2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
4 Copyright (C) 2008-2015 Marco Costalba, Joona Kiiski, Tord Romstad
5 Copyright (C) 2015-2016 Marco Costalba, Joona Kiiski, Gary Linscott, Tord Romstad
7 Stockfish is free software: you can redistribute it and/or modify
8 it under the terms of the GNU General Public License as published by
9 the Free Software Foundation, either version 3 of the License, or
10 (at your option) any later version.
12 Stockfish is distributed in the hope that it will be useful,
13 but WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 GNU General Public License for more details.
17 You should have received a copy of the GNU General Public License
18 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 // Pawn Rank based scaling factors used in KRPPKRP endgame
63 const int KRPPKRPScaleFactors[RANK_NB] = { 0, 9, 10, 14, 21, 44, 0, 0 };
66 bool verify_material(const Position& pos, Color c, Value npm, int pawnsCnt) {
67 return pos.non_pawn_material(c) == npm && pos.count<PAWN>(c) == pawnsCnt;
71 // Map the square as if strongSide is white and strongSide's only pawn
72 // is on the left half of the board.
73 Square normalize(const Position& pos, Color strongSide, Square sq) {
75 assert(pos.count<PAWN>(strongSide) == 1);
77 if (file_of(pos.square<PAWN>(strongSide)) >= FILE_E)
78 sq = Square(sq ^ 7); // Mirror SQ_H1 -> SQ_A1
80 if (strongSide == BLACK)
86 // Get the material key of Position out of the given endgame key code
87 // like "KBPKN". The trick here is to first forge an ad-hoc FEN string
88 // and then let a Position object do the work for us.
89 Key key(const string& code, Color c) {
91 assert(code.length() > 0 && code.length() < 8);
92 assert(code[0] == 'K');
94 string sides[] = { code.substr(code.find('K', 1)), // Weak
95 code.substr(0, code.find('K', 1)) }; // Strong
97 std::transform(sides[c].begin(), sides[c].end(), sides[c].begin(), tolower);
99 string fen = sides[0] + char(8 - sides[0].length() + '0') + "/8/8/8/8/8/8/"
100 + sides[1] + char(8 - sides[1].length() + '0') + " w - - 0 10";
103 return Position().set(fen, false, &st, nullptr).material_key();
109 /// Endgames members definitions
111 Endgames::Endgames() {
128 add<KBPPKB>("KBPPKB");
129 add<KRPPKRP>("KRPPKRP");
133 template<EndgameType E, typename T>
134 void Endgames::add(const string& code) {
135 map<T>()[key(code, WHITE)] = std::unique_ptr<EndgameBase<T>>(new Endgame<E>(WHITE));
136 map<T>()[key(code, BLACK)] = std::unique_ptr<EndgameBase<T>>(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(verify_material(pos, weakSide, VALUE_ZERO, 0));
148 assert(!pos.checkers()); // Eval is never called when in check
150 // Stalemate detection with lone king
151 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
154 Square winnerKSq = pos.square<KING>(strongSide);
155 Square loserKSq = pos.square<KING>(weakSide);
157 Value result = pos.non_pawn_material(strongSide)
158 + pos.count<PAWN>(strongSide) * PawnValueEg
159 + PushToEdges[loserKSq]
160 + PushClose[distance(winnerKSq, loserKSq)];
162 if ( pos.count<QUEEN>(strongSide)
163 || pos.count<ROOK>(strongSide)
164 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
165 ||(pos.count<BISHOP>(strongSide) > 1 && opposite_colors(pos.squares<BISHOP>(strongSide)[0],
166 pos.squares<BISHOP>(strongSide)[1])))
167 result = std::min(result + VALUE_KNOWN_WIN, VALUE_MATE_IN_MAX_PLY - 1);
169 return strongSide == pos.side_to_move() ? result : -result;
173 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
174 /// defending king towards a corner square of the right color.
176 Value Endgame<KBNK>::operator()(const Position& pos) const {
178 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
179 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
181 Square winnerKSq = pos.square<KING>(strongSide);
182 Square loserKSq = pos.square<KING>(weakSide);
183 Square bishopSq = pos.square<BISHOP>(strongSide);
185 // kbnk_mate_table() tries to drive toward corners A1 or H8. If we have a
186 // bishop that cannot reach the above squares, we flip the kings in order
187 // to drive the enemy toward corners A8 or H1.
