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) 2015-2019 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 that our bishop attacks.
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 // If our Bishop does not attack A1/H8, we flip the enemy king square
135 // to drive to opposite corners (A8/H1).
137 Value result = VALUE_KNOWN_WIN
138 + PushClose[distance(winnerKSq, loserKSq)]
139 + PushToCorners[opposite_colors(bishopSq, SQ_A1) ? ~loserKSq : loserKSq];
141 return strongSide == pos.side_to_move() ? result : -result;
145 /// KP vs K. This endgame is evaluated with the help of a bitbase.
147 Value Endgame<KPK>::operator()(const Position& pos) const {
149 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
150 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
152 // Assume strongSide is white and the pawn is on files A-D
153 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
154 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
155 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
157 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
159 if (!Bitbases::probe(wksq, psq, bksq, us))
162 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
164 return strongSide == pos.side_to_move() ? result : -result;
168 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
169 /// a bitbase. The function below returns drawish scores when the pawn is
170 /// far advanced with support of the king, while the attacking king is far
173 Value Endgame<KRKP>::operator()(const Position& pos) const {
175 assert(verify_material(pos, strongSide, RookValueMg, 0));
176 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
178 Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
179 Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
180 Square rsq = relative_square(strongSide, pos.square<ROOK>(strongSide));
181 Square psq = relative_square(strongSide, pos.square<PAWN>(weakSide));
183 Square queeningSq = make_square(file_of(psq), RANK_1);
186 // If the stronger side's king is in front of the pawn, it's a win
187 if (forward_file_bb(WHITE, wksq) & psq)
188 result = RookValueEg - distance(wksq, psq);
190 // If the weaker side's king is too far from the pawn and the rook,
192 else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
193 && distance(bksq, rsq) >= 3)
194 result = RookValueEg - distance(wksq, psq);
196 // If the pawn is far advanced and supported by the defending king,
197 // the position is drawish
198 else if ( rank_of(bksq) <= RANK_3
199 && distance(bksq, psq) == 1
200 && rank_of(wksq) >= RANK_4
201 && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
202 result = Value(80) - 8 * distance(wksq, psq);
205 result = Value(200) - 8 * ( distance(wksq, psq + SOUTH)
206 - distance(bksq, psq + SOUTH)
207 - distance(psq, queeningSq));
209 return strongSide == pos.side_to_move() ? result : -result;
213 /// KR vs KB. This is very simple, and always returns drawish scores. The
214 /// score is slightly bigger when the defending king is close to the edge.
216 Value Endgame<KRKB>::operator()(const Position& pos) const {
218 assert(verify_material(pos, strongSide, RookValueMg, 0));
219 assert(verify_material(pos, weakSide, BishopValueMg, 0));
221 Value result = Value(PushToEdges[pos.square<KING>(weakSide)]);
222 return strongSide == pos.side_to_move() ? result : -result;
226 /// KR vs KN. The attacking side has slightly better winning chances than
227 /// in KR vs KB, particularly if the king and the knight are far apart.
229 Value Endgame<KRKN>::operator()(const Position& pos) const {
231 assert(verify_material(pos, strongSide, RookValueMg, 0));
232 assert(verify_material(pos, weakSide, KnightValueMg, 0));
234 Square bksq = pos.square<KING>(weakSide);
235 Square bnsq = pos.square<KNIGHT>(weakSide);
236 Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
237 return strongSide == pos.side_to_move() ? result : -result;
241 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
242 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
243 /// with a king positioned next to it can be a draw, so in that case, we only
244 /// use the distance between the kings.
