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 - - 0 10";
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::map<EF>() const { return maps.first; }
105 template<> const Endgames::SFMap& Endgames::map<SF>() const { return maps.second; }
107 Endgames::Endgames() {
109 add<Value, KPK>("KPK");
110 add<Value, KNNK>("KNNK");
111 add<Value, KBNK>("KBNK");
112 add<Value, KRKP>("KRKP");
113 add<Value, KRKB>("KRKB");
114 add<Value, KRKN>("KRKN");
115 add<Value, KQKR>("KQKR");
116 add<Value, KBBKN>("KBBKN");
118 add<ScaleFactor, KNPK>("KNPK");
119 add<ScaleFactor, KRPKR>("KRPKR");
120 add<ScaleFactor, KBPKB>("KBPKB");
121 add<ScaleFactor, KBPKN>("KBPKN");
122 add<ScaleFactor, KBPPKB>("KBPPKB");
123 add<ScaleFactor, KRPPKRP>("KRPPKRP");
126 Endgames::~Endgames() {
128 for (EFMap::const_iterator it = map<EF>().begin(); it != map<EF>().end(); ++it)
131 for (SFMap::const_iterator it = map<SF>().begin(); it != map<SF>().end(); ++it)
135 template<typename T, EndgameType E>
136 void Endgames::add(const string& keyCode) {
138 typedef Endgame<T, E> EG;
139 typedef typename EG::Base B;
140 typedef std::map<Key, B*> M;
142 const_cast<M&>(map<B>()).insert(std::pair<Key, B*>(mat_key(keyCode), new EG(WHITE)));
143 const_cast<M&>(map<B>()).insert(std::pair<Key, B*>(mat_key(swap_colors(keyCode)), new EG(BLACK)));
147 EndgameBase<T>* Endgames::get(Key key) const {
149 typedef EndgameBase<T> E;
150 typename std::map<Key, E*>::const_iterator it = map<E>().find(key);
151 return it != map<E>().end() ? it->second : NULL;
154 // Explicit template instantiations
155 template EF* Endgames::get<Value>(Key key) const;
156 template SF* Endgames::get<ScaleFactor>(Key key) const;
159 /// Mate with KX vs K. This function is used to evaluate positions with
160 /// King and plenty of material vs a lone king. It simply gives the
161 /// attacking side a bonus for driving the defending king towards the edge
162 /// of the board, and for keeping the distance between the two kings small.
164 Value Endgame<Value, KXK>::apply(const Position& pos) const {
166 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
167 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
169 Square winnerKSq = pos.king_square(strongerSide);
170 Square loserKSq = pos.king_square(weakerSide);
172 Value result = pos.non_pawn_material(strongerSide)
173 + pos.piece_count(strongerSide, PAWN) * PawnValueEndgame
174 + MateTable[loserKSq]
175 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
177 if ( pos.piece_count(strongerSide, QUEEN)
178 || pos.piece_count(strongerSide, ROOK)
179 || pos.piece_count(strongerSide, BISHOP) > 1)
180 // TODO: check for two equal-colored bishops!
181 result += VALUE_KNOWN_WIN;
183 return strongerSide == pos.side_to_move() ? result : -result;
187 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
188 /// defending king towards a corner square of the right color.
190 Value Endgame<Value, KBNK>::apply(const Position& pos) const {
192 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
193 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
194 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame + BishopValueMidgame);
195 assert(pos.piece_count(strongerSide, BISHOP) == 1);
196 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
197 assert(pos.piece_count(strongerSide, PAWN) == 0);
199 Square winnerKSq = pos.king_square(strongerSide);
200 Square loserKSq = pos.king_square(weakerSide);
201 Square bishopSquare = pos.piece_list(strongerSide, BISHOP)[0];
203 // kbnk_mate_table() tries to drive toward corners A1 or H8,
204 // if we have a bishop that cannot reach the above squares we
205 // mirror the kings so to drive enemy toward corners A8 or H1.
206 if (opposite_color_squares(bishopSquare, SQ_A1))
208 winnerKSq = flop_square(winnerKSq);
209 loserKSq = flop_square(loserKSq);
212 Value result = VALUE_KNOWN_WIN
213 + DistanceBonus[square_distance(winnerKSq, loserKSq)]
214 + KBNKMateTable[loserKSq];
216 return strongerSide == pos.side_to_move() ? result : -result;
220 /// KP vs K. This endgame is evaluated with the help of a bitbase.