188 if (opposite_colors(bishopSq, SQ_A1))
190 winnerKSq = ~winnerKSq;
191 loserKSq = ~loserKSq;
194 Value result = VALUE_KNOWN_WIN
195 + PushClose[distance(winnerKSq, loserKSq)]
196 + PushToCorners[loserKSq];
198 return strongSide == pos.side_to_move() ? result : -result;
202 /// KP vs K. This endgame is evaluated with the help of a bitbase.
204 Value Endgame<KPK>::operator()(const Position& pos) const {
206 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
207 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
209 // Assume strongSide is white and the pawn is on files A-D
210 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
211 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
212 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
214 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
216 if (!Bitbases::probe(wksq, psq, bksq, us))
219 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
221 return strongSide == pos.side_to_move() ? result : -result;
225 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
226 /// a bitbase. The function below returns drawish scores when the pawn is
227 /// far advanced with support of the king, while the attacking king is far
230 Value Endgame<KRKP>::operator()(const Position& pos) const {
232 assert(verify_material(pos, strongSide, RookValueMg, 0));
233 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
235 Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
236 Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
237 Square rsq = relative_square(strongSide, pos.square<ROOK>(strongSide));
238 Square psq = relative_square(strongSide, pos.square<PAWN>(weakSide));
240 Square queeningSq = make_square(file_of(psq), RANK_1);
243 // If the stronger side's king is in front of the pawn, it's a win
244 if (wksq < psq && file_of(wksq) == file_of(psq))
245 result = RookValueEg - distance(wksq, psq);
247 // If the weaker side's king is too far from the pawn and the rook,
249 else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
250 && distance(bksq, rsq) >= 3)
251 result = RookValueEg - distance(wksq, psq);
253 // If the pawn is far advanced and supported by the defending king,
254 // the position is drawish
255 else if ( rank_of(bksq) <= RANK_3
256 && distance(bksq, psq) == 1
257 && rank_of(wksq) >= RANK_4
258 && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
259 result = Value(80) - 8 * distance(wksq, psq);
262 result = Value(200) - 8 * ( distance(wksq, psq + DELTA_S)
263 - distance(bksq, psq + DELTA_S)
264 - distance(psq, queeningSq));
266 return strongSide == pos.side_to_move() ? result : -result;
270 /// KR vs KB. This is very simple, and always returns drawish scores. The
271 /// score is slightly bigger when the defending king is close to the edge.
273 Value Endgame<KRKB>::operator()(const Position& pos) const {
275 assert(verify_material(pos, strongSide, RookValueMg, 0));
276 assert(verify_material(pos, weakSide, BishopValueMg, 0));
278 Value result = Value(PushToEdges[pos.square<KING>(weakSide)]);
279 return strongSide == pos.side_to_move() ? result : -result;
283 /// KR vs KN. The attacking side has slightly better winning chances than
284 /// in KR vs KB, particularly if the king and the knight are far apart.
286 Value Endgame<KRKN>::operator()(const Position& pos) const {
288 assert(verify_material(pos, strongSide, RookValueMg, 0));
289 assert(verify_material(pos, weakSide, KnightValueMg, 0));
291 Square bksq = pos.square<KING>(weakSide);
292 Square bnsq = pos.square<KNIGHT>(weakSide);
293 Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
294 return strongSide == pos.side_to_move() ? result : -result;
298 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
299 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
300 /// with a king positioned next to it can be a draw, so in that case, we only
301 /// use the distance between the kings.
