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 /// Mate with KX vs K. This function is used to evaluate positions with
90 /// king and plenty of material vs a lone king. It simply gives the
91 /// attacking side a bonus for driving the defending king towards the edge
92 /// of the board, and for keeping the distance between the two kings small.
94 Value Endgame<KXK>::operator()(const Position& pos) const {
96 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
97 assert(!pos.checkers()); // Eval is never called when in check
99 // Stalemate detection with lone king
100 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
103 Square winnerKSq = pos.square<KING>(strongSide);
104 Square loserKSq = pos.square<KING>(weakSide);
106 Value result = pos.non_pawn_material(strongSide)
107 + pos.count<PAWN>(strongSide) * PawnValueEg
108 + PushToEdges[loserKSq]
109 + PushClose[distance(winnerKSq, loserKSq)];
111 if ( pos.count<QUEEN>(strongSide)
112 || pos.count<ROOK>(strongSide)
113 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
114 || ( (pos.pieces(strongSide, BISHOP) & ~DarkSquares)
115 && (pos.pieces(strongSide, BISHOP) & DarkSquares)))
116 result = std::min(result + VALUE_KNOWN_WIN, VALUE_MATE_IN_MAX_PLY - 1);
118 return strongSide == pos.side_to_move() ? result : -result;
122 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
123 /// defending king towards a corner square of the right color.
125 Value Endgame<KBNK>::operator()(const Position& pos) const {
127 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
128 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
130 Square winnerKSq = pos.square<KING>(strongSide);
131 Square loserKSq = pos.square<KING>(weakSide);
132 Square bishopSq = pos.square<BISHOP>(strongSide);
134 // kbnk_mate_table() tries to drive toward corners A1 or H8. If we have a
135 // bishop that cannot reach the above squares, we flip the kings in order
136 // to drive the enemy toward corners A8 or H1.
137 if (opposite_colors(bishopSq, SQ_A1))
139 winnerKSq = ~winnerKSq;
140 loserKSq = ~loserKSq;
143 Value result = VALUE_KNOWN_WIN
144 + PushClose[distance(winnerKSq, loserKSq)]
145 + PushToCorners[loserKSq];
147 return strongSide == pos.side_to_move() ? result : -result;
151 /// KP vs K. This endgame is evaluated with the help of a bitbase.
153 Value Endgame<KPK>::operator()(const Position& pos) const {
155 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
156 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
158 // Assume strongSide is white and the pawn is on files A-D
159 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
160 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
161 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
163 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
165 if (!Bitbases::probe(wksq, psq, bksq, us))
168 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
170 return strongSide == pos.side_to_move() ? result : -result;
174 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
175 /// a bitbase. The function below returns drawish scores when the pawn is
176 /// far advanced with support of the king, while the attacking king is far
179 Value Endgame<KRKP>::operator()(const Position& pos) const {
181 assert(verify_material(pos, strongSide, RookValueMg, 0));
182 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
184 Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
185 Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
186 Square rsq = relative_square(strongSide, pos.square<ROOK>(strongSide));
187 Square psq = relative_square(strongSide, pos.square<PAWN>(weakSide));
189 Square queeningSq = make_square(file_of(psq), RANK_1);
192 // If the stronger side's king is in front of the pawn, it's a win
193 if (forward_file_bb(WHITE, wksq) & psq)
194 result = RookValueEg - distance(wksq, psq);
196 // If the weaker side's king is too far from the pawn and the rook,
198 else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
199 && distance(bksq, rsq) >= 3)
200 result = RookValueEg - distance(wksq, psq);
202 // If the pawn is far advanced and supported by the defending king,
203 // the position is drawish
204 else if ( rank_of(bksq) <= RANK_3
205 && distance(bksq, psq) == 1
206 && rank_of(wksq) >= RANK_4
207 && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
208 result = Value(80) - 8 * distance(wksq, psq);
211 result = Value(200) - 8 * ( distance(wksq, psq + SOUTH)
212 - distance(bksq, psq + SOUTH)
213 - distance(psq, queeningSq));
215 return strongSide == pos.side_to_move() ? result : -result;
219 /// KR vs KB. This is very simple, and always returns drawish scores. The
220 /// score is slightly bigger when the defending king is close to the edge.