222 Value Endgame<Value, KPK>::apply(const Position& pos) const {
224 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
225 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
226 assert(pos.piece_count(strongerSide, PAWN) == 1);
227 assert(pos.piece_count(weakerSide, PAWN) == 0);
229 Square wksq, bksq, wpsq;
232 if (strongerSide == WHITE)
234 wksq = pos.king_square(WHITE);
235 bksq = pos.king_square(BLACK);
236 wpsq = pos.piece_list(WHITE, PAWN)[0];
237 stm = pos.side_to_move();
241 wksq = flip_square(pos.king_square(BLACK));
242 bksq = flip_square(pos.king_square(WHITE));
243 wpsq = flip_square(pos.piece_list(BLACK, PAWN)[0]);
244 stm = opposite_color(pos.side_to_move());
247 if (square_file(wpsq) >= FILE_E)
249 wksq = flop_square(wksq);
250 bksq = flop_square(bksq);
251 wpsq = flop_square(wpsq);
254 if (!probe_kpk_bitbase(wksq, wpsq, bksq, stm))
257 Value result = VALUE_KNOWN_WIN
259 + Value(square_rank(wpsq));
261 return strongerSide == pos.side_to_move() ? result : -result;
265 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
266 /// a bitbase. The function below returns drawish scores when the pawn is
267 /// far advanced with support of the king, while the attacking king is far
270 Value Endgame<Value, KRKP>::apply(const Position& pos) const {
272 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
273 assert(pos.piece_count(strongerSide, PAWN) == 0);
274 assert(pos.non_pawn_material(weakerSide) == 0);
275 assert(pos.piece_count(weakerSide, PAWN) == 1);
277 Square wksq, wrsq, bksq, bpsq;
278 int tempo = (pos.side_to_move() == strongerSide);
280 wksq = pos.king_square(strongerSide);
281 wrsq = pos.piece_list(strongerSide, ROOK)[0];
282 bksq = pos.king_square(weakerSide);
283 bpsq = pos.piece_list(weakerSide, PAWN)[0];
285 if (strongerSide == BLACK)
287 wksq = flip_square(wksq);
288 wrsq = flip_square(wrsq);
289 bksq = flip_square(bksq);
290 bpsq = flip_square(bpsq);
293 Square queeningSq = make_square(square_file(bpsq), RANK_1);
296 // If the stronger side's king is in front of the pawn, it's a win
297 if (wksq < bpsq && square_file(wksq) == square_file(bpsq))
298 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
300 // If the weaker side's king is too far from the pawn and the rook,
302 else if ( square_distance(bksq, bpsq) - (tempo ^ 1) >= 3
303 && square_distance(bksq, wrsq) >= 3)
304 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
306 // If the pawn is far advanced and supported by the defending king,
307 // the position is drawish
308 else if ( square_rank(bksq) <= RANK_3
309 && square_distance(bksq, bpsq) == 1
310 && square_rank(wksq) >= RANK_4
311 && square_distance(wksq, bpsq) - tempo > 2)
312 result = Value(80 - square_distance(wksq, bpsq) * 8);
316 - Value(square_distance(wksq, bpsq + DELTA_S) * 8)
317 + Value(square_distance(bksq, bpsq + DELTA_S) * 8)
318 + Value(square_distance(bpsq, queeningSq) * 8);
320 return strongerSide == pos.side_to_move() ? result : -result;
324 /// KR vs KB. This is very simple, and always returns drawish scores. The
325 /// score is slightly bigger when the defending king is close to the edge.
327 Value Endgame<Value, KRKB>::apply(const Position& pos) const {
329 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
330 assert(pos.piece_count(strongerSide, PAWN) == 0);
331 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
332 assert(pos.piece_count(weakerSide, PAWN) == 0);
333 assert(pos.piece_count(weakerSide, BISHOP) == 1);
335 Value result = Value(MateTable[pos.king_square(weakerSide)]);
336 return strongerSide == pos.side_to_move() ? result : -result;
340 /// KR vs KN. The attacking side has slightly better winning chances than
341 /// in KR vs KB, particularly if the king and the knight are far apart.
