2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
4 Copyright (C) 2008-2010 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/>.
28 extern uint32_t probe_kpk_bitbase(Square wksq, Square wpsq, Square bksq, Color stm);
32 // Table used to drive the defending king towards the edge of the board
33 // in KX vs K and KQ vs KR endgames.
34 const int MateTable[64] = {
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 defending king towards a corner square of the
46 // right color in KBN vs K endgames.
47 const int KBNKMateTable[64] = {
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 // The attacking side is given a descending bonus based on distance between
59 // the two kings in basic endgames.
60 const int DistanceBonus[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
62 // Penalty for big distance between king and knight for the defending king
63 // and knight in KR vs KN endgames.
64 const int KRKNKingKnightDistancePenalty[8] = { 0, 0, 4, 10, 20, 32, 48, 70 };
66 // Build corresponding key code for the opposite color: "KBPKN" -> "KNKBP"
67 const string swap_colors(const string& keyCode) {
69 size_t idx = keyCode.find('K', 1);
70 return keyCode.substr(idx) + keyCode.substr(0, idx);
73 // Get the material key of a position out of the given endgame key code
74 // like "KBPKN". The trick here is to first build up a FEN string and then
75 // let a Position object to do the work for us. Note that the FEN string
76 // could correspond to an illegal position.
77 Key mat_key(const string& keyCode) {
79 assert(keyCode.length() > 0 && keyCode.length() < 8);
80 assert(keyCode[0] == 'K');
85 // First add white and then black pieces
86 do fen += keyCode[i]; while (keyCode[++i] != 'K');
87 do fen += char(tolower(keyCode[i])); while (++i < keyCode.length());
89 // Add file padding and remaining empty ranks
90 fen += string(1, '0' + int(8 - keyCode.length())) + "/8/8/8/8/8/8/8 w - -";
92 // Build a Position out of the fen string and get its material key
93 return Position(fen, false, 0).get_material_key();
96 typedef EndgameBase<Value> EF;
97 typedef EndgameBase<ScaleFactor> SF;
102 /// Endgames member definitions
104 template<> const Endgames::EFMap& Endgames::get<EF>() const { return maps.first; }
105 template<> const Endgames::SFMap& Endgames::get<SF>() const { return maps.second; }
107 Endgames::Endgames() {
109 add<Endgame<Value, KNNK> >("KNNK");
110 add<Endgame<Value, KPK> >("KPK");
111 add<Endgame<Value, KBNK> >("KBNK");
112 add<Endgame<Value, KRKP> >("KRKP");
113 add<Endgame<Value, KRKB> >("KRKB");
114 add<Endgame<Value, KRKN> >("KRKN");
115 add<Endgame<Value, KQKR> >("KQKR");
116 add<Endgame<Value, KBBKN> >("KBBKN");
118 add<Endgame<ScaleFactor, KNPK> >("KNPK");
119 add<Endgame<ScaleFactor, KRPKR> >("KRPKR");
120 add<Endgame<ScaleFactor, KBPKB> >("KBPKB");
121 add<Endgame<ScaleFactor, KBPPKB> >("KBPPKB");
122 add<Endgame<ScaleFactor, KBPKN> >("KBPKN");
123 add<Endgame<ScaleFactor, KRPPKRP> >("KRPPKRP");
126 Endgames::~Endgames() {
128 for (EFMap::const_iterator it = get<EF>().begin(); it != get<EF>().end(); ++it)
131 for (SFMap::const_iterator it = get<SF>().begin(); it != get<SF>().end(); ++it)
136 void Endgames::add(const string& keyCode) {
138 typedef typename T::Base F;
139 typedef std::map<Key, F*> M;
141 const_cast<M&>(get<F>()).insert(std::pair<Key, F*>(mat_key(keyCode), new T(WHITE)));
142 const_cast<M&>(get<F>()).insert(std::pair<Key, F*>(mat_key(swap_colors(keyCode)), new T(BLACK)));
146 T* Endgames::get(Key key) const {
148 typename std::map<Key, T*>::const_iterator it = get<T>().find(key);
149 return it != get<T>().end() ? it->second : NULL;
152 // Explicit template instantiations
153 template EF* Endgames::get<EF>(Key key) const;
154 template SF* Endgames::get<SF>(Key key) const;
157 /// Mate with KX vs K. This function is used to evaluate positions with
158 /// King and plenty of material vs a lone king. It simply gives the
159 /// attacking side a bonus for driving the defending king towards the edge
160 /// of the board, and for keeping the distance between the two kings small.