222 Value Endgame<KRKB>::operator()(const Position& pos) const {
224 assert(verify_material(pos, strongSide, RookValueMg, 0));
225 assert(verify_material(pos, weakSide, BishopValueMg, 0));
227 Value result = Value(PushToEdges[pos.square<KING>(weakSide)]);
228 return strongSide == pos.side_to_move() ? result : -result;
232 /// KR vs KN. The attacking side has slightly better winning chances than
233 /// in KR vs KB, particularly if the king and the knight are far apart.
235 Value Endgame<KRKN>::operator()(const Position& pos) const {
237 assert(verify_material(pos, strongSide, RookValueMg, 0));
238 assert(verify_material(pos, weakSide, KnightValueMg, 0));
240 Square bksq = pos.square<KING>(weakSide);
241 Square bnsq = pos.square<KNIGHT>(weakSide);
242 Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
243 return strongSide == pos.side_to_move() ? result : -result;
247 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
248 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
249 /// with a king positioned next to it can be a draw, so in that case, we only
250 /// use the distance between the kings.
252 Value Endgame<KQKP>::operator()(const Position& pos) const {
254 assert(verify_material(pos, strongSide, QueenValueMg, 0));
255 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
257 Square winnerKSq = pos.square<KING>(strongSide);
258 Square loserKSq = pos.square<KING>(weakSide);
259 Square pawnSq = pos.square<PAWN>(weakSide);
261 Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
263 if ( relative_rank(weakSide, pawnSq) != RANK_7
264 || distance(loserKSq, pawnSq) != 1
265 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
266 result += QueenValueEg - PawnValueEg;
268 return strongSide == pos.side_to_move() ? result : -result;
272 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
273 /// king a bonus for having the kings close together, and for forcing the
274 /// defending king towards the edge. If we also take care to avoid null move for
275 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
277 Value Endgame<KQKR>::operator()(const Position& pos) const {
279 assert(verify_material(pos, strongSide, QueenValueMg, 0));
280 assert(verify_material(pos, weakSide, RookValueMg, 0));
282 Square winnerKSq = pos.square<KING>(strongSide);
283 Square loserKSq = pos.square<KING>(weakSide);
285 Value result = QueenValueEg
287 + PushToEdges[loserKSq]
288 + PushClose[distance(winnerKSq, loserKSq)];
290 return strongSide == pos.side_to_move() ? result : -result;
294 /// Some cases of trivial draws
295 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
298 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
299 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
300 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
303 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
305 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
306 assert(pos.count<PAWN>(strongSide) >= 1);
308 // No assertions about the material of weakSide, because we want draws to
309 // be detected even when the weaker side has some pawns.
311 Bitboard pawns = pos.pieces(strongSide, PAWN);
312 File pawnsFile = file_of(lsb(pawns));
314 // All pawns are on a single rook file?
315 if ( (pawnsFile == FILE_A || pawnsFile == FILE_H)
316 && !(pawns & ~file_bb(pawnsFile)))
318 Square bishopSq = pos.square<BISHOP>(strongSide);
319 Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
320 Square kingSq = pos.square<KING>(weakSide);
322 if ( opposite_colors(queeningSq, bishopSq)
323 && distance(queeningSq, kingSq) <= 1)
324 return SCALE_FACTOR_DRAW;
327 // If all the pawns are on the same B or G file, then it's potentially a draw
328 if ( (pawnsFile == FILE_B || pawnsFile == FILE_G)
329 && !(pos.pieces(PAWN) & ~file_bb(pawnsFile))
330 && pos.non_pawn_material(weakSide) == 0
331 && pos.count<PAWN>(weakSide) >= 1)
333 // Get weakSide pawn that is closest to the home rank
334 Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
336 Square strongKingSq = pos.square<KING>(strongSide);
337 Square weakKingSq = pos.square<KING>(weakSide);
338 Square bishopSq = pos.square<BISHOP>(strongSide);
340 // There's potential for a draw if our pawn is blocked on the 7th rank,
341 // the bishop cannot attack it or they only have one pawn left
342 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
343 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
344 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
346 int strongKingDist = distance(weakPawnSq, strongKingSq);
347 int weakKingDist = distance(weakPawnSq, weakKingSq);
349 // It's a draw if the weak king is on its back two ranks, within 2
350 // squares of the blocking pawn and the strong king is not
351 // closer. (I think this rule only fails in practically
352 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
353 // and positions where qsearch will immediately correct the
354 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
355 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
357 && weakKingDist <= strongKingDist)
358 return SCALE_FACTOR_DRAW;
362 return SCALE_FACTOR_NONE;
366 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
367 /// the third rank defended by a pawn.