343 Value Endgame<Value, KRKN>::apply(const Position& pos) const {
345 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
346 assert(pos.piece_count(strongerSide, PAWN) == 0);
347 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
348 assert(pos.piece_count(weakerSide, PAWN) == 0);
349 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
351 Square defendingKSq = pos.king_square(weakerSide);
352 Square nSq = pos.piece_list(weakerSide, KNIGHT)[0];
354 int d = square_distance(defendingKSq, nSq);
355 Value result = Value(10)
356 + MateTable[defendingKSq]
357 + KRKNKingKnightDistancePenalty[d];
359 return strongerSide == pos.side_to_move() ? result : -result;
363 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
364 /// king a bonus for having the kings close together, and for forcing the
365 /// defending king towards the edge. If we also take care to avoid null move
366 /// for the defending side in the search, this is usually sufficient to be
367 /// able to win KQ vs KR.
369 Value Endgame<Value, KQKR>::apply(const Position& pos) const {
371 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
372 assert(pos.piece_count(strongerSide, PAWN) == 0);
373 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
374 assert(pos.piece_count(weakerSide, PAWN) == 0);
376 Square winnerKSq = pos.king_square(strongerSide);
377 Square loserKSq = pos.king_square(weakerSide);
379 Value result = QueenValueEndgame
381 + MateTable[loserKSq]
382 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
384 return strongerSide == pos.side_to_move() ? result : -result;
388 Value Endgame<Value, KBBKN>::apply(const Position& pos) const {
390 assert(pos.piece_count(strongerSide, BISHOP) == 2);
391 assert(pos.non_pawn_material(strongerSide) == 2*BishopValueMidgame);
392 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
393 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
394 assert(pos.pieces(PAWN) == EmptyBoardBB);
396 Value result = BishopValueEndgame;
397 Square wksq = pos.king_square(strongerSide);
398 Square bksq = pos.king_square(weakerSide);
399 Square nsq = pos.piece_list(weakerSide, KNIGHT)[0];
401 // Bonus for attacking king close to defending king
402 result += Value(DistanceBonus[square_distance(wksq, bksq)]);
404 // Bonus for driving the defending king and knight apart
405 result += Value(square_distance(bksq, nsq) * 32);
407 // Bonus for restricting the knight's mobility
408 result += Value((8 - count_1s<CNT32_MAX15>(pos.attacks_from<KNIGHT>(nsq))) * 8);
410 return strongerSide == pos.side_to_move() ? result : -result;
414 /// K and two minors vs K and one or two minors or K and two knights against
415 /// king alone are always draw.
417 Value Endgame<Value, KmmKm>::apply(const Position&) const {
422 Value Endgame<Value, KNNK>::apply(const Position&) const {
426 /// KBPKScalingFunction scales endgames where the stronger side has king,
427 /// bishop and one or more pawns. It checks for draws with rook pawns and a
428 /// bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_ZERO is
429 /// returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
432 ScaleFactor Endgame<ScaleFactor, KBPsK>::apply(const Position& pos) const {
434 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
435 assert(pos.piece_count(strongerSide, BISHOP) == 1);
436 assert(pos.piece_count(strongerSide, PAWN) >= 1);
438 // No assertions about the material of weakerSide, because we want draws to
439 // be detected even when the weaker side has some pawns.
441 Bitboard pawns = pos.pieces(PAWN, strongerSide);
442 File pawnFile = square_file(pos.piece_list(strongerSide, PAWN)[0]);
444 // All pawns are on a single rook file ?
445 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
446 && (pawns & ~file_bb(pawnFile)) == EmptyBoardBB)
448 Square bishopSq = pos.piece_list(strongerSide, BISHOP)[0];
449 Square queeningSq = relative_square(strongerSide, make_square(pawnFile, RANK_8));
450 Square kingSq = pos.king_square(weakerSide);
452 if ( opposite_color_squares(queeningSq, bishopSq)
453 && abs(square_file(kingSq) - pawnFile) <= 1)
455 // The bishop has the wrong color, and the defending king is on the
456 // file of the pawn(s) or the neighboring file. Find the rank of the
459 if (strongerSide == WHITE)
461 for (rank = RANK_7; (rank_bb(rank) & pawns) == EmptyBoardBB; rank--) {}
462 assert(rank >= RANK_2 && rank <= RANK_7);
466 for (rank = RANK_2; (rank_bb(rank) & pawns) == EmptyBoardBB; rank++) {}
467 rank = Rank(rank ^ 7); // HACK to get the relative rank
468 assert(rank >= RANK_2 && rank <= RANK_7);
470 // If the defending king has distance 1 to the promotion square or
471 // is placed somewhere in front of the pawn, it's a draw.