162 Value Endgame<Value, KXK>::apply(const Position& pos) const {
164 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
165 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
167 Square winnerKSq = pos.king_square(strongerSide);
168 Square loserKSq = pos.king_square(weakerSide);
170 Value result = pos.non_pawn_material(strongerSide)
171 + pos.piece_count(strongerSide, PAWN) * PawnValueEndgame
172 + MateTable[loserKSq]
173 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
175 if ( pos.piece_count(strongerSide, QUEEN)
176 || pos.piece_count(strongerSide, ROOK)
177 || pos.piece_count(strongerSide, BISHOP) > 1)
178 // TODO: check for two equal-colored bishops!
179 result += VALUE_KNOWN_WIN;
181 return strongerSide == pos.side_to_move() ? result : -result;
185 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
186 /// defending king towards a corner square of the right color.
188 Value Endgame<Value, KBNK>::apply(const Position& pos) const {
190 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
191 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
192 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame + BishopValueMidgame);
193 assert(pos.piece_count(strongerSide, BISHOP) == 1);
194 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
195 assert(pos.piece_count(strongerSide, PAWN) == 0);
197 Square winnerKSq = pos.king_square(strongerSide);
198 Square loserKSq = pos.king_square(weakerSide);
199 Square bishopSquare = pos.piece_list(strongerSide, BISHOP, 0);
201 // kbnk_mate_table() tries to drive toward corners A1 or H8,
202 // if we have a bishop that cannot reach the above squares we
203 // mirror the kings so to drive enemy toward corners A8 or H1.
204 if (opposite_color_squares(bishopSquare, SQ_A1))
206 winnerKSq = flop_square(winnerKSq);
207 loserKSq = flop_square(loserKSq);
210 Value result = VALUE_KNOWN_WIN
211 + DistanceBonus[square_distance(winnerKSq, loserKSq)]
212 + KBNKMateTable[loserKSq];
214 return strongerSide == pos.side_to_move() ? result : -result;
218 /// KP vs K. This endgame is evaluated with the help of a bitbase.
220 Value Endgame<Value, KPK>::apply(const Position& pos) const {
222 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
223 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
224 assert(pos.piece_count(strongerSide, PAWN) == 1);
225 assert(pos.piece_count(weakerSide, PAWN) == 0);
227 Square wksq, bksq, wpsq;
230 if (strongerSide == WHITE)
232 wksq = pos.king_square(WHITE);
233 bksq = pos.king_square(BLACK);
234 wpsq = pos.piece_list(WHITE, PAWN, 0);
235 stm = pos.side_to_move();
239 wksq = flip_square(pos.king_square(BLACK));
240 bksq = flip_square(pos.king_square(WHITE));
241 wpsq = flip_square(pos.piece_list(BLACK, PAWN, 0));
242 stm = opposite_color(pos.side_to_move());
245 if (square_file(wpsq) >= FILE_E)
247 wksq = flop_square(wksq);
248 bksq = flop_square(bksq);
249 wpsq = flop_square(wpsq);
252 if (!probe_kpk_bitbase(wksq, wpsq, bksq, stm))
255 Value result = VALUE_KNOWN_WIN
257 + Value(square_rank(wpsq));
259 return strongerSide == pos.side_to_move() ? result : -result;
263 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
264 /// a bitbase. The function below returns drawish scores when the pawn is
265 /// far advanced with support of the king, while the attacking king is far
268 Value Endgame<Value, KRKP>::apply(const Position& pos) const {
270 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