369 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
371 assert(verify_material(pos, strongSide, QueenValueMg, 0));
372 assert(pos.count<ROOK>(weakSide) == 1);
373 assert(pos.count<PAWN>(weakSide) >= 1);
375 Square kingSq = pos.square<KING>(weakSide);
376 Square rsq = pos.square<ROOK>(weakSide);
378 if ( relative_rank(weakSide, kingSq) <= RANK_2
379 && relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
380 && relative_rank(weakSide, rsq) == RANK_3
381 && ( pos.pieces(weakSide, PAWN)
382 & pos.attacks_from<KING>(kingSq)
383 & pos.attacks_from<PAWN>(rsq, strongSide)))
384 return SCALE_FACTOR_DRAW;
386 return SCALE_FACTOR_NONE;
390 /// KRP vs KR. This function knows a handful of the most important classes of
391 /// drawn positions, but is far from perfect. It would probably be a good idea
392 /// to add more knowledge in the future.
394 /// It would also be nice to rewrite the actual code for this function,
395 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
397 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
399 assert(verify_material(pos, strongSide, RookValueMg, 1));
400 assert(verify_material(pos, weakSide, RookValueMg, 0));
402 // Assume strongSide is white and the pawn is on files A-D
403 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
404 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
405 Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
406 Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
407 Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
409 File f = file_of(wpsq);
410 Rank r = rank_of(wpsq);
411 Square queeningSq = make_square(f, RANK_8);
412 int tempo = (pos.side_to_move() == strongSide);
414 // If the pawn is not too far advanced and the defending king defends the
415 // queening square, use the third-rank defence.
417 && distance(bksq, queeningSq) <= 1
419 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
420 return SCALE_FACTOR_DRAW;
422 // The defending side saves a draw by checking from behind in case the pawn
423 // has advanced to the 6th rank with the king behind.
425 && distance(bksq, queeningSq) <= 1
426 && rank_of(wksq) + tempo <= RANK_6
427 && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
428 return SCALE_FACTOR_DRAW;
431 && bksq == queeningSq
432 && rank_of(brsq) == RANK_1
433 && (!tempo || distance(wksq, wpsq) >= 2))
434 return SCALE_FACTOR_DRAW;
436 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
437 // and the black rook is behind the pawn.
440 && (bksq == SQ_H7 || bksq == SQ_G7)
441 && file_of(brsq) == FILE_A
442 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
443 return SCALE_FACTOR_DRAW;
445 // If the defending king blocks the pawn and the attacking king is too far
446 // away, it's a draw.
448 && bksq == wpsq + NORTH
449 && distance(wksq, wpsq) - tempo >= 2
450 && distance(wksq, brsq) - tempo >= 2)
451 return SCALE_FACTOR_DRAW;
453 // Pawn on the 7th rank supported by the rook from behind usually wins if the
454 // attacking king is closer to the queening square than the defending king,
455 // and the defending king cannot gain tempi by threatening the attacking rook.
458 && file_of(wrsq) == f
459 && wrsq != queeningSq
460 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
461 && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
462 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
464 // Similar to the above, but with the pawn further back
466 && file_of(wrsq) == f
468 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
469 && (distance(wksq, wpsq + NORTH) < distance(bksq, wpsq + NORTH) - 2 + tempo)
470 && ( distance(bksq, wrsq) + tempo >= 3
471 || ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
472 && (distance(wksq, wpsq + NORTH) < distance(bksq, wrsq) + tempo))))
473 return ScaleFactor( SCALE_FACTOR_MAX
474 - 8 * distance(wpsq, queeningSq)
475 - 2 * distance(wksq, queeningSq));
477 // If the pawn is not far advanced and the defending king is somewhere in
478 // the pawn's path, it's probably a draw.
