) == RookValueMg);
636 assert(pos.count<PAWN>(strongerSide) == 2);
637 assert(pos.count<PAWN>(weakerSide ) == 1);
639 Square wpsq1 = pos.list<PAWN>(strongerSide)[0];
640 Square wpsq2 = pos.list<PAWN>(strongerSide)[1];
641 Square bksq = pos.king_square(weakerSide);
643 // Does the stronger side have a passed pawn?
644 if (pos.pawn_passed(strongerSide, wpsq1) || pos.pawn_passed(strongerSide, wpsq2))
645 return SCALE_FACTOR_NONE;
647 Rank r = std::max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
649 if ( file_distance(bksq, wpsq1) <= 1
650 && file_distance(bksq, wpsq2) <= 1
651 && relative_rank(strongerSide, bksq) > r)
654 case RANK_2: return ScaleFactor(10);
655 case RANK_3: return ScaleFactor(10);
656 case RANK_4: return ScaleFactor(15);
657 case RANK_5: return ScaleFactor(20);
658 case RANK_6: return ScaleFactor(40);
659 default: assert(false);
662 return SCALE_FACTOR_NONE;
666 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
667 /// are on the same rook file and are blocked by the defending king, it's a draw.
669 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
671 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
672 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
673 assert(pos.count<PAWN>(strongerSide) >= 2);
674 assert(pos.count<PAWN>(weakerSide ) == 0);
676 Square ksq = pos.king_square(weakerSide);
677 Bitboard pawns = pos.pieces(strongerSide, PAWN);
679 // Are all pawns on the 'a' file?
680 if (!(pawns & ~FileABB))
682 // Does the defending king block the pawns?
683 if ( square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
684 || ( file_of(ksq) == FILE_A
685 && !(in_front_bb(strongerSide, rank_of(ksq)) & pawns)))
686 return SCALE_FACTOR_DRAW;
688 // Are all pawns on the 'h' file?
689 else if (!(pawns & ~FileHBB))
691 // Does the defending king block the pawns?
692 if ( square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
693 || ( file_of(ksq) == FILE_H
694 && !(in_front_bb(strongerSide, rank_of(ksq)) & pawns)))
695 return SCALE_FACTOR_DRAW;
697 return SCALE_FACTOR_NONE;
701 /// K, bishop and a pawn vs K and a bishop. There are two rules: If the defending
702 /// king is somewhere along the path of the pawn, and the square of the king is
703 /// not of the same color as the stronger side's bishop, it's a draw. If the two
704 /// bishops have opposite color, it's almost always a draw.
706 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
708 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
709 assert(pos.non_pawn_material(weakerSide ) == BishopValueMg);
710 assert(pos.count<BISHOP>(strongerSide) == 1);
711 assert(pos.count<BISHOP>(weakerSide ) == 1);
712 assert(pos.count< PAWN>(strongerSide) == 1);
713 assert(pos.count< PAWN>(weakerSide ) == 0);
715 Square pawnSq = pos.list<PAWN>(strongerSide)[0];
716 Square strongerBishopSq = pos.list<BISHOP>(strongerSide)[0];
717 Square weakerBishopSq = pos.list<BISHOP>(weakerSide)[0];
718 Square weakerKingSq = pos.king_square(weakerSide);
720 // Case 1: Defending king blocks the pawn, and cannot be driven away
721 if ( file_of(weakerKingSq) == file_of(pawnSq)
722 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
723 && ( opposite_colors(weakerKingSq, strongerBishopSq)
724 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
725 return SCALE_FACTOR_DRAW;
727 // Case 2: Opposite colored bishops
728 if (opposite_colors(strongerBishopSq, weakerBishopSq))
730 // We assume that the position is drawn in the following three situations:
732 // a. The pawn is on rank 5 or further back.
733 // b. The defending king is somewhere in the pawn's path.
734 // c. The defending bishop attacks some square along the pawn's path,
735 // and is at least three squares away from the pawn.
737 // These rules are probably not perfect, but in practice they work
740 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
741 return SCALE_FACTOR_DRAW;
744 Bitboard path = forward_bb(strongerSide, pawnSq);
746 if (path & pos.pieces(weakerSide, KING))
747 return SCALE_FACTOR_DRAW;
749 if ( (pos.attacks_from<BISHOP>(weakerBishopSq) & path)
750 && square_distance(weakerBishopSq, pawnSq) >= 3)
751 return SCALE_FACTOR_DRAW;
754 return SCALE_FACTOR_NONE;
758 /// K, bishop and two pawns vs K and bishop. It detects a few basic draws with
759 /// opposite-colored bishops.
761 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
763 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
764 assert(pos.non_pawn_material(weakerSide ) == BishopValueMg);
765 assert(pos.count<BISHOP>(strongerSide) == 1);
766 assert(pos.count<BISHOP>(weakerSide ) == 1);
767 assert(pos.count< PAWN>(strongerSide) == 2);
768 assert(pos.count< PAWN>(weakerSide ) == 0);
770 Square wbsq = pos.list<BISHOP>(strongerSide)[0];
771 Square bbsq = pos.list<BISHOP>(weakerSide)[0];
773 if (!opposite_colors(wbsq, bbsq))
774 return SCALE_FACTOR_NONE;
776 Square ksq = pos.king_square(weakerSide);
777 Square psq1 = pos.list<PAWN>(strongerSide)[0];
778 Square psq2 = pos.list<PAWN>(strongerSide)[1];
779 Rank r1 = rank_of(psq1);
780 Rank r2 = rank_of(psq2);
781 Square blockSq1, blockSq2;
783 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
785 blockSq1 = psq1 + pawn_push(strongerSide);
786 blockSq2 = file_of(psq2) | rank_of(psq1);
790 blockSq1 = psq2 + pawn_push(strongerSide);
791 blockSq2 = file_of(psq1) | rank_of(psq2);
794 switch (file_distance(psq1, psq2))
797 // Both pawns are on the same file. Easy draw if defender firmly controls
798 // some square in the frontmost pawn's path.