271 assert(pos.piece_count(strongerSide, PAWN) == 0);
272 assert(pos.non_pawn_material(weakerSide) == 0);
273 assert(pos.piece_count(weakerSide, PAWN) == 1);
275 Square wksq, wrsq, bksq, bpsq;
276 int tempo = (pos.side_to_move() == strongerSide);
278 wksq = pos.king_square(strongerSide);
279 wrsq = pos.piece_list(strongerSide, ROOK, 0);
280 bksq = pos.king_square(weakerSide);
281 bpsq = pos.piece_list(weakerSide, PAWN, 0);
283 if (strongerSide == BLACK)
285 wksq = flip_square(wksq);
286 wrsq = flip_square(wrsq);
287 bksq = flip_square(bksq);
288 bpsq = flip_square(bpsq);
291 Square queeningSq = make_square(square_file(bpsq), RANK_1);
294 // If the stronger side's king is in front of the pawn, it's a win
295 if (wksq < bpsq && square_file(wksq) == square_file(bpsq))
296 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
298 // If the weaker side's king is too far from the pawn and the rook,
300 else if ( square_distance(bksq, bpsq) - (tempo ^ 1) >= 3
301 && square_distance(bksq, wrsq) >= 3)
302 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
304 // If the pawn is far advanced and supported by the defending king,
305 // the position is drawish
306 else if ( square_rank(bksq) <= RANK_3
307 && square_distance(bksq, bpsq) == 1
308 && square_rank(wksq) >= RANK_4
309 && square_distance(wksq, bpsq) - tempo > 2)
310 result = Value(80 - square_distance(wksq, bpsq) * 8);
314 - Value(square_distance(wksq, bpsq + DELTA_S) * 8)
315 + Value(square_distance(bksq, bpsq + DELTA_S) * 8)
316 + Value(square_distance(bpsq, queeningSq) * 8);
318 return strongerSide == pos.side_to_move() ? result : -result;
322 /// KR vs KB. This is very simple, and always returns drawish scores. The
323 /// score is slightly bigger when the defending king is close to the edge.
325 Value Endgame<Value, KRKB>::apply(const Position& pos) const {
327 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
328 assert(pos.piece_count(strongerSide, PAWN) == 0);
329 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
330 assert(pos.piece_count(weakerSide, PAWN) == 0);
331 assert(pos.piece_count(weakerSide, BISHOP) == 1);
333 Value result = Value(MateTable[pos.king_square(weakerSide)]);
334 return strongerSide == pos.side_to_move() ? result : -result;
338 /// KR vs KN. The attacking side has slightly better winning chances than
339 /// in KR vs KB, particularly if the king and the knight are far apart.
341 Value Endgame<Value, KRKN>::apply(const Position& pos) const {
343 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
344 assert(pos.piece_count(strongerSide, PAWN) == 0);
345 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
346 assert(pos.piece_count(weakerSide, PAWN) == 0);
347 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
349 Square defendingKSq = pos.king_square(weakerSide);
350 Square nSq = pos.piece_list(weakerSide, KNIGHT, 0);
352 int d = square_distance(defendingKSq, nSq);
353 Value result = Value(10)
354 + MateTable[defendingKSq]
355 + KRKNKingKnightDistancePenalty[d];
357 return strongerSide == pos.side_to_move() ? result : -result;
361 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
362 /// king a bonus for having the kings close together, and for forcing the
363 /// defending king towards the edge. If we also take care to avoid null move
364 /// for the defending side in the search, this is usually sufficient to be
365 /// able to win KQ vs KR.