479 if (r <= RANK_4 && bksq > wpsq)
481 if (file_of(bksq) == file_of(wpsq))
482 return ScaleFactor(10);
483 if ( distance<File>(bksq, wpsq) == 1
484 && distance(wksq, bksq) > 2)
485 return ScaleFactor(24 - 2 * distance(wksq, bksq));
487 return SCALE_FACTOR_NONE;
491 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
493 assert(verify_material(pos, strongSide, RookValueMg, 1));
494 assert(verify_material(pos, weakSide, BishopValueMg, 0));
496 // Test for a rook pawn
497 if (pos.pieces(PAWN) & (FileABB | FileHBB))
499 Square ksq = pos.square<KING>(weakSide);
500 Square bsq = pos.square<BISHOP>(weakSide);
501 Square psq = pos.square<PAWN>(strongSide);
502 Rank rk = relative_rank(strongSide, psq);
503 Direction push = pawn_push(strongSide);
505 // If the pawn is on the 5th rank and the pawn (currently) is on
506 // the same color square as the bishop then there is a chance of
507 // a fortress. Depending on the king position give a moderate
508 // reduction or a stronger one if the defending king is near the
509 // corner but not trapped there.
510 if (rk == RANK_5 && !opposite_colors(bsq, psq))
512 int d = distance(psq + 3 * push, ksq);
514 if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
515 return ScaleFactor(24);
517 return ScaleFactor(48);
520 // When the pawn has moved to the 6th rank we can be fairly sure
521 // it's drawn if the bishop attacks the square in front of the
522 // pawn from a reasonable distance and the defending king is near
525 && distance(psq + 2 * push, ksq) <= 1
526 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
527 && distance<File>(bsq, psq) >= 2)
528 return ScaleFactor(8);
531 return SCALE_FACTOR_NONE;
534 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
535 /// pawns and the defending king is actively placed, the position is drawish.
537 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
539 assert(verify_material(pos, strongSide, RookValueMg, 2));
540 assert(verify_material(pos, weakSide, RookValueMg, 1));
542 Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
543 Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
544 Square bksq = pos.square<KING>(weakSide);
546 // Does the stronger side have a passed pawn?
547 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
548 return SCALE_FACTOR_NONE;
550 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
552 if ( distance<File>(bksq, wpsq1) <= 1
553 && distance<File>(bksq, wpsq2) <= 1
554 && relative_rank(strongSide, bksq) > r)
556 assert(r > RANK_1 && r < RANK_7);
557 return ScaleFactor(KRPPKRPScaleFactors[r]);
559 return SCALE_FACTOR_NONE;
563 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
564 /// are on the same rook file and are blocked by the defending king, it's a draw.
566 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
568 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
569 assert(pos.count<PAWN>(strongSide) >= 2);
570 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
572 Square ksq = pos.square<KING>(weakSide);
573 Bitboard pawns = pos.pieces(strongSide, PAWN);
575 // If all pawns are ahead of the king, on a single rook file and
576 // the king is within one file of the pawns, it's a draw.
577 if ( !(pawns & ~forward_ranks_bb(weakSide, ksq))
578 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
579 && distance<File>(ksq, lsb(pawns)) <= 1)
580 return SCALE_FACTOR_DRAW;
582 return SCALE_FACTOR_NONE;
586 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
587 /// path of the pawn, and the square of the king is not of the same color as the
588 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
589 /// it's almost always a draw.
591 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
593 assert(verify_material(pos, strongSide, BishopValueMg, 1));
594 assert(verify_material(pos, weakSide, BishopValueMg, 0));
596 Square pawnSq = pos.square<PAWN>(strongSide);
597 Square strongBishopSq = pos.square<BISHOP>(strongSide);
598 Square weakBishopSq = pos.square<BISHOP>(weakSide);
599 Square weakKingSq = pos.square<KING>(weakSide);
601 // Case 1: Defending king blocks the pawn, and cannot be driven away
602 if ( file_of(weakKingSq) == file_of(pawnSq)
603 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
604 && ( opposite_colors(weakKingSq, strongBishopSq)
605 || relative_rank(strongSide, weakKingSq) <= RANK_6))
606 return SCALE_FACTOR_DRAW;
608 // Case 2: Opposite colored bishops
609 if (opposite_colors(strongBishopSq, weakBishopSq))
610 return SCALE_FACTOR_DRAW;
612 return SCALE_FACTOR_NONE;
616 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
618 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
620 assert(verify_material(pos, strongSide, BishopValueMg, 2));
621 assert(verify_material(pos, weakSide, BishopValueMg, 0));
623 Square wbsq = pos.square<BISHOP>(strongSide);
624 Square bbsq = pos.square<BISHOP>(weakSide);
626 if (!opposite_colors(wbsq, bbsq))
627 return SCALE_FACTOR_NONE;
629 Square ksq = pos.square<KING>(weakSide);
630 Square psq1 = pos.squares<PAWN>(strongSide)[0];
631 Square psq2 = pos.squares<PAWN>(strongSide)[1];
632 Rank r1 = rank_of(psq1);
633 Rank r2 = rank_of(psq2);
634 Square blockSq1, blockSq2;
636 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
638 blockSq1 = psq1 + pawn_push(strongSide);
639 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
643 blockSq1 = psq2 + pawn_push(strongSide);
644 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
647 switch (distance<File>(psq1, psq2))
650 // Both pawns are on the same file. It's an easy draw if the defender firmly
651 // controls some square in the frontmost pawn's path.