472 if ( square_distance(kingSq, queeningSq) <= 1
473 || relative_rank(strongerSide, kingSq) >= rank)
474 return SCALE_FACTOR_ZERO;
477 return SCALE_FACTOR_NONE;
481 /// KQKRPScalingFunction scales endgames where the stronger side has only
482 /// king and queen, while the weaker side has at least a rook and a pawn.
483 /// It tests for fortress draws with a rook on the third rank defended by
486 ScaleFactor Endgame<ScaleFactor, KQKRPs>::apply(const Position& pos) const {
488 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
489 assert(pos.piece_count(strongerSide, QUEEN) == 1);
490 assert(pos.piece_count(strongerSide, PAWN) == 0);
491 assert(pos.piece_count(weakerSide, ROOK) == 1);
492 assert(pos.piece_count(weakerSide, PAWN) >= 1);
494 Square kingSq = pos.king_square(weakerSide);
495 if ( relative_rank(weakerSide, kingSq) <= RANK_2
496 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
497 && (pos.pieces(ROOK, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_3)))
498 && (pos.pieces(PAWN, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_2)))
499 && (pos.attacks_from<KING>(kingSq) & pos.pieces(PAWN, weakerSide)))
501 Square rsq = pos.piece_list(weakerSide, ROOK)[0];
502 if (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(PAWN, weakerSide))
503 return SCALE_FACTOR_ZERO;
505 return SCALE_FACTOR_NONE;
509 /// KRPKRScalingFunction scales KRP vs KR endgames. This function knows a
510 /// handful of the most important classes of drawn positions, but is far
511 /// from perfect. It would probably be a good idea to add more knowledge
514 /// It would also be nice to rewrite the actual code for this function,
515 /// which is mostly copied from Glaurung 1.x, and not very pretty.
517 ScaleFactor Endgame<ScaleFactor, KRPKR>::apply(const Position& pos) const {
519 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
520 assert(pos.piece_count(strongerSide, PAWN) == 1);
521 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
522 assert(pos.piece_count(weakerSide, PAWN) == 0);
524 Square wksq = pos.king_square(strongerSide);
525 Square wrsq = pos.piece_list(strongerSide, ROOK)[0];
526 Square wpsq = pos.piece_list(strongerSide, PAWN)[0];
527 Square bksq = pos.king_square(weakerSide);
528 Square brsq = pos.piece_list(weakerSide, ROOK)[0];
530 // Orient the board in such a way that the stronger side is white, and the
531 // pawn is on the left half of the board.
532 if (strongerSide == BLACK)
534 wksq = flip_square(wksq);
535 wrsq = flip_square(wrsq);
536 wpsq = flip_square(wpsq);
537 bksq = flip_square(bksq);
538 brsq = flip_square(brsq);
540 if (square_file(wpsq) > FILE_D)
542 wksq = flop_square(wksq);
543 wrsq = flop_square(wrsq);
544 wpsq = flop_square(wpsq);
545 bksq = flop_square(bksq);
546 brsq = flop_square(brsq);
549 File f = square_file(wpsq);
550 Rank r = square_rank(wpsq);
551 Square queeningSq = make_square(f, RANK_8);
552 int tempo = (pos.side_to_move() == strongerSide);
554 // If the pawn is not too far advanced and the defending king defends the
555 // queening square, use the third-rank defence.
557 && square_distance(bksq, queeningSq) <= 1
559 && (square_rank(brsq) == RANK_6 || (r <= RANK_3 && square_rank(wrsq) != RANK_6)))
560 return SCALE_FACTOR_ZERO;
562 // The defending side saves a draw by checking from behind in case the pawn
563 // has advanced to the 6th rank with the king behind.
565 && square_distance(bksq, queeningSq) <= 1
566 && square_rank(wksq) + tempo <= RANK_6
567 && (square_rank(brsq) == RANK_1 || (!tempo && abs(square_file(brsq) - f) >= 3)))
568 return SCALE_FACTOR_ZERO;
571 && bksq == queeningSq
572 && square_rank(brsq) == RANK_1
573 && (!tempo || square_distance(wksq, wpsq) >= 2))
574 return SCALE_FACTOR_ZERO;
576 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
577 // and the black rook is behind the pawn.