367 Value Endgame<Value, KQKR>::apply(const Position& pos) const {
369 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
370 assert(pos.piece_count(strongerSide, PAWN) == 0);
371 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
372 assert(pos.piece_count(weakerSide, PAWN) == 0);
374 Square winnerKSq = pos.king_square(strongerSide);
375 Square loserKSq = pos.king_square(weakerSide);
377 Value result = QueenValueEndgame
379 + MateTable[loserKSq]
380 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
382 return strongerSide == pos.side_to_move() ? result : -result;
386 Value Endgame<Value, KBBKN>::apply(const Position& pos) const {
388 assert(pos.piece_count(strongerSide, BISHOP) == 2);
389 assert(pos.non_pawn_material(strongerSide) == 2*BishopValueMidgame);
390 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
391 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
392 assert(pos.pieces(PAWN) == EmptyBoardBB);
394 Value result = BishopValueEndgame;
395 Square wksq = pos.king_square(strongerSide);
396 Square bksq = pos.king_square(weakerSide);
397 Square nsq = pos.piece_list(weakerSide, KNIGHT, 0);
399 // Bonus for attacking king close to defending king
400 result += Value(DistanceBonus[square_distance(wksq, bksq)]);
402 // Bonus for driving the defending king and knight apart
403 result += Value(square_distance(bksq, nsq) * 32);
405 // Bonus for restricting the knight's mobility
406 result += Value((8 - count_1s<CNT32_MAX15>(pos.attacks_from<KNIGHT>(nsq))) * 8);
408 return strongerSide == pos.side_to_move() ? result : -result;
412 /// K and two minors vs K and one or two minors or K and two knights against
413 /// king alone are always draw.
415 Value Endgame<Value, KmmKm>::apply(const Position&) const {
420 Value Endgame<Value, KNNK>::apply(const Position&) const {
424 /// KBPKScalingFunction scales endgames where the stronger side has king,
425 /// bishop and one or more pawns. It checks for draws with rook pawns and a
426 /// bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_ZERO is
427 /// returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
430 ScaleFactor Endgame<ScaleFactor, KBPsK>::apply(const Position& pos) const {
432 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
433 assert(pos.piece_count(strongerSide, BISHOP) == 1);
434 assert(pos.piece_count(strongerSide, PAWN) >= 1);
436 // No assertions about the material of weakerSide, because we want draws to
437 // be detected even when the weaker side has some pawns.
439 Bitboard pawns = pos.pieces(PAWN, strongerSide);
440 File pawnFile = square_file(pos.piece_list(strongerSide, PAWN, 0));
442 // All pawns are on a single rook file ?
443 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
444 && (pawns & ~file_bb(pawnFile)) == EmptyBoardBB)
446 Square bishopSq = pos.piece_list(strongerSide, BISHOP, 0);
447 Square queeningSq = relative_square(strongerSide, make_square(pawnFile, RANK_8));
448 Square kingSq = pos.king_square(weakerSide);
450 if ( opposite_color_squares(queeningSq, bishopSq)
451 && abs(square_file(kingSq) - pawnFile) <= 1)
453 // The bishop has the wrong color, and the defending king is on the
454 // file of the pawn(s) or the neighboring file. Find the rank of the
457 if (strongerSide == WHITE)
459 for (rank = RANK_7; (rank_bb(rank) & pawns) == EmptyBoardBB; rank--) {}
460 assert(rank >= RANK_2 && rank <= RANK_7);
464 for (rank = RANK_2; (rank_bb(rank) & pawns) == EmptyBoardBB; rank++) {}
465 rank = Rank(rank ^ 7); // HACK to get the relative rank
466 assert(rank >= RANK_2 && rank <= RANK_7);
468 // If the defending king has distance 1 to the promotion square or
469 // is placed somewhere in front of the pawn, it's a draw.
470 if ( square_distance(kingSq, queeningSq) <= 1
471 || relative_rank(strongerSide, kingSq) >= rank)
472 return SCALE_FACTOR_ZERO;
475 return SCALE_FACTOR_NONE;
479 /// KQKRPScalingFunction scales endgames where the stronger side has only
480 /// king and queen, while the weaker side has at least a rook and a pawn.