303 Value Endgame<KQKP>::operator()(const Position& pos) const {
305 assert(verify_material(pos, strongSide, QueenValueMg, 0));
306 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
308 Square winnerKSq = pos.square<KING>(strongSide);
309 Square loserKSq = pos.square<KING>(weakSide);
310 Square pawnSq = pos.square<PAWN>(weakSide);
312 Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
314 if ( relative_rank(weakSide, pawnSq) != RANK_7
315 || distance(loserKSq, pawnSq) != 1
316 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
317 result += QueenValueEg - PawnValueEg;
319 return strongSide == pos.side_to_move() ? result : -result;
323 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
324 /// king a bonus for having the kings close together, and for forcing the
325 /// defending king towards the edge. If we also take care to avoid null move for
326 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
328 Value Endgame<KQKR>::operator()(const Position& pos) const {
330 assert(verify_material(pos, strongSide, QueenValueMg, 0));
331 assert(verify_material(pos, weakSide, RookValueMg, 0));
333 Square winnerKSq = pos.square<KING>(strongSide);
334 Square loserKSq = pos.square<KING>(weakSide);
336 Value result = QueenValueEg
338 + PushToEdges[loserKSq]
339 + PushClose[distance(winnerKSq, loserKSq)];
341 return strongSide == pos.side_to_move() ? result : -result;
345 /// Some cases of trivial draws
346 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
349 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
350 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
351 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
354 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
356 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
357 assert(pos.count<PAWN>(strongSide) >= 1);
359 // No assertions about the material of weakSide, because we want draws to
360 // be detected even when the weaker side has some pawns.
362 Bitboard pawns = pos.pieces(strongSide, PAWN);
363 File pawnsFile = file_of(lsb(pawns));
365 // All pawns are on a single rook file?
366 if ( (pawnsFile == FILE_A || pawnsFile == FILE_H)
367 && !(pawns & ~file_bb(pawnsFile)))
369 Square bishopSq = pos.square<BISHOP>(strongSide);
370 Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
371 Square kingSq = pos.square<KING>(weakSide);
373 if ( opposite_colors(queeningSq, bishopSq)
374 && distance(queeningSq, kingSq) <= 1)
375 return SCALE_FACTOR_DRAW;
378 // If all the pawns are on the same B or G file, then it's potentially a draw
379 if ( (pawnsFile == FILE_B || pawnsFile == FILE_G)
380 && !(pos.pieces(PAWN) & ~file_bb(pawnsFile))
381 && pos.non_pawn_material(weakSide) == 0
382 && pos.count<PAWN>(weakSide) >= 1)
384 // Get weakSide pawn that is closest to the home rank
385 Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
387 Square strongKingSq = pos.square<KING>(strongSide);
388 Square weakKingSq = pos.square<KING>(weakSide);
389 Square bishopSq = pos.square<BISHOP>(strongSide);
391 // There's potential for a draw if our pawn is blocked on the 7th rank,
392 // the bishop cannot attack it or they only have one pawn left
393 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
394 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
395 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
397 int strongKingDist = distance(weakPawnSq, strongKingSq);
398 int weakKingDist = distance(weakPawnSq, weakKingSq);
400 // It's a draw if the weak king is on its back two ranks, within 2
401 // squares of the blocking pawn and the strong king is not
402 // closer. (I think this rule only fails in practically
403 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
404 // and positions where qsearch will immediately correct the
405 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
406 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
408 && weakKingDist <= strongKingDist)
409 return SCALE_FACTOR_DRAW;
413 return SCALE_FACTOR_NONE;
417 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
418 /// the third rank defended by a pawn.
420 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
422 assert(verify_material(pos, strongSide, QueenValueMg, 0));
423 assert(pos.count<ROOK>(weakSide) == 1);
424 assert(pos.count<PAWN>(weakSide) >= 1);
426 Square kingSq = pos.square<KING>(weakSide);
427 Square rsq = pos.square<ROOK>(weakSide);
429 if ( relative_rank(weakSide, kingSq) <= RANK_2
430 && relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
431 && relative_rank(weakSide, rsq) == RANK_3
432 && ( pos.pieces(weakSide, PAWN)
433 & pos.attacks_from<KING>(kingSq)
434 & pos.attacks_from<PAWN>(rsq, strongSide)))
435 return SCALE_FACTOR_DRAW;
437 return SCALE_FACTOR_NONE;
441 /// KRP vs KR. This function knows a handful of the most important classes of
442 /// drawn positions, but is far from perfect. It would probably be a good idea
443 /// to add more knowledge in the future.