580 && (bksq == SQ_H7 || bksq == SQ_G7)
581 && square_file(brsq) == FILE_A
582 && (square_rank(brsq) <= RANK_3 || square_file(wksq) >= FILE_D || square_rank(wksq) <= RANK_5))
583 return SCALE_FACTOR_ZERO;
585 // If the defending king blocks the pawn and the attacking king is too far
586 // away, it's a draw.
588 && bksq == wpsq + DELTA_N
589 && square_distance(wksq, wpsq) - tempo >= 2
590 && square_distance(wksq, brsq) - tempo >= 2)
591 return SCALE_FACTOR_ZERO;
593 // Pawn on the 7th rank supported by the rook from behind usually wins if the
594 // attacking king is closer to the queening square than the defending king,
595 // and the defending king cannot gain tempi by threatening the attacking rook.
598 && square_file(wrsq) == f
599 && wrsq != queeningSq
600 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
601 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
602 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
604 // Similar to the above, but with the pawn further back
606 && square_file(wrsq) == f
608 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
609 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
610 && ( square_distance(bksq, wrsq) + tempo >= 3
611 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
612 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
613 return ScaleFactor( SCALE_FACTOR_MAX
614 - 8 * square_distance(wpsq, queeningSq)
615 - 2 * square_distance(wksq, queeningSq));
617 // If the pawn is not far advanced, and the defending king is somewhere in
618 // the pawn's path, it's probably a draw.
619 if (r <= RANK_4 && bksq > wpsq)
621 if (square_file(bksq) == square_file(wpsq))
622 return ScaleFactor(10);
623 if ( abs(square_file(bksq) - square_file(wpsq)) == 1
624 && square_distance(wksq, bksq) > 2)
625 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
627 return SCALE_FACTOR_NONE;
631 /// KRPPKRPScalingFunction scales KRPP vs KRP endgames. There is only a
632 /// single pattern: If the stronger side has no pawns and the defending king
633 /// is actively placed, the position is drawish.
635 ScaleFactor Endgame<ScaleFactor, KRPPKRP>::apply(const Position& pos) const {
637 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
638 assert(pos.piece_count(strongerSide, PAWN) == 2);
639 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
640 assert(pos.piece_count(weakerSide, PAWN) == 1);
642 Square wpsq1 = pos.piece_list(strongerSide, PAWN)[0];
643 Square wpsq2 = pos.piece_list(strongerSide, PAWN)[1];
644 Square bksq = pos.king_square(weakerSide);
646 // Does the stronger side have a passed pawn?
647 if ( pos.pawn_is_passed(strongerSide, wpsq1)
648 || pos.pawn_is_passed(strongerSide, wpsq2))
649 return SCALE_FACTOR_NONE;
651 Rank r = Max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
653 if ( file_distance(bksq, wpsq1) <= 1
654 && file_distance(bksq, wpsq2) <= 1
655 && relative_rank(strongerSide, bksq) > r)
658 case RANK_2: return ScaleFactor(10);
659 case RANK_3: return ScaleFactor(10);
660 case RANK_4: return ScaleFactor(15);
661 case RANK_5: return ScaleFactor(20);
662 case RANK_6: return ScaleFactor(40);
663 default: assert(false);
666 return SCALE_FACTOR_NONE;
670 /// KPsKScalingFunction scales endgames with king and two or more pawns
671 /// against king. There is just a single rule here: If all pawns are on
672 /// the same rook file and are blocked by the defending king, it's a draw.
674 ScaleFactor Endgame<ScaleFactor, KPsK>::apply(const Position& pos) const {
676 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
677 assert(pos.piece_count(strongerSide, PAWN) >= 2);
678 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
679 assert(pos.piece_count(weakerSide, PAWN) == 0);
681 Square ksq = pos.king_square(weakerSide);
682 Bitboard pawns = pos.pieces(PAWN, strongerSide);
684 // Are all pawns on the 'a' file?
685 if ((pawns & ~FileABB) == EmptyBoardBB)
687 // Does the defending king block the pawns?