481 /// It tests for fortress draws with a rook on the third rank defended by
484 ScaleFactor Endgame<ScaleFactor, KQKRPs>::apply(const Position& pos) const {
486 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
487 assert(pos.piece_count(strongerSide, QUEEN) == 1);
488 assert(pos.piece_count(strongerSide, PAWN) == 0);
489 assert(pos.piece_count(weakerSide, ROOK) == 1);
490 assert(pos.piece_count(weakerSide, PAWN) >= 1);
492 Square kingSq = pos.king_square(weakerSide);
493 if ( relative_rank(weakerSide, kingSq) <= RANK_2
494 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
495 && (pos.pieces(ROOK, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_3)))
496 && (pos.pieces(PAWN, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_2)))
497 && (pos.attacks_from<KING>(kingSq) & pos.pieces(PAWN, weakerSide)))
499 Square rsq = pos.piece_list(weakerSide, ROOK, 0);
500 if (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(PAWN, weakerSide))
501 return SCALE_FACTOR_ZERO;
503 return SCALE_FACTOR_NONE;
507 /// KRPKRScalingFunction scales KRP vs KR endgames. This function knows a
508 /// handful of the most important classes of drawn positions, but is far
509 /// from perfect. It would probably be a good idea to add more knowledge
512 /// It would also be nice to rewrite the actual code for this function,
513 /// which is mostly copied from Glaurung 1.x, and not very pretty.
515 ScaleFactor Endgame<ScaleFactor, KRPKR>::apply(const Position& pos) const {
517 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
518 assert(pos.piece_count(strongerSide, PAWN) == 1);
519 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
520 assert(pos.piece_count(weakerSide, PAWN) == 0);
522 Square wksq = pos.king_square(strongerSide);
523 Square wrsq = pos.piece_list(strongerSide, ROOK, 0);
524 Square wpsq = pos.piece_list(strongerSide, PAWN, 0);
525 Square bksq = pos.king_square(weakerSide);
526 Square brsq = pos.piece_list(weakerSide, ROOK, 0);
528 // Orient the board in such a way that the stronger side is white, and the
529 // pawn is on the left half of the board.
530 if (strongerSide == BLACK)
532 wksq = flip_square(wksq);
533 wrsq = flip_square(wrsq);
534 wpsq = flip_square(wpsq);
535 bksq = flip_square(bksq);
536 brsq = flip_square(brsq);
538 if (square_file(wpsq) > FILE_D)
540 wksq = flop_square(wksq);
541 wrsq = flop_square(wrsq);
542 wpsq = flop_square(wpsq);
543 bksq = flop_square(bksq);
544 brsq = flop_square(brsq);
547 File f = square_file(wpsq);
548 Rank r = square_rank(wpsq);
549 Square queeningSq = make_square(f, RANK_8);
550 int tempo = (pos.side_to_move() == strongerSide);
552 // If the pawn is not too far advanced and the defending king defends the
553 // queening square, use the third-rank defence.
555 && square_distance(bksq, queeningSq) <= 1
557 && (square_rank(brsq) == RANK_6 || (r <= RANK_3 && square_rank(wrsq) != RANK_6)))
558 return SCALE_FACTOR_ZERO;
560 // The defending side saves a draw by checking from behind in case the pawn
561 // has advanced to the 6th rank with the king behind.
563 && square_distance(bksq, queeningSq) <= 1
564 && square_rank(wksq) + tempo <= RANK_6
565 && (square_rank(brsq) == RANK_1 || (!tempo && abs(square_file(brsq) - f) >= 3)))
566 return SCALE_FACTOR_ZERO;
569 && bksq == queeningSq
570 && square_rank(brsq) == RANK_1
571 && (!tempo || square_distance(wksq, wpsq) >= 2))
572 return SCALE_FACTOR_ZERO;
574 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
575 // and the black rook is behind the pawn.
578 && (bksq == SQ_H7 || bksq == SQ_G7)
579 && square_file(brsq) == FILE_A
580 && (square_rank(brsq) <= RANK_3 || square_file(wksq) >= FILE_D || square_rank(wksq) <= RANK_5))
581 return SCALE_FACTOR_ZERO;
583 // If the defending king blocks the pawn and the attacking king is too far
584 // away, it's a draw.
586 && bksq == wpsq + DELTA_N
587 && square_distance(wksq, wpsq) - tempo >= 2
588 && square_distance(wksq, brsq) - tempo >= 2)
589 return SCALE_FACTOR_ZERO;
591 // Pawn on the 7th rank supported by the rook from behind usually wins if the
592 // attacking king is closer to the queening square than the defending king,
593 // and the defending king cannot gain tempi by threatening the attacking rook.
