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
6 Stockfish is free software: you can redistribute it and/or modify
7 it under the terms of the GNU General Public License as published by
8 the Free Software Foundation, either version 3 of the License, or
9 (at your option) any later version.
11 Stockfish is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 GNU General Public License for more details.
16 You should have received a copy of the GNU General Public License
17 along with this program. If not, see <http://www.gnu.org/licenses/>.
32 // Table used to drive the king towards the edge of the board
33 // in KX vs K and KQ vs KR endgames.
34 const int PushToEdges[SQUARE_NB] = {
35 100, 90, 80, 70, 70, 80, 90, 100,
36 90, 70, 60, 50, 50, 60, 70, 90,
37 80, 60, 40, 30, 30, 40, 60, 80,
38 70, 50, 30, 20, 20, 30, 50, 70,
39 70, 50, 30, 20, 20, 30, 50, 70,
40 80, 60, 40, 30, 30, 40, 60, 80,
41 90, 70, 60, 50, 50, 60, 70, 90,
42 100, 90, 80, 70, 70, 80, 90, 100,
45 // Table used to drive the king towards a corner square of the
46 // right color in KBN vs K endgames.
47 const int PushToCorners[SQUARE_NB] = {
48 200, 190, 180, 170, 160, 150, 140, 130,
49 190, 180, 170, 160, 150, 140, 130, 140,
50 180, 170, 155, 140, 140, 125, 140, 150,
51 170, 160, 140, 120, 110, 140, 150, 160,
52 160, 150, 140, 110, 120, 140, 160, 170,
53 150, 140, 125, 140, 140, 155, 170, 180,
54 140, 130, 140, 150, 160, 170, 180, 190,
55 130, 140, 150, 160, 170, 180, 190, 200
58 // Tables used to drive a piece towards or away from another piece
59 const int PushClose[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
60 const int PushAway [8] = { 0, 5, 20, 40, 60, 80, 90, 100 };
62 // 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";
102 return Position(fen, false, nullptr).material_key();
108 /// Endgames members definitions
110 Endgames::Endgames() {
127 add<KBPPKB>("KBPPKB");
128 add<KRPPKRP>("KRPPKRP");
132 template<EndgameType E, typename T>
133 void Endgames::add(const string& code) {
134 map<T>()[key(code, WHITE)] = std::unique_ptr<EndgameBase<T>>(new Endgame<E>(WHITE));
135 map<T>()[key(code, BLACK)] = std::unique_ptr<EndgameBase<T>>(new Endgame<E>(BLACK));
139 /// Mate with KX vs K. This function is used to evaluate positions with
140 /// king and plenty of material vs a lone king. It simply gives the
141 /// attacking side a bonus for driving the defending king towards the edge
142 /// of the board, and for keeping the distance between the two kings small.
144 Value Endgame<KXK>::operator()(const Position& pos) const {
146 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
147 assert(!pos.checkers()); // Eval is never called when in check
149 // Stalemate detection with lone king
150 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
153 Square winnerKSq = pos.square<KING>(strongSide);
154 Square loserKSq = pos.square<KING>(weakSide);
156 Value result = pos.non_pawn_material(strongSide)
157 + pos.count<PAWN>(strongSide) * PawnValueEg
158 + PushToEdges[loserKSq]
159 + PushClose[distance(winnerKSq, loserKSq)];
161 if ( pos.count<QUEEN>(strongSide)
162 || pos.count<ROOK>(strongSide)
163 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
164 ||(pos.count<BISHOP>(strongSide) > 1 && opposite_colors(pos.squares<BISHOP>(strongSide)[0],
165 pos.squares<BISHOP>(strongSide)[1])))
166 result += VALUE_KNOWN_WIN;
168 return strongSide == pos.side_to_move() ? result : -result;
172 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
173 /// defending king towards a corner square of the right color.
175 Value Endgame<KBNK>::operator()(const Position& pos) const {
177 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
178 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
180 Square winnerKSq = pos.square<KING>(strongSide);
181 Square loserKSq = pos.square<KING>(weakSide);
182 Square bishopSq = pos.square<BISHOP>(strongSide);
184 // kbnk_mate_table() tries to drive toward corners A1 or H8. If we have a
185 // bishop that cannot reach the above squares, we flip the kings in order
186 // to drive the enemy toward corners A8 or H1.