246 Value Endgame<KQKP>::operator()(const Position& pos) const {
248 assert(verify_material(pos, strongSide, QueenValueMg, 0));
249 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
251 Square winnerKSq = pos.square<KING>(strongSide);
252 Square loserKSq = pos.square<KING>(weakSide);
253 Square pawnSq = pos.square<PAWN>(weakSide);
255 Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
257 if ( relative_rank(weakSide, pawnSq) != RANK_7
258 || distance(loserKSq, pawnSq) != 1
259 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
260 result += QueenValueEg - PawnValueEg;
262 return strongSide == pos.side_to_move() ? result : -result;
266 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
267 /// king a bonus for having the kings close together, and for forcing the
268 /// defending king towards the edge. If we also take care to avoid null move for
269 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
271 Value Endgame<KQKR>::operator()(const Position& pos) const {
273 assert(verify_material(pos, strongSide, QueenValueMg, 0));
274 assert(verify_material(pos, weakSide, RookValueMg, 0));
276 Square winnerKSq = pos.square<KING>(strongSide);
277 Square loserKSq = pos.square<KING>(weakSide);
279 Value result = QueenValueEg
281 + PushToEdges[loserKSq]
282 + PushClose[distance(winnerKSq, loserKSq)];
284 return strongSide == pos.side_to_move() ? result : -result;
288 /// Some cases of trivial draws
289 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
292 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
293 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
294 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
297 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
299 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
300 assert(pos.count<PAWN>(strongSide) >= 1);
302 // No assertions about the material of weakSide, because we want draws to
303 // be detected even when the weaker side has some pawns.
305 Bitboard pawns = pos.pieces(strongSide, PAWN);
306 File pawnsFile = file_of(lsb(pawns));
308 // All pawns are on a single rook file?
309 if ( (pawnsFile == FILE_A || pawnsFile == FILE_H)
310 && !(pawns & ~file_bb(pawnsFile)))
312 Square bishopSq = pos.square<BISHOP>(strongSide);
313 Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
314 Square kingSq = pos.square<KING>(weakSide);
316 if ( opposite_colors(queeningSq, bishopSq)
317 && distance(queeningSq, kingSq) <= 1)
318 return SCALE_FACTOR_DRAW;
321 // If all the pawns are on the same B or G file, then it's potentially a draw
322 if ( (pawnsFile == FILE_B || pawnsFile == FILE_G)
323 && !(pos.pieces(PAWN) & ~file_bb(pawnsFile))
324 && pos.non_pawn_material(weakSide) == 0
325 && pos.count<PAWN>(weakSide) >= 1)
327 // Get weakSide pawn that is closest to the home rank
328 Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
330 Square strongKingSq = pos.square<KING>(strongSide);
331 Square weakKingSq = pos.square<KING>(weakSide);
332 Square bishopSq = pos.square<BISHOP>(strongSide);
334 // There's potential for a draw if our pawn is blocked on the 7th rank,
335 // the bishop cannot attack it or they only have one pawn left
336 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
337 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
338 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
340 int strongKingDist = distance(weakPawnSq, strongKingSq);
341 int weakKingDist = distance(weakPawnSq, weakKingSq);
343 // It's a draw if the weak king is on its back two ranks, within 2
344 // squares of the blocking pawn and the strong king is not
345 // closer. (I think this rule only fails in practically
346 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
347 // and positions where qsearch will immediately correct the
348 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
349 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
351 && weakKingDist <= strongKingDist)
352 return SCALE_FACTOR_DRAW;
356 return SCALE_FACTOR_NONE;
360 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
361 /// the third rank defended by a pawn.
363 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
365 assert(verify_material(pos, strongSide, QueenValueMg, 0));
366 assert(pos.count<ROOK>(weakSide) == 1);
367 assert(pos.count<PAWN>(weakSide) >= 1);
369 Square kingSq = pos.square<KING>(weakSide);
370 Square rsq = pos.square<ROOK>(weakSide);
372 if ( relative_rank(weakSide, kingSq) <= RANK_2
373 && relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
374 && relative_rank(weakSide, rsq) == RANK_3
375 && ( pos.pieces(weakSide, PAWN)
376 & pos.attacks_from<KING>(kingSq)
377 & pos.attacks_from<PAWN>(rsq, strongSide)))
378 return SCALE_FACTOR_DRAW;
380 return SCALE_FACTOR_NONE;
384 /// KRP vs KR. This function knows a handful of the most important classes of
385 /// drawn positions, but is far from perfect. It would probably be a good idea
386 /// to add more knowledge in the future.