596 && square_file(wrsq) == f
597 && wrsq != queeningSq
598 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
599 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
600 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
602 // Similar to the above, but with the pawn further back
604 && square_file(wrsq) == f
606 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
607 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
608 && ( square_distance(bksq, wrsq) + tempo >= 3
609 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
610 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
611 return ScaleFactor( SCALE_FACTOR_MAX
612 - 8 * square_distance(wpsq, queeningSq)
613 - 2 * square_distance(wksq, queeningSq));
615 // If the pawn is not far advanced, and the defending king is somewhere in
616 // the pawn's path, it's probably a draw.
617 if (r <= RANK_4 && bksq > wpsq)
619 if (square_file(bksq) == square_file(wpsq))
620 return ScaleFactor(10);
621 if ( abs(square_file(bksq) - square_file(wpsq)) == 1
622 && square_distance(wksq, bksq) > 2)
623 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
625 return SCALE_FACTOR_NONE;
629 /// KRPPKRPScalingFunction scales KRPP vs KRP endgames. There is only a
630 /// single pattern: If the stronger side has no pawns and the defending king
631 /// is actively placed, the position is drawish.
633 ScaleFactor Endgame<ScaleFactor, KRPPKRP>::apply(const Position& pos) const {
635 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
636 assert(pos.piece_count(strongerSide, PAWN) == 2);
637 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
638 assert(pos.piece_count(weakerSide, PAWN) == 1);
640 Square wpsq1 = pos.piece_list(strongerSide, PAWN, 0);
641 Square wpsq2 = pos.piece_list(strongerSide, PAWN, 1);
642 Square bksq = pos.king_square(weakerSide);
644 // Does the stronger side have a passed pawn?
645 if ( pos.pawn_is_passed(strongerSide, wpsq1)
646 || pos.pawn_is_passed(strongerSide, wpsq2))
647 return SCALE_FACTOR_NONE;
649 Rank r = Max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
651 if ( file_distance(bksq, wpsq1) <= 1
652 && file_distance(bksq, wpsq2) <= 1
653 && relative_rank(strongerSide, bksq) > r)
656 case RANK_2: return ScaleFactor(10);
657 case RANK_3: return ScaleFactor(10);
658 case RANK_4: return ScaleFactor(15);
659 case RANK_5: return ScaleFactor(20);
660 case RANK_6: return ScaleFactor(40);
661 default: assert(false);
664 return SCALE_FACTOR_NONE;
668 /// KPsKScalingFunction scales endgames with king and two or more pawns
669 /// against king. There is just a single rule here: If all pawns are on
670 /// the same rook file and are blocked by the defending king, it's a draw.
672 ScaleFactor Endgame<ScaleFactor, KPsK>::apply(const Position& pos) const {
674 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
675 assert(pos.piece_count(strongerSide, PAWN) >= 2);
676 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
677 assert(pos.piece_count(weakerSide, PAWN) == 0);
679 Square ksq = pos.king_square(weakerSide);
680 Bitboard pawns = pos.pieces(PAWN, strongerSide);
682 // Are all pawns on the 'a' file?
683 if ((pawns & ~FileABB) == EmptyBoardBB)
685 // Does the defending king block the pawns?
686 if ( square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
687 || ( square_file(ksq) == FILE_A
688 && (in_front_bb(strongerSide, ksq) & pawns) == EmptyBoardBB))
689 return SCALE_FACTOR_ZERO;
691 // Are all pawns on the 'h' file?
692 else if ((pawns & ~FileHBB) == EmptyBoardBB)
694 // Does the defending king block the pawns?
