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) 2015-2018 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 constexpr 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 constexpr 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 constexpr int PushClose[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
60 constexpr int PushAway [8] = { 0, 5, 20, 40, 60, 80, 90, 100 };
62 // Pawn Rank based scaling factors used in KRPPKRP endgame
63 constexpr 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)
89 /// Endgames members definitions
91 Endgames::Endgames() {
108 add<KBPPKB>("KBPPKB");
109 add<KRPPKRP>("KRPPKRP");
113 /// Mate with KX vs K. This function is used to evaluate positions with
114 /// king and plenty of material vs a lone king. It simply gives the
115 /// attacking side a bonus for driving the defending king towards the edge
116 /// of the board, and for keeping the distance between the two kings small.
118 Value Endgame<KXK>::operator()(const Position& pos) const {
120 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
121 assert(!pos.checkers()); // Eval is never called when in check
123 // Stalemate detection with lone king
124 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
127 Square winnerKSq = pos.square<KING>(strongSide);
128 Square loserKSq = pos.square<KING>(weakSide);
130 Value result = pos.non_pawn_material(strongSide)
131 + pos.count<PAWN>(strongSide) * PawnValueEg
132 + PushToEdges[loserKSq]
133 + PushClose[distance(winnerKSq, loserKSq)];
135 if ( pos.count<QUEEN>(strongSide)
136 || pos.count<ROOK>(strongSide)
137 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
138 || ( (pos.pieces(strongSide, BISHOP) & ~DarkSquares)
139 && (pos.pieces(strongSide, BISHOP) & DarkSquares)))
140 result = std::min(result + VALUE_KNOWN_WIN, VALUE_MATE_IN_MAX_PLY - 1);
142 return strongSide == pos.side_to_move() ? result : -result;
146 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
147 /// defending king towards a corner square of the right color.
149 Value Endgame<KBNK>::operator()(const Position& pos) const {
151 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
152 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
154 Square winnerKSq = pos.square<KING>(strongSide);
155 Square loserKSq = pos.square<KING>(weakSide);
156 Square bishopSq = pos.square<BISHOP>(strongSide);
158 // kbnk_mate_table() tries to drive toward corners A1 or H8. If we have a
159 // bishop that cannot reach the above squares, we flip the kings in order
160 // to drive the enemy toward corners A8 or H1.
161 if (opposite_colors(bishopSq, SQ_A1))
163 winnerKSq = ~winnerKSq;
164 loserKSq = ~loserKSq;
167 Value result = VALUE_KNOWN_WIN
168 + PushClose[distance(winnerKSq, loserKSq)]
169 + PushToCorners[loserKSq];
171 return strongSide == pos.side_to_move() ? result : -result;
175 /// KP vs K. This endgame is evaluated with the help of a bitbase.
177 Value Endgame<KPK>::operator()(const Position& pos) const {
179 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
180 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
182 // Assume strongSide is white and the pawn is on files A-D
183 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
184 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
185 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
187 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
189 if (!Bitbases::probe(wksq, psq, bksq, us))
192 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
194 return strongSide == pos.side_to_move() ? result : -result;
198 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
199 /// a bitbase. The function below returns drawish scores when the pawn is
200 /// far advanced with support of the king, while the attacking king is far
203 Value Endgame<KRKP>::operator()(const Position& pos) const {
205 assert(verify_material(pos, strongSide, RookValueMg, 0));
206 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
208 Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
209 Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
210 Square rsq = relative_square(strongSide, pos.square<ROOK>(strongSide));
211 Square psq = relative_square(strongSide, pos.square<PAWN>(weakSide));
213 Square queeningSq = make_square(file_of(psq), RANK_1);
216 // If the stronger side's king is in front of the pawn, it's a win
217 if (forward_file_bb(WHITE, wksq) & psq)
218 result = RookValueEg - distance(wksq, psq);
220 // If the weaker side's king is too far from the pawn and the rook,
222 else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
223 && distance(bksq, rsq) >= 3)
224 result = RookValueEg - distance(wksq, psq);
226 // If the pawn is far advanced and supported by the defending king,
227 // the position is drawish
228 else if ( rank_of(bksq) <= RANK_3
229 && distance(bksq, psq) == 1
230 && rank_of(wksq) >= RANK_4
231 && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
232 result = Value(80) - 8 * distance(wksq, psq);
235 result = Value(200) - 8 * ( distance(wksq, psq + SOUTH)
236 - distance(bksq, psq + SOUTH)
237 - distance(psq, queeningSq));
239 return strongSide == pos.side_to_move() ? result : -result;
243 /// KR vs KB. This is very simple, and always returns drawish scores. The
244 /// score is slightly bigger when the defending king is close to the edge.