388 /// It would also be nice to rewrite the actual code for this function,
389 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
391 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
393 assert(verify_material(pos, strongSide, RookValueMg, 1));
394 assert(verify_material(pos, weakSide, RookValueMg, 0));
396 // Assume strongSide is white and the pawn is on files A-D
397 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
398 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
399 Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
400 Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
401 Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
403 File f = file_of(wpsq);
404 Rank r = rank_of(wpsq);
405 Square queeningSq = make_square(f, RANK_8);
406 int tempo = (pos.side_to_move() == strongSide);
408 // If the pawn is not too far advanced and the defending king defends the
409 // queening square, use the third-rank defence.
411 && distance(bksq, queeningSq) <= 1
413 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
414 return SCALE_FACTOR_DRAW;
416 // The defending side saves a draw by checking from behind in case the pawn
417 // has advanced to the 6th rank with the king behind.
419 && distance(bksq, queeningSq) <= 1
420 && rank_of(wksq) + tempo <= RANK_6
421 && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
422 return SCALE_FACTOR_DRAW;
425 && bksq == queeningSq
426 && rank_of(brsq) == RANK_1
427 && (!tempo || distance(wksq, wpsq) >= 2))
428 return SCALE_FACTOR_DRAW;
430 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
431 // and the black rook is behind the pawn.
434 && (bksq == SQ_H7 || bksq == SQ_G7)
435 && file_of(brsq) == FILE_A
436 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
437 return SCALE_FACTOR_DRAW;
439 // If the defending king blocks the pawn and the attacking king is too far
440 // away, it's a draw.
442 && bksq == wpsq + NORTH
443 && distance(wksq, wpsq) - tempo >= 2
444 && distance(wksq, brsq) - tempo >= 2)
445 return SCALE_FACTOR_DRAW;
447 // Pawn on the 7th rank supported by the rook from behind usually wins if the
448 // attacking king is closer to the queening square than the defending king,
449 // and the defending king cannot gain tempi by threatening the attacking rook.
452 && file_of(wrsq) == f
453 && wrsq != queeningSq
454 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
455 && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
456 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
458 // Similar to the above, but with the pawn further back
460 && file_of(wrsq) == f
462 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
463 && (distance(wksq, wpsq + NORTH) < distance(bksq, wpsq + NORTH) - 2 + tempo)
464 && ( distance(bksq, wrsq) + tempo >= 3
465 || ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
466 && (distance(wksq, wpsq + NORTH) < distance(bksq, wrsq) + tempo))))
467 return ScaleFactor( SCALE_FACTOR_MAX
468 - 8 * distance(wpsq, queeningSq)
469 - 2 * distance(wksq, queeningSq));
471 // If the pawn is not far advanced and the defending king is somewhere in
472 // the pawn's path, it's probably a draw.
473 if (r <= RANK_4 && bksq > wpsq)
475 if (file_of(bksq) == file_of(wpsq))
476 return ScaleFactor(10);
477 if ( distance<File>(bksq, wpsq) == 1
478 && distance(wksq, bksq) > 2)
479 return ScaleFactor(24 - 2 * distance(wksq, bksq));
481 return SCALE_FACTOR_NONE;
485 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
487 assert(verify_material(pos, strongSide, RookValueMg, 1));
488 assert(verify_material(pos, weakSide, BishopValueMg, 0));
490 // Test for a rook pawn
491 if (pos.pieces(PAWN) & (FileABB | FileHBB))
493 Square ksq = pos.square<KING>(weakSide);
494 Square bsq = pos.square<BISHOP>(weakSide);
495 Square psq = pos.square<PAWN>(strongSide);
496 Rank rk = relative_rank(strongSide, psq);
497 Direction push = pawn_push(strongSide);
499 // If the pawn is on the 5th rank and the pawn (currently) is on
500 // the same color square as the bishop then there is a chance of
501 // a fortress. Depending on the king position give a moderate
502 // reduction or a stronger one if the defending king is near the
503 // corner but not trapped there.