187 if (opposite_colors(bishopSq, SQ_A1))
189 winnerKSq = ~winnerKSq;
190 loserKSq = ~loserKSq;
193 Value result = VALUE_KNOWN_WIN
194 + PushClose[distance(winnerKSq, loserKSq)]
195 + PushToCorners[loserKSq];
197 return strongSide == pos.side_to_move() ? result : -result;
201 /// KP vs K. This endgame is evaluated with the help of a bitbase.
203 Value Endgame<KPK>::operator()(const Position& pos) const {
205 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
206 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
208 // Assume strongSide is white and the pawn is on files A-D
209 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
210 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
211 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
213 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
215 if (!Bitbases::probe(wksq, psq, bksq, us))
218 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
220 return strongSide == pos.side_to_move() ? result : -result;
224 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
225 /// a bitbase. The function below returns drawish scores when the pawn is
226 /// far advanced with support of the king, while the attacking king is far
229 Value Endgame<KRKP>::operator()(const Position& pos) const {
231 assert(verify_material(pos, strongSide, RookValueMg, 0));
232 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
234 Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
235 Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
236 Square rsq = relative_square(strongSide, pos.square<ROOK>(strongSide));
237 Square psq = relative_square(strongSide, pos.square<PAWN>(weakSide));
239 Square queeningSq = make_square(file_of(psq), RANK_1);
242 // If the stronger side's king is in front of the pawn, it's a win
243 if (wksq < psq && file_of(wksq) == file_of(psq))
244 result = RookValueEg - distance(wksq, psq);
246 // If the weaker side's king is too far from the pawn and the rook,
248 else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
249 && distance(bksq, rsq) >= 3)
250 result = RookValueEg - distance(wksq, psq);
252 // If the pawn is far advanced and supported by the defending king,
253 // the position is drawish
254 else if ( rank_of(bksq) <= RANK_3
255 && distance(bksq, psq) == 1
256 && rank_of(wksq) >= RANK_4
257 && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
258 result = Value(80) - 8 * distance(wksq, psq);
261 result = Value(200) - 8 * ( distance(wksq, psq + DELTA_S)
262 - distance(bksq, psq + DELTA_S)
263 - distance(psq, queeningSq));
265 return strongSide == pos.side_to_move() ? result : -result;
269 /// KR vs KB. This is very simple, and always returns drawish scores. The
270 /// score is slightly bigger when the defending king is close to the edge.
272 Value Endgame<KRKB>::operator()(const Position& pos) const {
274 assert(verify_material(pos, strongSide, RookValueMg, 0));
275 assert(verify_material(pos, weakSide, BishopValueMg, 0));
277 Value result = Value(PushToEdges[pos.square<KING>(weakSide)]);
278 return strongSide == pos.side_to_move() ? result : -result;
282 /// KR vs KN. The attacking side has slightly better winning chances than
283 /// in KR vs KB, particularly if the king and the knight are far apart.
285 Value Endgame<KRKN>::operator()(const Position& pos) const {
287 assert(verify_material(pos, strongSide, RookValueMg, 0));
288 assert(verify_material(pos, weakSide, KnightValueMg, 0));
290 Square bksq = pos.square<KING>(weakSide);
291 Square bnsq = pos.square<KNIGHT>(weakSide);
292 Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
293 return strongSide == pos.side_to_move() ? result : -result;
297 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
298 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
299 /// with a king positioned next to it can be a draw, so in that case, we only
300 /// use the distance between the kings.