246 Value Endgame<KRKB>::operator()(const Position& pos) const {
248 assert(verify_material(pos, strongSide, RookValueMg, 0));
249 assert(verify_material(pos, weakSide, BishopValueMg, 0));
251 Value result = Value(PushToEdges[pos.square<KING>(weakSide)]);
252 return strongSide == pos.side_to_move() ? result : -result;
256 /// KR vs KN. The attacking side has slightly better winning chances than
257 /// in KR vs KB, particularly if the king and the knight are far apart.
259 Value Endgame<KRKN>::operator()(const Position& pos) const {
261 assert(verify_material(pos, strongSide, RookValueMg, 0));
262 assert(verify_material(pos, weakSide, KnightValueMg, 0));
264 Square bksq = pos.square<KING>(weakSide);
265 Square bnsq = pos.square<KNIGHT>(weakSide);
266 Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
267 return strongSide == pos.side_to_move() ? result : -result;
271 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
272 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
273 /// with a king positioned next to it can be a draw, so in that case, we only
274 /// use the distance between the kings.
276 Value Endgame<KQKP>::operator()(const Position& pos) const {
278 assert(verify_material(pos, strongSide, QueenValueMg, 0));
279 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
281 Square winnerKSq = pos.square<KING>(strongSide);
282 Square loserKSq = pos.square<KING>(weakSide);
283 Square pawnSq = pos.square<PAWN>(weakSide);
285 Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
287 if ( relative_rank(weakSide, pawnSq) != RANK_7
288 || distance(loserKSq, pawnSq) != 1
289 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
290 result += QueenValueEg - PawnValueEg;
292 return strongSide == pos.side_to_move() ? result : -result;
296 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
297 /// king a bonus for having the kings close together, and for forcing the
298 /// defending king towards the edge. If we also take care to avoid null move for
299 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
301 Value Endgame<KQKR>::operator()(const Position& pos) const {
303 assert(verify_material(pos, strongSide, QueenValueMg, 0));
304 assert(verify_material(pos, weakSide, RookValueMg, 0));
306 Square winnerKSq = pos.square<KING>(strongSide);
307 Square loserKSq = pos.square<KING>(weakSide);
309 Value result = QueenValueEg
311 + PushToEdges[loserKSq]
312 + PushClose[distance(winnerKSq, loserKSq)];
314 return strongSide == pos.side_to_move() ? result : -result;
318 /// Some cases of trivial draws
319 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
322 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
323 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
324 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
327 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
329 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
330 assert(pos.count<PAWN>(strongSide) >= 1);
332 // No assertions about the material of weakSide, because we want draws to
333 // be detected even when the weaker side has some pawns.
335 Bitboard pawns = pos.pieces(strongSide, PAWN);
336 File pawnsFile = file_of(lsb(pawns));
338 // All pawns are on a single rook file?
339 if ( (pawnsFile == FILE_A || pawnsFile == FILE_H)
340 && !(pawns & ~file_bb(pawnsFile)))
342 Square bishopSq = pos.square<BISHOP>(strongSide);
343 Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
344 Square kingSq = pos.square<KING>(weakSide);
346 if ( opposite_colors(queeningSq, bishopSq)
347 && distance(queeningSq, kingSq) <= 1)
348 return SCALE_FACTOR_DRAW;
351 // If all the pawns are on the same B or G file, then it's potentially a draw
352 if ( (pawnsFile == FILE_B || pawnsFile == FILE_G)
353 && !(pos.pieces(PAWN) & ~file_bb(pawnsFile))
354 && pos.non_pawn_material(weakSide) == 0
355 && pos.count<PAWN>(weakSide) >= 1)
357 // Get weakSide pawn that is closest to the home rank
358 Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
360 Square strongKingSq = pos.square<KING>(strongSide);
361 Square weakKingSq = pos.square<KING>(weakSide);
362 Square bishopSq = pos.square<BISHOP>(strongSide);
364 // There's potential for a draw if our pawn is blocked on the 7th rank,
365 // the bishop cannot attack it or they only have one pawn left
366 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
367 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
368 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
370 int strongKingDist = distance(weakPawnSq, strongKingSq);
371 int weakKingDist = distance(weakPawnSq, weakKingSq);
373 // It's a draw if the weak king is on its back two ranks, within 2
374 // squares of the blocking pawn and the strong king is not
375 // closer. (I think this rule only fails in practically
376 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
377 // and positions where qsearch will immediately correct the
378 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
379 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
381 && weakKingDist <= strongKingDist)
382 return SCALE_FACTOR_DRAW;
386 return SCALE_FACTOR_NONE;
390 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
391 /// the third rank defended by a pawn.