504 if (rk == RANK_5 && !opposite_colors(bsq, psq))
506 int d = distance(psq + 3 * push, ksq);
508 if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
509 return ScaleFactor(24);
511 return ScaleFactor(48);
514 // When the pawn has moved to the 6th rank we can be fairly sure
515 // it's drawn if the bishop attacks the square in front of the
516 // pawn from a reasonable distance and the defending king is near
519 && distance(psq + 2 * push, ksq) <= 1
520 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
521 && distance<File>(bsq, psq) >= 2)
522 return ScaleFactor(8);
525 return SCALE_FACTOR_NONE;
528 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
529 /// pawns and the defending king is actively placed, the position is drawish.
531 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
533 assert(verify_material(pos, strongSide, RookValueMg, 2));
534 assert(verify_material(pos, weakSide, RookValueMg, 1));
536 Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
537 Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
538 Square bksq = pos.square<KING>(weakSide);
540 // Does the stronger side have a passed pawn?
541 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
542 return SCALE_FACTOR_NONE;
544 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
546 if ( distance<File>(bksq, wpsq1) <= 1
547 && distance<File>(bksq, wpsq2) <= 1
548 && relative_rank(strongSide, bksq) > r)
550 assert(r > RANK_1 && r < RANK_7);
551 return ScaleFactor(KRPPKRPScaleFactors[r]);
553 return SCALE_FACTOR_NONE;
557 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
558 /// are on the same rook file and are blocked by the defending king, it's a draw.
560 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
562 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
563 assert(pos.count<PAWN>(strongSide) >= 2);
564 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
566 Square ksq = pos.square<KING>(weakSide);
567 Bitboard pawns = pos.pieces(strongSide, PAWN);
569 // If all pawns are ahead of the king, on a single rook file and
570 // the king is within one file of the pawns, it's a draw.
571 if ( !(pawns & ~forward_ranks_bb(weakSide, ksq))
572 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
573 && distance<File>(ksq, lsb(pawns)) <= 1)
574 return SCALE_FACTOR_DRAW;
576 return SCALE_FACTOR_NONE;
580 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
581 /// path of the pawn, and the square of the king is not of the same color as the
582 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
583 /// it's almost always a draw.
585 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
587 assert(verify_material(pos, strongSide, BishopValueMg, 1));
588 assert(verify_material(pos, weakSide, BishopValueMg, 0));
590 Square pawnSq = pos.square<PAWN>(strongSide);
591 Square strongBishopSq = pos.square<BISHOP>(strongSide);
592 Square weakBishopSq = pos.square<BISHOP>(weakSide);
593 Square weakKingSq = pos.square<KING>(weakSide);
595 // Case 1: Defending king blocks the pawn, and cannot be driven away
596 if ( file_of(weakKingSq) == file_of(pawnSq)
597 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
598 && ( opposite_colors(weakKingSq, strongBishopSq)
599 || relative_rank(strongSide, weakKingSq) <= RANK_6))
600 return SCALE_FACTOR_DRAW;
602 // Case 2: Opposite colored bishops
603 if (opposite_colors(strongBishopSq, weakBishopSq))
604 return SCALE_FACTOR_DRAW;
606 return SCALE_FACTOR_NONE;
610 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
612 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
614 assert(verify_material(pos, strongSide, BishopValueMg, 2));
615 assert(verify_material(pos, weakSide, BishopValueMg, 0));
617 Square wbsq = pos.square<BISHOP>(strongSide);
618 Square bbsq = pos.square<BISHOP>(weakSide);
620 if (!opposite_colors(wbsq, bbsq))
621 return SCALE_FACTOR_NONE;
623 Square ksq = pos.square<KING>(weakSide);
624 Square psq1 = pos.squares<PAWN>(strongSide)[0];
625 Square psq2 = pos.squares<PAWN>(strongSide)[1];
626 Rank r1 = rank_of(psq1);
627 Rank r2 = rank_of(psq2);
628 Square blockSq1, blockSq2;
630 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
632 blockSq1 = psq1 + pawn_push(strongSide);
633 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
637 blockSq1 = psq2 + pawn_push(strongSide);
638 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
641 switch (distance<File>(psq1, psq2))
644 // Both pawns are on the same file. It's an easy draw if the defender firmly
645 // controls some square in the frontmost pawn's path.