799 if ( file_of(ksq) == file_of(blockSq1)
800 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
801 && opposite_colors(ksq, wbsq))
802 return SCALE_FACTOR_DRAW;
804 return SCALE_FACTOR_NONE;
807 // Pawns on adjacent files. Draw if defender firmly controls the square
808 // in front of the frontmost pawn's path, and the square diagonally behind
809 // this square on the file of the other pawn.
811 && opposite_colors(ksq, wbsq)
812 && ( bbsq == blockSq2
813 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakerSide, BISHOP))
814 || abs(r1 - r2) >= 2))
815 return SCALE_FACTOR_DRAW;
817 else if ( ksq == blockSq2
818 && opposite_colors(ksq, wbsq)
819 && ( bbsq == blockSq1
820 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakerSide, BISHOP))))
821 return SCALE_FACTOR_DRAW;
823 return SCALE_FACTOR_NONE;
826 // The pawns are not on the same file or adjacent files. No scaling.
827 return SCALE_FACTOR_NONE;
832 /// K, bisop and a pawn vs K and knight. There is a single rule: If the defending
833 /// king is somewhere along the path of the pawn, and the square of the king is
834 /// not of the same color as the stronger side's bishop, it's a draw.
836 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
838 assert(pos.non_pawn_material(strongerSide) == BishopValueMg);
839 assert(pos.non_pawn_material(weakerSide ) == KnightValueMg);
840 assert(pos.count<BISHOP>(strongerSide) == 1);
841 assert(pos.count<KNIGHT>(weakerSide ) == 1);
842 assert(pos.count< PAWN>(strongerSide) == 1);
843 assert(pos.count< PAWN>(weakerSide ) == 0);
845 Square pawnSq = pos.list<PAWN>(strongerSide)[0];
846 Square strongerBishopSq = pos.list<BISHOP>(strongerSide)[0];
847 Square weakerKingSq = pos.king_square(weakerSide);
849 if ( file_of(weakerKingSq) == file_of(pawnSq)
850 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
851 && ( opposite_colors(weakerKingSq, strongerBishopSq)
852 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
853 return SCALE_FACTOR_DRAW;
855 return SCALE_FACTOR_NONE;
859 /// K, knight and a pawn vs K. There is a single rule: If the pawn is a rook pawn
860 /// on the 7th rank and the defending king prevents the pawn from advancing, the
861 /// position is drawn.
863 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
865 assert(pos.non_pawn_material(strongerSide) == KnightValueMg);
866 assert(pos.non_pawn_material(weakerSide ) == VALUE_ZERO);
867 assert(pos.count<KNIGHT>(strongerSide) == 1);
868 assert(pos.count< PAWN>(strongerSide) == 1);
869 assert(pos.count< PAWN>(weakerSide ) == 0);
871 Square pawnSq = pos.list<PAWN>(strongerSide)[0];
872 Square weakerKingSq = pos.king_square(weakerSide);
874 if ( pawnSq == relative_square(strongerSide, SQ_A7)
875 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
876 return SCALE_FACTOR_DRAW;
878 if ( pawnSq == relative_square(strongerSide, SQ_H7)
879 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
880 return SCALE_FACTOR_DRAW;
882 return SCALE_FACTOR_NONE;
886 /// K, knight and a pawn vs K and bishop. If knight can block bishop from taking
887 /// pawn, it's a win. Otherwise, drawn.
889 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
891 Square pawnSq = pos.list<PAWN>(strongerSide)[0];
892 Square bishopSq = pos.list<BISHOP>(weakerSide)[0];
893 Square weakerKingSq = pos.king_square(weakerSide);
895 // King needs to get close to promoting pawn to prevent knight from blocking.
896 // Rules for this are very tricky, so just approximate.
897 if (forward_bb(strongerSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
898 return ScaleFactor(square_distance(weakerKingSq, pawnSq));
900 return SCALE_FACTOR_NONE;
904 /// K and a pawn vs K and a pawn. This is done by removing the weakest side's
905 /// pawn and probing the KP vs K bitbase: If the weakest side has a draw without
906 /// the pawn, she probably has at least a draw with the pawn as well. The exception
907 /// is when the stronger side's pawn is far advanced and not on a rook file; in
908 /// this case it is often possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
910 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
912 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
913 assert(pos.non_pawn_material(weakerSide ) == VALUE_ZERO);
914 assert(pos.count<PAWN>(WHITE) == 1);
915 assert(pos.count<PAWN>(BLACK) == 1);
917 Square wksq = pos.king_square(strongerSide);
918 Square bksq = pos.king_square(weakerSide);
919 Square psq = pos.list<PAWN>(strongerSide)[0];
920 Color us = pos.side_to_move();
922 if (strongerSide == BLACK)
930 if (file_of(psq) >= FILE_E)
937 // If the pawn has advanced to the fifth rank or further, and is not a
938 // rook pawn, it's too dangerous to assume that it's at least a draw.
939 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
940 return SCALE_FACTOR_NONE;
942 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
943 // it's probably at least a draw even with the pawn.
944 return Bitbases::probe_kpk(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;