688 if ( square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
689 || ( square_file(ksq) == FILE_A
690 && (in_front_bb(strongerSide, ksq) & pawns) == EmptyBoardBB))
691 return SCALE_FACTOR_ZERO;
693 // Are all pawns on the 'h' file?
694 else if ((pawns & ~FileHBB) == EmptyBoardBB)
696 // Does the defending king block the pawns?
697 if ( square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
698 || ( square_file(ksq) == FILE_H
699 && (in_front_bb(strongerSide, ksq) & pawns) == EmptyBoardBB))
700 return SCALE_FACTOR_ZERO;
702 return SCALE_FACTOR_NONE;
706 /// KBPKBScalingFunction scales KBP vs KB endgames. There are two rules:
707 /// If the defending king is somewhere along the path of the pawn, and the
708 /// square of the king is not of the same color as the stronger side's bishop,
709 /// it's a draw. If the two bishops have opposite color, it's almost always
712 ScaleFactor Endgame<ScaleFactor, KBPKB>::apply(const Position& pos) const {
714 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
715 assert(pos.piece_count(strongerSide, BISHOP) == 1);
716 assert(pos.piece_count(strongerSide, PAWN) == 1);
717 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
718 assert(pos.piece_count(weakerSide, BISHOP) == 1);
719 assert(pos.piece_count(weakerSide, PAWN) == 0);
721 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
722 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
723 Square weakerBishopSq = pos.piece_list(weakerSide, BISHOP)[0];
724 Square weakerKingSq = pos.king_square(weakerSide);
726 // Case 1: Defending king blocks the pawn, and cannot be driven away
727 if ( square_file(weakerKingSq) == square_file(pawnSq)
728 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
729 && ( opposite_color_squares(weakerKingSq, strongerBishopSq)
730 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
731 return SCALE_FACTOR_ZERO;
733 // Case 2: Opposite colored bishops
734 if (opposite_color_squares(strongerBishopSq, weakerBishopSq))
736 // We assume that the position is drawn in the following three situations:
738 // a. The pawn is on rank 5 or further back.
739 // b. The defending king is somewhere in the pawn's path.
740 // c. The defending bishop attacks some square along the pawn's path,
741 // and is at least three squares away from the pawn.
743 // These rules are probably not perfect, but in practice they work
746 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
747 return SCALE_FACTOR_ZERO;
750 Bitboard path = squares_in_front_of(strongerSide, pawnSq);
752 if (path & pos.pieces(KING, weakerSide))
753 return SCALE_FACTOR_ZERO;
755 if ( (pos.attacks_from<BISHOP>(weakerBishopSq) & path)
756 && square_distance(weakerBishopSq, pawnSq) >= 3)
757 return SCALE_FACTOR_ZERO;
760 return SCALE_FACTOR_NONE;
764 /// KBPPKBScalingFunction scales KBPP vs KB endgames. It detects a few basic
765 /// draws with opposite-colored bishops.
767 ScaleFactor Endgame<ScaleFactor, KBPPKB>::apply(const Position& pos) const {
769 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
770 assert(pos.piece_count(strongerSide, BISHOP) == 1);
771 assert(pos.piece_count(strongerSide, PAWN) == 2);
772 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
773 assert(pos.piece_count(weakerSide, BISHOP) == 1);
774 assert(pos.piece_count(weakerSide, PAWN) == 0);
776 Square wbsq = pos.piece_list(strongerSide, BISHOP)[0];
777 Square bbsq = pos.piece_list(weakerSide, BISHOP)[0];
779 if (!opposite_color_squares(wbsq, bbsq))
780 return SCALE_FACTOR_NONE;
782 Square ksq = pos.king_square(weakerSide);
783 Square psq1 = pos.piece_list(strongerSide, PAWN)[0];
784 Square psq2 = pos.piece_list(strongerSide, PAWN)[1];
785 Rank r1 = square_rank(psq1);
786 Rank r2 = square_rank(psq2);
787 Square blockSq1, blockSq2;
789 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
791 blockSq1 = psq1 + pawn_push(strongerSide);
792 blockSq2 = make_square(square_file(psq2), square_rank(psq1));
796 blockSq1 = psq2 + pawn_push(strongerSide);
797 blockSq2 = make_square(square_file(psq1), square_rank(psq2));
800 switch (file_distance(psq1, psq2))
803 // Both pawns are on the same file. Easy draw if defender firmly controls
804 // some square in the frontmost pawn's path.