445 /// It would also be nice to rewrite the actual code for this function,
446 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
448 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
450 assert(verify_material(pos, strongSide, RookValueMg, 1));
451 assert(verify_material(pos, weakSide, RookValueMg, 0));
453 // Assume strongSide is white and the pawn is on files A-D
454 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
455 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
456 Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
457 Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
458 Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
460 File f = file_of(wpsq);
461 Rank r = rank_of(wpsq);
462 Square queeningSq = make_square(f, RANK_8);
463 int tempo = (pos.side_to_move() == strongSide);
465 // If the pawn is not too far advanced and the defending king defends the
466 // queening square, use the third-rank defence.
468 && distance(bksq, queeningSq) <= 1
470 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
471 return SCALE_FACTOR_DRAW;
473 // The defending side saves a draw by checking from behind in case the pawn
474 // has advanced to the 6th rank with the king behind.
476 && distance(bksq, queeningSq) <= 1
477 && rank_of(wksq) + tempo <= RANK_6
478 && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
479 return SCALE_FACTOR_DRAW;
482 && bksq == queeningSq
483 && rank_of(brsq) == RANK_1
484 && (!tempo || distance(wksq, wpsq) >= 2))
485 return SCALE_FACTOR_DRAW;
487 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
488 // and the black rook is behind the pawn.
491 && (bksq == SQ_H7 || bksq == SQ_G7)
492 && file_of(brsq) == FILE_A
493 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
494 return SCALE_FACTOR_DRAW;
496 // If the defending king blocks the pawn and the attacking king is too far
497 // away, it's a draw.
499 && bksq == wpsq + DELTA_N
500 && distance(wksq, wpsq) - tempo >= 2
501 && distance(wksq, brsq) - tempo >= 2)
502 return SCALE_FACTOR_DRAW;
504 // Pawn on the 7th rank supported by the rook from behind usually wins if the
505 // attacking king is closer to the queening square than the defending king,
506 // and the defending king cannot gain tempi by threatening the attacking rook.
509 && file_of(wrsq) == f
510 && wrsq != queeningSq
511 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
512 && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
513 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
515 // Similar to the above, but with the pawn further back
517 && file_of(wrsq) == f
519 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
520 && (distance(wksq, wpsq + DELTA_N) < distance(bksq, wpsq + DELTA_N) - 2 + tempo)
521 && ( distance(bksq, wrsq) + tempo >= 3
522 || ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
523 && (distance(wksq, wpsq + DELTA_N) < distance(bksq, wrsq) + tempo))))
524 return ScaleFactor( SCALE_FACTOR_MAX
525 - 8 * distance(wpsq, queeningSq)
526 - 2 * distance(wksq, queeningSq));
528 // If the pawn is not far advanced and the defending king is somewhere in
529 // the pawn's path, it's probably a draw.
530 if (r <= RANK_4 && bksq > wpsq)
532 if (file_of(bksq) == file_of(wpsq))
533 return ScaleFactor(10);
534 if ( distance<File>(bksq, wpsq) == 1
535 && distance(wksq, bksq) > 2)
536 return ScaleFactor(24 - 2 * distance(wksq, bksq));
538 return SCALE_FACTOR_NONE;
542 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
544 assert(verify_material(pos, strongSide, RookValueMg, 1));
545 assert(verify_material(pos, weakSide, BishopValueMg, 0));
547 // Test for a rook pawn
548 if (pos.pieces(PAWN) & (FileABB | FileHBB))
550 Square ksq = pos.square<KING>(weakSide);
551 Square bsq = pos.square<BISHOP>(weakSide);
552 Square psq = pos.square<PAWN>(strongSide);
553 Rank rk = relative_rank(strongSide, psq);
554 Square push = pawn_push(strongSide);
556 // If the pawn is on the 5th rank and the pawn (currently) is on
557 // the same color square as the bishop then there is a chance of
558 // a fortress. Depending on the king position give a moderate
559 // reduction or a stronger one if the defending king is near the
560 // corner but not trapped there.