695 if ( square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
696 || ( square_file(ksq) == FILE_H
697 && (in_front_bb(strongerSide, ksq) & pawns) == EmptyBoardBB))
698 return SCALE_FACTOR_ZERO;
700 return SCALE_FACTOR_NONE;
704 /// KBPKBScalingFunction scales KBP vs KB endgames. There are two rules:
705 /// If the defending king is somewhere along the path of the pawn, and the
706 /// square of the king is not of the same color as the stronger side's bishop,
707 /// it's a draw. If the two bishops have opposite color, it's almost always
710 ScaleFactor Endgame<ScaleFactor, KBPKB>::apply(const Position& pos) const {
712 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
713 assert(pos.piece_count(strongerSide, BISHOP) == 1);
714 assert(pos.piece_count(strongerSide, PAWN) == 1);
715 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
716 assert(pos.piece_count(weakerSide, BISHOP) == 1);
717 assert(pos.piece_count(weakerSide, PAWN) == 0);
719 Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
720 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP, 0);
721 Square weakerBishopSq = pos.piece_list(weakerSide, BISHOP, 0);
722 Square weakerKingSq = pos.king_square(weakerSide);
724 // Case 1: Defending king blocks the pawn, and cannot be driven away
725 if ( square_file(weakerKingSq) == square_file(pawnSq)
726 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
727 && ( opposite_color_squares(weakerKingSq, strongerBishopSq)
728 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
729 return SCALE_FACTOR_ZERO;
731 // Case 2: Opposite colored bishops
732 if (opposite_color_squares(strongerBishopSq, weakerBishopSq))
734 // We assume that the position is drawn in the following three situations:
736 // a. The pawn is on rank 5 or further back.
737 // b. The defending king is somewhere in the pawn's path.
738 // c. The defending bishop attacks some square along the pawn's path,
739 // and is at least three squares away from the pawn.
741 // These rules are probably not perfect, but in practice they work
744 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
745 return SCALE_FACTOR_ZERO;
748 Bitboard path = squares_in_front_of(strongerSide, pawnSq);
750 if (path & pos.pieces(KING, weakerSide))
751 return SCALE_FACTOR_ZERO;
753 if ( (pos.attacks_from<BISHOP>(weakerBishopSq) & path)
754 && square_distance(weakerBishopSq, pawnSq) >= 3)
755 return SCALE_FACTOR_ZERO;
758 return SCALE_FACTOR_NONE;
762 /// KBPPKBScalingFunction scales KBPP vs KB endgames. It detects a few basic
763 /// draws with opposite-colored bishops.
765 ScaleFactor Endgame<ScaleFactor, KBPPKB>::apply(const Position& pos) const {
767 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
768 assert(pos.piece_count(strongerSide, BISHOP) == 1);
769 assert(pos.piece_count(strongerSide, PAWN) == 2);
770 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
771 assert(pos.piece_count(weakerSide, BISHOP) == 1);
772 assert(pos.piece_count(weakerSide, PAWN) == 0);
774 Square wbsq = pos.piece_list(strongerSide, BISHOP, 0);
775 Square bbsq = pos.piece_list(weakerSide, BISHOP, 0);
777 if (!opposite_color_squares(wbsq, bbsq))
778 return SCALE_FACTOR_NONE;
780 Square ksq = pos.king_square(weakerSide);
781 Square psq1 = pos.piece_list(strongerSide, PAWN, 0);
782 Square psq2 = pos.piece_list(strongerSide, PAWN, 1);
783 Rank r1 = square_rank(psq1);
784 Rank r2 = square_rank(psq2);
785 Square blockSq1, blockSq2;
787 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
789 blockSq1 = psq1 + pawn_push(strongerSide);
790 blockSq2 = make_square(square_file(psq2), square_rank(psq1));
794 blockSq1 = psq2 + pawn_push(strongerSide);
795 blockSq2 = make_square(square_file(psq1), square_rank(psq2));
798 switch (file_distance(psq1, psq2))
801 // Both pawns are on the same file. Easy draw if defender firmly controls
802 // some square in the frontmost pawn's path.
803 if ( square_file(ksq) == square_file(blockSq1)
804 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
805 && opposite_color_squares(ksq, wbsq))
806 return SCALE_FACTOR_ZERO;
808 return SCALE_FACTOR_NONE;
811 // Pawns on neighboring files. Draw if defender firmly controls the square
812 // in front of the frontmost pawn's path, and the square diagonally behind
813 // this square on the file of the other pawn.