393 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
395 assert(verify_material(pos, strongSide, QueenValueMg, 0));
396 assert(pos.count<ROOK>(weakSide) == 1);
397 assert(pos.count<PAWN>(weakSide) >= 1);
399 Square kingSq = pos.square<KING>(weakSide);
400 Square rsq = pos.square<ROOK>(weakSide);
402 if ( relative_rank(weakSide, kingSq) <= RANK_2
403 && relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
404 && relative_rank(weakSide, rsq) == RANK_3
405 && ( pos.pieces(weakSide, PAWN)
406 & pos.attacks_from<KING>(kingSq)
407 & pos.attacks_from<PAWN>(rsq, strongSide)))
408 return SCALE_FACTOR_DRAW;
410 return SCALE_FACTOR_NONE;
414 /// KRP vs KR. This function knows a handful of the most important classes of
415 /// drawn positions, but is far from perfect. It would probably be a good idea
416 /// to add more knowledge in the future.
418 /// It would also be nice to rewrite the actual code for this function,
419 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
421 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
423 assert(verify_material(pos, strongSide, RookValueMg, 1));
424 assert(verify_material(pos, weakSide, RookValueMg, 0));
426 // Assume strongSide is white and the pawn is on files A-D
427 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
428 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
429 Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
430 Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
431 Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
433 File f = file_of(wpsq);
434 Rank r = rank_of(wpsq);
435 Square queeningSq = make_square(f, RANK_8);
436 int tempo = (pos.side_to_move() == strongSide);
438 // If the pawn is not too far advanced and the defending king defends the
439 // queening square, use the third-rank defence.
441 && distance(bksq, queeningSq) <= 1
443 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
444 return SCALE_FACTOR_DRAW;
446 // The defending side saves a draw by checking from behind in case the pawn
447 // has advanced to the 6th rank with the king behind.
449 && distance(bksq, queeningSq) <= 1
450 && rank_of(wksq) + tempo <= RANK_6
451 && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
452 return SCALE_FACTOR_DRAW;
455 && bksq == queeningSq
456 && rank_of(brsq) == RANK_1
457 && (!tempo || distance(wksq, wpsq) >= 2))
458 return SCALE_FACTOR_DRAW;
460 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
461 // and the black rook is behind the pawn.
464 && (bksq == SQ_H7 || bksq == SQ_G7)
465 && file_of(brsq) == FILE_A
466 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
467 return SCALE_FACTOR_DRAW;
469 // If the defending king blocks the pawn and the attacking king is too far
470 // away, it's a draw.
472 && bksq == wpsq + NORTH
473 && distance(wksq, wpsq) - tempo >= 2
474 && distance(wksq, brsq) - tempo >= 2)
475 return SCALE_FACTOR_DRAW;
477 // Pawn on the 7th rank supported by the rook from behind usually wins if the
478 // attacking king is closer to the queening square than the defending king,
479 // and the defending king cannot gain tempi by threatening the attacking rook.
482 && file_of(wrsq) == f
483 && wrsq != queeningSq
484 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
485 && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
486 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
488 // Similar to the above, but with the pawn further back
490 && file_of(wrsq) == f
492 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
493 && (distance(wksq, wpsq + NORTH) < distance(bksq, wpsq + NORTH) - 2 + tempo)
494 && ( distance(bksq, wrsq) + tempo >= 3
495 || ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
496 && (distance(wksq, wpsq + NORTH) < distance(bksq, wrsq) + tempo))))
497 return ScaleFactor( SCALE_FACTOR_MAX
498 - 8 * distance(wpsq, queeningSq)
499 - 2 * distance(wksq, queeningSq));
501 // If the pawn is not far advanced and the defending king is somewhere in
502 // the pawn's path, it's probably a draw.