561 if (rk == RANK_5 && !opposite_colors(bsq, psq))
563 int d = distance(psq + 3 * push, ksq);
565 if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
566 return ScaleFactor(24);
568 return ScaleFactor(48);
571 // When the pawn has moved to the 6th rank we can be fairly sure
572 // it's drawn if the bishop attacks the square in front of the
573 // pawn from a reasonable distance and the defending king is near
576 && distance(psq + 2 * push, ksq) <= 1
577 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
578 && distance<File>(bsq, psq) >= 2)
579 return ScaleFactor(8);
582 return SCALE_FACTOR_NONE;
585 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
586 /// pawns and the defending king is actively placed, the position is drawish.
588 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
590 assert(verify_material(pos, strongSide, RookValueMg, 2));
591 assert(verify_material(pos, weakSide, RookValueMg, 1));
593 Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
594 Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
595 Square bksq = pos.square<KING>(weakSide);
597 // Does the stronger side have a passed pawn?
598 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
599 return SCALE_FACTOR_NONE;
601 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
603 if ( distance<File>(bksq, wpsq1) <= 1
604 && distance<File>(bksq, wpsq2) <= 1
605 && relative_rank(strongSide, bksq) > r)
607 assert(r > RANK_1 && r < RANK_7);
608 return ScaleFactor(KRPPKRPScaleFactors[r]);
610 return SCALE_FACTOR_NONE;
614 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
615 /// are on the same rook file and are blocked by the defending king, it's a draw.
617 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
619 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
620 assert(pos.count<PAWN>(strongSide) >= 2);
621 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
623 Square ksq = pos.square<KING>(weakSide);
624 Bitboard pawns = pos.pieces(strongSide, PAWN);
626 // If all pawns are ahead of the king, on a single rook file and
627 // the king is within one file of the pawns, it's a draw.
628 if ( !(pawns & ~in_front_bb(weakSide, rank_of(ksq)))
629 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
630 && distance<File>(ksq, lsb(pawns)) <= 1)
631 return SCALE_FACTOR_DRAW;
633 return SCALE_FACTOR_NONE;
637 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
638 /// path of the pawn, and the square of the king is not of the same color as the
639 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
640 /// it's almost always a draw.
642 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
644 assert(verify_material(pos, strongSide, BishopValueMg, 1));
645 assert(verify_material(pos, weakSide, BishopValueMg, 0));
647 Square pawnSq = pos.square<PAWN>(strongSide);
648 Square strongBishopSq = pos.square<BISHOP>(strongSide);
649 Square weakBishopSq = pos.square<BISHOP>(weakSide);
650 Square weakKingSq = pos.square<KING>(weakSide);
652 // Case 1: Defending king blocks the pawn, and cannot be driven away
653 if ( file_of(weakKingSq) == file_of(pawnSq)
654 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
655 && ( opposite_colors(weakKingSq, strongBishopSq)
656 || relative_rank(strongSide, weakKingSq) <= RANK_6))
657 return SCALE_FACTOR_DRAW;
659 // Case 2: Opposite colored bishops
660 if (opposite_colors(strongBishopSq, weakBishopSq))
662 // We assume that the position is drawn in the following three situations:
664 // a. The pawn is on rank 5 or further back.
665 // b. The defending king is somewhere in the pawn's path.
666 // c. The defending bishop attacks some square along the pawn's path,
667 // and is at least three squares away from the pawn.