302 Value Endgame<KQKP>::operator()(const Position& pos) const {
304 assert(verify_material(pos, strongSide, QueenValueMg, 0));
305 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
307 Square winnerKSq = pos.square<KING>(strongSide);
308 Square loserKSq = pos.square<KING>(weakSide);
309 Square pawnSq = pos.square<PAWN>(weakSide);
311 Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
313 if ( relative_rank(weakSide, pawnSq) != RANK_7
314 || distance(loserKSq, pawnSq) != 1
315 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
316 result += QueenValueEg - PawnValueEg;
318 return strongSide == pos.side_to_move() ? result : -result;
322 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
323 /// king a bonus for having the kings close together, and for forcing the
324 /// defending king towards the edge. If we also take care to avoid null move for
325 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
327 Value Endgame<KQKR>::operator()(const Position& pos) const {
329 assert(verify_material(pos, strongSide, QueenValueMg, 0));
330 assert(verify_material(pos, weakSide, RookValueMg, 0));
332 Square winnerKSq = pos.square<KING>(strongSide);
333 Square loserKSq = pos.square<KING>(weakSide);
335 Value result = QueenValueEg
337 + PushToEdges[loserKSq]
338 + PushClose[distance(winnerKSq, loserKSq)];
340 return strongSide == pos.side_to_move() ? result : -result;
344 /// Some cases of trivial draws
345 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
348 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
349 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
350 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
353 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
355 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
356 assert(pos.count<PAWN>(strongSide) >= 1);
358 // No assertions about the material of weakSide, because we want draws to
359 // be detected even when the weaker side has some pawns.
361 Bitboard pawns = pos.pieces(strongSide, PAWN);
362 File pawnsFile = file_of(lsb(pawns));
364 // All pawns are on a single rook file?
365 if ( (pawnsFile == FILE_A || pawnsFile == FILE_H)
366 && !(pawns & ~file_bb(pawnsFile)))
368 Square bishopSq = pos.square<BISHOP>(strongSide);
369 Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
370 Square kingSq = pos.square<KING>(weakSide);
372 if ( opposite_colors(queeningSq, bishopSq)
373 && distance(queeningSq, kingSq) <= 1)
374 return SCALE_FACTOR_DRAW;
377 // If all the pawns are on the same B or G file, then it's potentially a draw
378 if ( (pawnsFile == FILE_B || pawnsFile == FILE_G)
379 && !(pos.pieces(PAWN) & ~file_bb(pawnsFile))
380 && pos.non_pawn_material(weakSide) == 0
381 && pos.count<PAWN>(weakSide) >= 1)
383 // Get weakSide pawn that is closest to the home rank
384 Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
386 Square strongKingSq = pos.square<KING>(strongSide);
387 Square weakKingSq = pos.square<KING>(weakSide);
388 Square bishopSq = pos.square<BISHOP>(strongSide);
390 // There's potential for a draw if our pawn is blocked on the 7th rank,
391 // the bishop cannot attack it or they only have one pawn left
392 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
393 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
394 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
396 int strongKingDist = distance(weakPawnSq, strongKingSq);
397 int weakKingDist = distance(weakPawnSq, weakKingSq);
399 // It's a draw if the weak king is on its back two ranks, within 2
400 // squares of the blocking pawn and the strong king is not
401 // closer. (I think this rule only fails in practically
402 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
403 // and positions where qsearch will immediately correct the
404 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
405 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
407 && weakKingDist <= strongKingDist)
408 return SCALE_FACTOR_DRAW;
412 return SCALE_FACTOR_NONE;
416 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
417 /// the third rank defended by a pawn.
419 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
421 assert(verify_material(pos, strongSide, QueenValueMg, 0));
422 assert(pos.count<ROOK>(weakSide) == 1);
423 assert(pos.count<PAWN>(weakSide) >= 1);
425 Square kingSq = pos.square<KING>(weakSide);
426 Square rsq = pos.square<ROOK>(weakSide);
428 if ( relative_rank(weakSide, kingSq) <= RANK_2
429 && relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
430 && relative_rank(weakSide, rsq) == RANK_3
431 && ( pos.pieces(weakSide, PAWN)
432 & pos.attacks_from<KING>(kingSq)
433 & pos.attacks_from<PAWN>(rsq, strongSide)))
434 return SCALE_FACTOR_DRAW;
436 return SCALE_FACTOR_NONE;
440 /// KRP vs KR. This function knows a handful of the most important classes of
441 /// drawn positions, but is far from perfect. It would probably be a good idea
442 /// to add more knowledge in the future.