646 if ( file_of(ksq) == file_of(blockSq1)
647 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
648 && opposite_colors(ksq, wbsq))
649 return SCALE_FACTOR_DRAW;
651 return SCALE_FACTOR_NONE;
654 // Pawns on adjacent files. It's a draw if the defender firmly controls the
655 // square in front of the frontmost pawn's path, and the square diagonally
656 // behind this square on the file of the other pawn.
658 && opposite_colors(ksq, wbsq)
659 && ( bbsq == blockSq2
660 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
661 || distance(r1, r2) >= 2))
662 return SCALE_FACTOR_DRAW;
664 else if ( ksq == blockSq2
665 && opposite_colors(ksq, wbsq)
666 && ( bbsq == blockSq1
667 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
668 return SCALE_FACTOR_DRAW;
670 return SCALE_FACTOR_NONE;
673 // The pawns are not on the same file or adjacent files. No scaling.
674 return SCALE_FACTOR_NONE;
679 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
680 /// the path of the pawn, and the square of the king is not of the same color as
681 /// the stronger side's bishop, it's a draw.
683 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
685 assert(verify_material(pos, strongSide, BishopValueMg, 1));
686 assert(verify_material(pos, weakSide, KnightValueMg, 0));
688 Square pawnSq = pos.square<PAWN>(strongSide);
689 Square strongBishopSq = pos.square<BISHOP>(strongSide);
690 Square weakKingSq = pos.square<KING>(weakSide);
692 if ( file_of(weakKingSq) == file_of(pawnSq)
693 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
694 && ( opposite_colors(weakKingSq, strongBishopSq)
695 || relative_rank(strongSide, weakKingSq) <= RANK_6))
696 return SCALE_FACTOR_DRAW;
698 return SCALE_FACTOR_NONE;
702 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
703 /// and the defending king prevents the pawn from advancing, the position is drawn.
705 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
707 assert(verify_material(pos, strongSide, KnightValueMg, 1));
708 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
710 // Assume strongSide is white and the pawn is on files A-D
711 Square pawnSq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
712 Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
714 if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
715 return SCALE_FACTOR_DRAW;
717 return SCALE_FACTOR_NONE;
721 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
722 /// Otherwise the position is drawn.
724 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
726 Square pawnSq = pos.square<PAWN>(strongSide);
727 Square bishopSq = pos.square<BISHOP>(weakSide);
728 Square weakKingSq = pos.square<KING>(weakSide);
730 // King needs to get close to promoting pawn to prevent knight from blocking.
731 // Rules for this are very tricky, so just approximate.
732 if (forward_file_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
733 return ScaleFactor(distance(weakKingSq, pawnSq));
735 return SCALE_FACTOR_NONE;
739 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
740 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
741 /// has at least a draw with the pawn as well. The exception is when the stronger
742 /// side's pawn is far advanced and not on a rook file; in this case it is often
743 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
745 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
747 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
748 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
750 // Assume strongSide is white and the pawn is on files A-D
751 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
752 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
753 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
755 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
757 // If the pawn has advanced to the fifth rank or further, and is not a
758 // rook pawn, it's too dangerous to assume that it's at least a draw.
759 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
760 return SCALE_FACTOR_NONE;
762 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
763 // it's probably at least a draw even with the pawn.
764 return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;