503 if (r <= RANK_4 && bksq > wpsq)
505 if (file_of(bksq) == file_of(wpsq))
506 return ScaleFactor(10);
507 if ( distance<File>(bksq, wpsq) == 1
508 && distance(wksq, bksq) > 2)
509 return ScaleFactor(24 - 2 * distance(wksq, bksq));
511 return SCALE_FACTOR_NONE;
515 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
517 assert(verify_material(pos, strongSide, RookValueMg, 1));
518 assert(verify_material(pos, weakSide, BishopValueMg, 0));
520 // Test for a rook pawn
521 if (pos.pieces(PAWN) & (FileABB | FileHBB))
523 Square ksq = pos.square<KING>(weakSide);
524 Square bsq = pos.square<BISHOP>(weakSide);
525 Square psq = pos.square<PAWN>(strongSide);
526 Rank rk = relative_rank(strongSide, psq);
527 Direction push = pawn_push(strongSide);
529 // If the pawn is on the 5th rank and the pawn (currently) is on
530 // the same color square as the bishop then there is a chance of
531 // a fortress. Depending on the king position give a moderate
532 // reduction or a stronger one if the defending king is near the
533 // corner but not trapped there.
534 if (rk == RANK_5 && !opposite_colors(bsq, psq))
536 int d = distance(psq + 3 * push, ksq);
538 if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
539 return ScaleFactor(24);
541 return ScaleFactor(48);
544 // When the pawn has moved to the 6th rank we can be fairly sure
545 // it's drawn if the bishop attacks the square in front of the
546 // pawn from a reasonable distance and the defending king is near
549 && distance(psq + 2 * push, ksq) <= 1
550 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
551 && distance<File>(bsq, psq) >= 2)
552 return ScaleFactor(8);
555 return SCALE_FACTOR_NONE;
558 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
559 /// pawns and the defending king is actively placed, the position is drawish.
561 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
563 assert(verify_material(pos, strongSide, RookValueMg, 2));
564 assert(verify_material(pos, weakSide, RookValueMg, 1));
566 Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
567 Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
568 Square bksq = pos.square<KING>(weakSide);
570 // Does the stronger side have a passed pawn?
571 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
572 return SCALE_FACTOR_NONE;
574 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
576 if ( distance<File>(bksq, wpsq1) <= 1
577 && distance<File>(bksq, wpsq2) <= 1
578 && relative_rank(strongSide, bksq) > r)
580 assert(r > RANK_1 && r < RANK_7);
581 return ScaleFactor(KRPPKRPScaleFactors[r]);
583 return SCALE_FACTOR_NONE;
587 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
588 /// are on the same rook file and are blocked by the defending king, it's a draw.
590 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
592 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
593 assert(pos.count<PAWN>(strongSide) >= 2);
594 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
596 Square ksq = pos.square<KING>(weakSide);
597 Bitboard pawns = pos.pieces(strongSide, PAWN);
599 // If all pawns are ahead of the king, on a single rook file and
600 // the king is within one file of the pawns, it's a draw.
601 if ( !(pawns & ~forward_ranks_bb(weakSide, ksq))
602 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
603 && distance<File>(ksq, lsb(pawns)) <= 1)
604 return SCALE_FACTOR_DRAW;
606 return SCALE_FACTOR_NONE;
610 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
611 /// path of the pawn, and the square of the king is not of the same color as the
612 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
613 /// it's almost always a draw.