444 /// It would also be nice to rewrite the actual code for this function,
445 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
447 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
449 assert(verify_material(pos, strongSide, RookValueMg, 1));
450 assert(verify_material(pos, weakSide, RookValueMg, 0));
452 // Assume strongSide is white and the pawn is on files A-D
453 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
454 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
455 Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
456 Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
457 Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
459 File f = file_of(wpsq);
460 Rank r = rank_of(wpsq);
461 Square queeningSq = make_square(f, RANK_8);
462 int tempo = (pos.side_to_move() == strongSide);
464 // If the pawn is not too far advanced and the defending king defends the
465 // queening square, use the third-rank defence.
467 && distance(bksq, queeningSq) <= 1
469 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
470 return SCALE_FACTOR_DRAW;
472 // The defending side saves a draw by checking from behind in case the pawn
473 // has advanced to the 6th rank with the king behind.
475 && distance(bksq, queeningSq) <= 1
476 && rank_of(wksq) + tempo <= RANK_6
477 && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
478 return SCALE_FACTOR_DRAW;
481 && bksq == queeningSq
482 && rank_of(brsq) == RANK_1
483 && (!tempo || distance(wksq, wpsq) >= 2))
484 return SCALE_FACTOR_DRAW;
486 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
487 // and the black rook is behind the pawn.
490 && (bksq == SQ_H7 || bksq == SQ_G7)
491 && file_of(brsq) == FILE_A
492 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
493 return SCALE_FACTOR_DRAW;
495 // If the defending king blocks the pawn and the attacking king is too far
496 // away, it's a draw.
498 && bksq == wpsq + DELTA_N
499 && distance(wksq, wpsq) - tempo >= 2
500 && distance(wksq, brsq) - tempo >= 2)
501 return SCALE_FACTOR_DRAW;
503 // Pawn on the 7th rank supported by the rook from behind usually wins if the
504 // attacking king is closer to the queening square than the defending king,
505 // and the defending king cannot gain tempi by threatening the attacking rook.
508 && file_of(wrsq) == f
509 && wrsq != queeningSq
510 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
511 && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
512 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
514 // Similar to the above, but with the pawn further back
516 && file_of(wrsq) == f
518 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
519 && (distance(wksq, wpsq + DELTA_N) < distance(bksq, wpsq + DELTA_N) - 2 + tempo)
520 && ( distance(bksq, wrsq) + tempo >= 3
521 || ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
522 && (distance(wksq, wpsq + DELTA_N) < distance(bksq, wrsq) + tempo))))
523 return ScaleFactor( SCALE_FACTOR_MAX
524 - 8 * distance(wpsq, queeningSq)
525 - 2 * distance(wksq, queeningSq));
527 // If the pawn is not far advanced and the defending king is somewhere in
528 // the pawn's path, it's probably a draw.
529 if (r <= RANK_4 && bksq > wpsq)
531 if (file_of(bksq) == file_of(wpsq))
532 return ScaleFactor(10);
533 if ( distance<File>(bksq, wpsq) == 1
534 && distance(wksq, bksq) > 2)
535 return ScaleFactor(24 - 2 * distance(wksq, bksq));
537 return SCALE_FACTOR_NONE;
541 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
543 assert(verify_material(pos, strongSide, RookValueMg, 1));
544 assert(verify_material(pos, weakSide, BishopValueMg, 0));
546 // Test for a rook pawn
547 if (pos.pieces(PAWN) & (FileABB | FileHBB))
549 Square ksq = pos.square<KING>(weakSide);
550 Square bsq = pos.square<BISHOP>(weakSide);
551 Square psq = pos.square<PAWN>(strongSide);
552 Rank rk = relative_rank(strongSide, psq);
553 Square push = pawn_push(strongSide);
555 // If the pawn is on the 5th rank and the pawn (currently) is on
556 // the same color square as the bishop then there is a chance of
557 // a fortress. Depending on the king position give a moderate
558 // reduction or a stronger one if the defending king is near the
559 // corner but not trapped there.