652 if ( file_of(ksq) == file_of(blockSq1)
653 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
654 && opposite_colors(ksq, wbsq))
655 return SCALE_FACTOR_DRAW;
657 return SCALE_FACTOR_NONE;
660 // Pawns on adjacent files. It's a draw if the defender firmly controls the
661 // square in front of the frontmost pawn's path, and the square diagonally
662 // behind this square on the file of the other pawn.
664 && opposite_colors(ksq, wbsq)
665 && ( bbsq == blockSq2
666 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
667 || distance(r1, r2) >= 2))
668 return SCALE_FACTOR_DRAW;
670 else if ( ksq == blockSq2
671 && opposite_colors(ksq, wbsq)
672 && ( bbsq == blockSq1
673 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
674 return SCALE_FACTOR_DRAW;
676 return SCALE_FACTOR_NONE;
679 // The pawns are not on the same file or adjacent files. No scaling.
680 return SCALE_FACTOR_NONE;
685 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
686 /// the path of the pawn, and the square of the king is not of the same color as
687 /// the stronger side's bishop, it's a draw.
689 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
691 assert(verify_material(pos, strongSide, BishopValueMg, 1));
692 assert(verify_material(pos, weakSide, KnightValueMg, 0));
694 Square pawnSq = pos.square<PAWN>(strongSide);
695 Square strongBishopSq = pos.square<BISHOP>(strongSide);
696 Square weakKingSq = pos.square<KING>(weakSide);
698 if ( file_of(weakKingSq) == file_of(pawnSq)
699 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
700 && ( opposite_colors(weakKingSq, strongBishopSq)
701 || relative_rank(strongSide, weakKingSq) <= RANK_6))
702 return SCALE_FACTOR_DRAW;
704 return SCALE_FACTOR_NONE;
708 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
709 /// and the defending king prevents the pawn from advancing, the position is drawn.
711 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
713 assert(verify_material(pos, strongSide, KnightValueMg, 1));
714 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
716 // Assume strongSide is white and the pawn is on files A-D
717 Square pawnSq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
718 Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
720 if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
721 return SCALE_FACTOR_DRAW;
723 return SCALE_FACTOR_NONE;
727 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
728 /// Otherwise the position is drawn.
730 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
732 Square pawnSq = pos.square<PAWN>(strongSide);
733 Square bishopSq = pos.square<BISHOP>(weakSide);
734 Square weakKingSq = pos.square<KING>(weakSide);
736 // King needs to get close to promoting pawn to prevent knight from blocking.
737 // Rules for this are very tricky, so just approximate.
738 if (forward_file_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
739 return ScaleFactor(distance(weakKingSq, pawnSq));
741 return SCALE_FACTOR_NONE;
745 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
746 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
747 /// has at least a draw with the pawn as well. The exception is when the stronger
748 /// side's pawn is far advanced and not on a rook file; in this case it is often
749 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
751 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
753 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
754 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
756 // Assume strongSide is white and the pawn is on files A-D
757 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
758 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
759 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
761 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
763 // If the pawn has advanced to the fifth rank or further, and is not a
764 // rook pawn, it's too dangerous to assume that it's at least a draw.
765 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
766 return SCALE_FACTOR_NONE;
768 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
769 // it's probably at least a draw even with the pawn.
770 return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;