669 // These rules are probably not perfect, but in practice they work
672 if (relative_rank(strongSide, pawnSq) <= RANK_5)
673 return SCALE_FACTOR_DRAW;
676 Bitboard path = forward_bb(strongSide, pawnSq);
678 if (path & pos.pieces(weakSide, KING))
679 return SCALE_FACTOR_DRAW;
681 if ( (pos.attacks_from<BISHOP>(weakBishopSq) & path)
682 && distance(weakBishopSq, pawnSq) >= 3)
683 return SCALE_FACTOR_DRAW;
686 return SCALE_FACTOR_NONE;
690 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
692 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
694 assert(verify_material(pos, strongSide, BishopValueMg, 2));
695 assert(verify_material(pos, weakSide, BishopValueMg, 0));
697 Square wbsq = pos.square<BISHOP>(strongSide);
698 Square bbsq = pos.square<BISHOP>(weakSide);
700 if (!opposite_colors(wbsq, bbsq))
701 return SCALE_FACTOR_NONE;
703 Square ksq = pos.square<KING>(weakSide);
704 Square psq1 = pos.squares<PAWN>(strongSide)[0];
705 Square psq2 = pos.squares<PAWN>(strongSide)[1];
706 Rank r1 = rank_of(psq1);
707 Rank r2 = rank_of(psq2);
708 Square blockSq1, blockSq2;
710 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
712 blockSq1 = psq1 + pawn_push(strongSide);
713 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
717 blockSq1 = psq2 + pawn_push(strongSide);
718 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
721 switch (distance<File>(psq1, psq2))
724 // Both pawns are on the same file. It's an easy draw if the defender firmly
725 // controls some square in the frontmost pawn's path.
726 if ( file_of(ksq) == file_of(blockSq1)
727 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
728 && opposite_colors(ksq, wbsq))
729 return SCALE_FACTOR_DRAW;
731 return SCALE_FACTOR_NONE;
734 // Pawns on adjacent files. It's a draw if the defender firmly controls the
735 // square in front of the frontmost pawn's path, and the square diagonally
736 // behind this square on the file of the other pawn.
738 && opposite_colors(ksq, wbsq)
739 && ( bbsq == blockSq2
740 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
741 || distance(r1, r2) >= 2))
742 return SCALE_FACTOR_DRAW;
744 else if ( ksq == blockSq2
745 && opposite_colors(ksq, wbsq)
746 && ( bbsq == blockSq1
747 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
748 return SCALE_FACTOR_DRAW;
750 return SCALE_FACTOR_NONE;
753 // The pawns are not on the same file or adjacent files. No scaling.
754 return SCALE_FACTOR_NONE;
759 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
760 /// the path of the pawn, and the square of the king is not of the same color as
761 /// the stronger side's bishop, it's a draw.
763 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
765 assert(verify_material(pos, strongSide, BishopValueMg, 1));
766 assert(verify_material(pos, weakSide, KnightValueMg, 0));
768 Square pawnSq = pos.square<PAWN>(strongSide);
769 Square strongBishopSq = pos.square<BISHOP>(strongSide);
770 Square weakKingSq = pos.square<KING>(weakSide);
772 if ( file_of(weakKingSq) == file_of(pawnSq)
773 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
774 && ( opposite_colors(weakKingSq, strongBishopSq)
775 || relative_rank(strongSide, weakKingSq) <= RANK_6))
776 return SCALE_FACTOR_DRAW;
778 return SCALE_FACTOR_NONE;
782 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
783 /// and the defending king prevents the pawn from advancing, the position is drawn.
785 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
787 assert(verify_material(pos, strongSide, KnightValueMg, 1));
788 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
790 // Assume strongSide is white and the pawn is on files A-D
791 Square pawnSq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
792 Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
794 if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
795 return SCALE_FACTOR_DRAW;
797 return SCALE_FACTOR_NONE;
801 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
802 /// Otherwise the position is drawn.
804 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
806 Square pawnSq = pos.square<PAWN>(strongSide);
807 Square bishopSq = pos.square<BISHOP>(weakSide);
808 Square weakKingSq = pos.square<KING>(weakSide);
810 // King needs to get close to promoting pawn to prevent knight from blocking.
811 // Rules for this are very tricky, so just approximate.
812 if (forward_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
813 return ScaleFactor(distance(weakKingSq, pawnSq));
815 return SCALE_FACTOR_NONE;
819 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
820 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
821 /// has at least a draw with the pawn as well. The exception is when the stronger
822 /// side's pawn is far advanced and not on a rook file; in this case it is often
823 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
825 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
827 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
828 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
830 // Assume strongSide is white and the pawn is on files A-D
831 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
832 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
833 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
835 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
837 // If the pawn has advanced to the fifth rank or further, and is not a
838 // rook pawn, it's too dangerous to assume that it's at least a draw.
839 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
840 return SCALE_FACTOR_NONE;
842 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
843 // it's probably at least a draw even with the pawn.
844 return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;