560 if (rk == RANK_5 && !opposite_colors(bsq, psq))
562 int d = distance(psq + 3 * push, ksq);
564 if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
565 return ScaleFactor(24);
567 return ScaleFactor(48);
570 // When the pawn has moved to the 6th rank we can be fairly sure
571 // it's drawn if the bishop attacks the square in front of the
572 // pawn from a reasonable distance and the defending king is near
575 && distance(psq + 2 * push, ksq) <= 1
576 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
577 && distance<File>(bsq, psq) >= 2)
578 return ScaleFactor(8);
581 return SCALE_FACTOR_NONE;
584 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
585 /// pawns and the defending king is actively placed, the position is drawish.
587 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
589 assert(verify_material(pos, strongSide, RookValueMg, 2));
590 assert(verify_material(pos, weakSide, RookValueMg, 1));
592 Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
593 Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
594 Square bksq = pos.square<KING>(weakSide);
596 // Does the stronger side have a passed pawn?
597 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
598 return SCALE_FACTOR_NONE;
600 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
602 if ( distance<File>(bksq, wpsq1) <= 1
603 && distance<File>(bksq, wpsq2) <= 1
604 && relative_rank(strongSide, bksq) > r)
606 assert(r > RANK_1 && r < RANK_7);
607 return ScaleFactor(KRPPKRPScaleFactors[r]);
609 return SCALE_FACTOR_NONE;
613 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
614 /// are on the same rook file and are blocked by the defending king, it's a draw.
616 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
618 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
619 assert(pos.count<PAWN>(strongSide) >= 2);
620 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
622 Square ksq = pos.square<KING>(weakSide);
623 Bitboard pawns = pos.pieces(strongSide, PAWN);
625 // If all pawns are ahead of the king, on a single rook file and
626 // the king is within one file of the pawns, it's a draw.
627 if ( !(pawns & ~in_front_bb(weakSide, rank_of(ksq)))
628 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
629 && distance<File>(ksq, lsb(pawns)) <= 1)
630 return SCALE_FACTOR_DRAW;
632 return SCALE_FACTOR_NONE;
636 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
637 /// path of the pawn, and the square of the king is not of the same color as the
638 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
639 /// it's almost always a draw.
641 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
643 assert(verify_material(pos, strongSide, BishopValueMg, 1));
644 assert(verify_material(pos, weakSide, BishopValueMg, 0));
646 Square pawnSq = pos.square<PAWN>(strongSide);
647 Square strongBishopSq = pos.square<BISHOP>(strongSide);
648 Square weakBishopSq = pos.square<BISHOP>(weakSide);
649 Square weakKingSq = pos.square<KING>(weakSide);
651 // Case 1: Defending king blocks the pawn, and cannot be driven away
652 if ( file_of(weakKingSq) == file_of(pawnSq)
653 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
654 && ( opposite_colors(weakKingSq, strongBishopSq)
655 || relative_rank(strongSide, weakKingSq) <= RANK_6))
656 return SCALE_FACTOR_DRAW;
658 // Case 2: Opposite colored bishops
659 if (opposite_colors(strongBishopSq, weakBishopSq))
661 // We assume that the position is drawn in the following three situations:
663 // a. The pawn is on rank 5 or further back.
664 // b. The defending king is somewhere in the pawn's path.
665 // c. The defending bishop attacks some square along the pawn's path,
666 // and is at least three squares away from the pawn.
668 // These rules are probably not perfect, but in practice they work
671 if (relative_rank(strongSide, pawnSq) <= RANK_5)
672 return SCALE_FACTOR_DRAW;
675 Bitboard path = forward_bb(strongSide, pawnSq);
677 if (path & pos.pieces(weakSide, KING))
678 return SCALE_FACTOR_DRAW;
680 if ( (pos.attacks_from<BISHOP>(weakBishopSq) & path)
681 && distance(weakBishopSq, pawnSq) >= 3)
682 return SCALE_FACTOR_DRAW;
685 return SCALE_FACTOR_NONE;
689 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
691 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
693 assert(verify_material(pos, strongSide, BishopValueMg, 2));
694 assert(verify_material(pos, weakSide, BishopValueMg, 0));
696 Square wbsq = pos.square<BISHOP>(strongSide);
697 Square bbsq = pos.square<BISHOP>(weakSide);
699 if (!opposite_colors(wbsq, bbsq))
700 return SCALE_FACTOR_NONE;
702 Square ksq = pos.square<KING>(weakSide);
703 Square psq1 = pos.squares<PAWN>(strongSide)[0];
704 Square psq2 = pos.squares<PAWN>(strongSide)[1];
705 Rank r1 = rank_of(psq1);
706 Rank r2 = rank_of(psq2);
707 Square blockSq1, blockSq2;
709 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
711 blockSq1 = psq1 + pawn_push(strongSide);
712 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
716 blockSq1 = psq2 + pawn_push(strongSide);
717 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
720 switch (distance<File>(psq1, psq2))
723 // Both pawns are on the same file. It's an easy draw if the defender firmly
724 // controls some square in the frontmost pawn's path.