815 && opposite_color_squares(ksq, wbsq)
816 && ( bbsq == blockSq2
817 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(BISHOP, weakerSide))
818 || abs(r1 - r2) >= 2))
819 return SCALE_FACTOR_ZERO;
821 else if ( ksq == blockSq2
822 && opposite_color_squares(ksq, wbsq)
823 && ( bbsq == blockSq1
824 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(BISHOP, weakerSide))))
825 return SCALE_FACTOR_ZERO;
827 return SCALE_FACTOR_NONE;
830 // The pawns are not on the same file or adjacent files. No scaling.
831 return SCALE_FACTOR_NONE;
836 /// KBPKNScalingFunction scales KBP vs KN endgames. There is a single rule:
837 /// If the defending king is somewhere along the path of the pawn, and the
838 /// square of the king is not of the same color as the stronger side's bishop,
841 ScaleFactor Endgame<ScaleFactor, KBPKN>::apply(const Position& pos) const {
843 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
844 assert(pos.piece_count(strongerSide, BISHOP) == 1);
845 assert(pos.piece_count(strongerSide, PAWN) == 1);
846 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
847 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
848 assert(pos.piece_count(weakerSide, PAWN) == 0);
850 Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
851 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP, 0);
852 Square weakerKingSq = pos.king_square(weakerSide);
854 if ( square_file(weakerKingSq) == square_file(pawnSq)
855 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
856 && ( opposite_color_squares(weakerKingSq, strongerBishopSq)
857 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
858 return SCALE_FACTOR_ZERO;
860 return SCALE_FACTOR_NONE;
864 /// KNPKScalingFunction scales KNP vs K endgames. There is a single rule:
865 /// If the pawn is a rook pawn on the 7th rank and the defending king prevents
866 /// the pawn from advancing, the position is drawn.
868 ScaleFactor Endgame<ScaleFactor, KNPK>::apply(const Position& pos) const {
870 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame);
871 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
872 assert(pos.piece_count(strongerSide, PAWN) == 1);
873 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
874 assert(pos.piece_count(weakerSide, PAWN) == 0);
876 Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
877 Square weakerKingSq = pos.king_square(weakerSide);
879 if ( pawnSq == relative_square(strongerSide, SQ_A7)
880 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
881 return SCALE_FACTOR_ZERO;
883 if ( pawnSq == relative_square(strongerSide, SQ_H7)
884 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
885 return SCALE_FACTOR_ZERO;
887 return SCALE_FACTOR_NONE;
891 /// KPKPScalingFunction scales KP vs KP endgames. This is done by removing
892 /// the weakest side's pawn and probing the KP vs K bitbase: If the weakest
893 /// side has a draw without the pawn, she probably has at least a draw with
894 /// the pawn as well. The exception is when the stronger side's pawn is far
895 /// advanced and not on a rook file; in this case it is often possible to win
896 /// (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
898 ScaleFactor Endgame<ScaleFactor, KPKP>::apply(const Position& pos) const {
900 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
901 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
902 assert(pos.piece_count(WHITE, PAWN) == 1);
903 assert(pos.piece_count(BLACK, PAWN) == 1);
905 Square wksq, bksq, wpsq;
908 if (strongerSide == WHITE)
910 wksq = pos.king_square(WHITE);
911 bksq = pos.king_square(BLACK);
912 wpsq = pos.piece_list(WHITE, PAWN, 0);
913 stm = pos.side_to_move();
917 wksq = flip_square(pos.king_square(BLACK));
918 bksq = flip_square(pos.king_square(WHITE));
919 wpsq = flip_square(pos.piece_list(BLACK, PAWN, 0));
920 stm = opposite_color(pos.side_to_move());
923 if (square_file(wpsq) >= FILE_E)
925 wksq = flop_square(wksq);
926 bksq = flop_square(bksq);
927 wpsq = flop_square(wpsq);
930 // If the pawn has advanced to the fifth rank or further, and is not a
931 // rook pawn, it's too dangerous to assume that it's at least a draw.
932 if ( square_rank(wpsq) >= RANK_5
933 && square_file(wpsq) != FILE_A)
934 return SCALE_FACTOR_NONE;
936 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a
937 // draw, it's probably at least a draw even with the pawn.
938 return probe_kpk_bitbase(wksq, wpsq, bksq, stm) ? SCALE_FACTOR_NONE : SCALE_FACTOR_ZERO;