615 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
617 assert(verify_material(pos, strongSide, BishopValueMg, 1));
618 assert(verify_material(pos, weakSide, BishopValueMg, 0));
620 Square pawnSq = pos.square<PAWN>(strongSide);
621 Square strongBishopSq = pos.square<BISHOP>(strongSide);
622 Square weakBishopSq = pos.square<BISHOP>(weakSide);
623 Square weakKingSq = pos.square<KING>(weakSide);
625 // Case 1: Defending king blocks the pawn, and cannot be driven away
626 if ( file_of(weakKingSq) == file_of(pawnSq)
627 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
628 && ( opposite_colors(weakKingSq, strongBishopSq)
629 || relative_rank(strongSide, weakKingSq) <= RANK_6))
630 return SCALE_FACTOR_DRAW;
632 // Case 2: Opposite colored bishops
633 if (opposite_colors(strongBishopSq, weakBishopSq))
634 return SCALE_FACTOR_DRAW;
636 return SCALE_FACTOR_NONE;
640 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
642 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
644 assert(verify_material(pos, strongSide, BishopValueMg, 2));
645 assert(verify_material(pos, weakSide, BishopValueMg, 0));
647 Square wbsq = pos.square<BISHOP>(strongSide);
648 Square bbsq = pos.square<BISHOP>(weakSide);
650 if (!opposite_colors(wbsq, bbsq))
651 return SCALE_FACTOR_NONE;
653 Square ksq = pos.square<KING>(weakSide);
654 Square psq1 = pos.squares<PAWN>(strongSide)[0];
655 Square psq2 = pos.squares<PAWN>(strongSide)[1];
656 Rank r1 = rank_of(psq1);
657 Rank r2 = rank_of(psq2);
658 Square blockSq1, blockSq2;
660 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
662 blockSq1 = psq1 + pawn_push(strongSide);
663 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
667 blockSq1 = psq2 + pawn_push(strongSide);
668 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
671 switch (distance<File>(psq1, psq2))
674 // Both pawns are on the same file. It's an easy draw if the defender firmly
675 // controls some square in the frontmost pawn's path.
676 if ( file_of(ksq) == file_of(blockSq1)
677 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
678 && opposite_colors(ksq, wbsq))
679 return SCALE_FACTOR_DRAW;
681 return SCALE_FACTOR_NONE;
684 // Pawns on adjacent files. It's a draw if the defender firmly controls the
685 // square in front of the frontmost pawn's path, and the square diagonally
686 // behind this square on the file of the other pawn.
688 && opposite_colors(ksq, wbsq)
689 && ( bbsq == blockSq2
690 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
691 || distance(r1, r2) >= 2))
692 return SCALE_FACTOR_DRAW;
694 else if ( ksq == blockSq2
695 && opposite_colors(ksq, wbsq)
696 && ( bbsq == blockSq1
697 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
698 return SCALE_FACTOR_DRAW;
700 return SCALE_FACTOR_NONE;
703 // The pawns are not on the same file or adjacent files. No scaling.
704 return SCALE_FACTOR_NONE;
709 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
710 /// the path of the pawn, and the square of the king is not of the same color as
711 /// the stronger side's bishop, it's a draw.
713 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
715 assert(verify_material(pos, strongSide, BishopValueMg, 1));
716 assert(verify_material(pos, weakSide, KnightValueMg, 0));
718 Square pawnSq = pos.square<PAWN>(strongSide);
719 Square strongBishopSq = pos.square<BISHOP>(strongSide);
720 Square weakKingSq = pos.square<KING>(weakSide);
722 if ( file_of(weakKingSq) == file_of(pawnSq)
723 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
724 && ( opposite_colors(weakKingSq, strongBishopSq)
725 || relative_rank(strongSide, weakKingSq) <= RANK_6))
726 return SCALE_FACTOR_DRAW;
728 return SCALE_FACTOR_NONE;
732 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
733 /// and the defending king prevents the pawn from advancing, the position is drawn.
735 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
737 assert(verify_material(pos, strongSide, KnightValueMg, 1));
738 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
740 // Assume strongSide is white and the pawn is on files A-D
741 Square pawnSq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
742 Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
744 if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
745 return SCALE_FACTOR_DRAW;
747 return SCALE_FACTOR_NONE;
751 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
752 /// Otherwise the position is drawn.
754 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
756 Square pawnSq = pos.square<PAWN>(strongSide);
757 Square bishopSq = pos.square<BISHOP>(weakSide);
758 Square weakKingSq = pos.square<KING>(weakSide);
760 // King needs to get close to promoting pawn to prevent knight from blocking.
761 // Rules for this are very tricky, so just approximate.
762 if (forward_file_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
763 return ScaleFactor(distance(weakKingSq, pawnSq));
765 return SCALE_FACTOR_NONE;
769 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
770 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
771 /// has at least a draw with the pawn as well. The exception is when the stronger
772 /// side's pawn is far advanced and not on a rook file; in this case it is often
773 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
775 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
777 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
778 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
780 // Assume strongSide is white and the pawn is on files A-D
781 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
782 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
783 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
785 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
787 // If the pawn has advanced to the fifth rank or further, and is not a
788 // rook pawn, it's too dangerous to assume that it's at least a draw.
789 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
790 return SCALE_FACTOR_NONE;
792 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
793 // it's probably at least a draw even with the pawn.
794 return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;