725 if ( file_of(ksq) == file_of(blockSq1)
726 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
727 && opposite_colors(ksq, wbsq))
728 return SCALE_FACTOR_DRAW;
730 return SCALE_FACTOR_NONE;
733 // Pawns on adjacent files. It's a draw if the defender firmly controls the
734 // square in front of the frontmost pawn's path, and the square diagonally
735 // behind this square on the file of the other pawn.
737 && opposite_colors(ksq, wbsq)
738 && ( bbsq == blockSq2
739 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
740 || distance(r1, r2) >= 2))
741 return SCALE_FACTOR_DRAW;
743 else if ( ksq == blockSq2
744 && opposite_colors(ksq, wbsq)
745 && ( bbsq == blockSq1
746 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
747 return SCALE_FACTOR_DRAW;
749 return SCALE_FACTOR_NONE;
752 // The pawns are not on the same file or adjacent files. No scaling.
753 return SCALE_FACTOR_NONE;
758 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
759 /// the path of the pawn, and the square of the king is not of the same color as
760 /// the stronger side's bishop, it's a draw.
762 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
764 assert(verify_material(pos, strongSide, BishopValueMg, 1));
765 assert(verify_material(pos, weakSide, KnightValueMg, 0));
767 Square pawnSq = pos.square<PAWN>(strongSide);
768 Square strongBishopSq = pos.square<BISHOP>(strongSide);
769 Square weakKingSq = pos.square<KING>(weakSide);
771 if ( file_of(weakKingSq) == file_of(pawnSq)
772 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
773 && ( opposite_colors(weakKingSq, strongBishopSq)
774 || relative_rank(strongSide, weakKingSq) <= RANK_6))
775 return SCALE_FACTOR_DRAW;
777 return SCALE_FACTOR_NONE;
781 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
782 /// and the defending king prevents the pawn from advancing, the position is drawn.
784 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
786 assert(verify_material(pos, strongSide, KnightValueMg, 1));
787 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
789 // Assume strongSide is white and the pawn is on files A-D
790 Square pawnSq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
791 Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
793 if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
794 return SCALE_FACTOR_DRAW;
796 return SCALE_FACTOR_NONE;
800 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
801 /// Otherwise the position is drawn.
803 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
805 Square pawnSq = pos.square<PAWN>(strongSide);
806 Square bishopSq = pos.square<BISHOP>(weakSide);
807 Square weakKingSq = pos.square<KING>(weakSide);
809 // King needs to get close to promoting pawn to prevent knight from blocking.
810 // Rules for this are very tricky, so just approximate.
811 if (forward_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
812 return ScaleFactor(distance(weakKingSq, pawnSq));
814 return SCALE_FACTOR_NONE;
818 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
819 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
820 /// has at least a draw with the pawn as well. The exception is when the stronger
821 /// side's pawn is far advanced and not on a rook file; in this case it is often
822 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
824 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
826 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
827 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
829 // Assume strongSide is white and the pawn is on files A-D
830 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
831 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
832 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
834 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
836 // If the pawn has advanced to the fifth rank or further, and is not a
837 // rook pawn, it's too dangerous to assume that it's at least a draw.
838 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
839 return SCALE_FACTOR_NONE;
841 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
842 // it's probably at least a draw even with the pawn.
843 return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;