805 if ( square_file(ksq) == square_file(blockSq1)
806 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
807 && opposite_color_squares(ksq, wbsq))
808 return SCALE_FACTOR_ZERO;
810 return SCALE_FACTOR_NONE;
813 // Pawns on neighboring files. Draw if defender firmly controls the square
814 // in front of the frontmost pawn's path, and the square diagonally behind
815 // this square on the file of the other pawn.
817 && opposite_color_squares(ksq, wbsq)
818 && ( bbsq == blockSq2
819 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(BISHOP, weakerSide))
820 || abs(r1 - r2) >= 2))
821 return SCALE_FACTOR_ZERO;
823 else if ( ksq == blockSq2
824 && opposite_color_squares(ksq, wbsq)
825 && ( bbsq == blockSq1
826 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(BISHOP, weakerSide))))
827 return SCALE_FACTOR_ZERO;
829 return SCALE_FACTOR_NONE;
832 // The pawns are not on the same file or adjacent files. No scaling.
833 return SCALE_FACTOR_NONE;
838 /// KBPKNScalingFunction scales KBP vs KN endgames. There is a single rule:
839 /// If the defending king is somewhere along the path of the pawn, and the
840 /// square of the king is not of the same color as the stronger side's bishop,
843 ScaleFactor Endgame<ScaleFactor, KBPKN>::apply(const Position& pos) const {
845 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
846 assert(pos.piece_count(strongerSide, BISHOP) == 1);
847 assert(pos.piece_count(strongerSide, PAWN) == 1);
848 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
849 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
850 assert(pos.piece_count(weakerSide, PAWN) == 0);
852 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
853 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP)[0];
854 Square weakerKingSq = pos.king_square(weakerSide);
856 if ( square_file(weakerKingSq) == square_file(pawnSq)
857 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
858 && ( opposite_color_squares(weakerKingSq, strongerBishopSq)
859 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
860 return SCALE_FACTOR_ZERO;
862 return SCALE_FACTOR_NONE;
866 /// KNPKScalingFunction scales KNP vs K endgames. There is a single rule:
867 /// If the pawn is a rook pawn on the 7th rank and the defending king prevents
868 /// the pawn from advancing, the position is drawn.
870 ScaleFactor Endgame<ScaleFactor, KNPK>::apply(const Position& pos) const {
872 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame);
873 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
874 assert(pos.piece_count(strongerSide, PAWN) == 1);
875 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
876 assert(pos.piece_count(weakerSide, PAWN) == 0);
878 Square pawnSq = pos.piece_list(strongerSide, PAWN)[0];
879 Square weakerKingSq = pos.king_square(weakerSide);
881 if ( pawnSq == relative_square(strongerSide, SQ_A7)
882 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
883 return SCALE_FACTOR_ZERO;
885 if ( pawnSq == relative_square(strongerSide, SQ_H7)
886 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
887 return SCALE_FACTOR_ZERO;
889 return SCALE_FACTOR_NONE;
893 /// KPKPScalingFunction scales KP vs KP endgames. This is done by removing
894 /// the weakest side's pawn and probing the KP vs K bitbase: If the weakest
895 /// side has a draw without the pawn, she probably has at least a draw with
896 /// the pawn as well. The exception is when the stronger side's pawn is far
897 /// advanced and not on a rook file; in this case it is often possible to win
898 /// (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
900 ScaleFactor Endgame<ScaleFactor, KPKP>::apply(const Position& pos) const {
902 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
903 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
904 assert(pos.piece_count(WHITE, PAWN) == 1);
905 assert(pos.piece_count(BLACK, PAWN) == 1);
907 Square wksq, bksq, wpsq;
910 if (strongerSide == WHITE)
912 wksq = pos.king_square(WHITE);
913 bksq = pos.king_square(BLACK);
914 wpsq = pos.piece_list(WHITE, PAWN)[0];
915 stm = pos.side_to_move();
919 wksq = flip_square(pos.king_square(BLACK));
920 bksq = flip_square(pos.king_square(WHITE));
921 wpsq = flip_square(pos.piece_list(BLACK, PAWN)[0]);
922 stm = opposite_color(pos.side_to_move());
925 if (square_file(wpsq) >= FILE_E)
927 wksq = flop_square(wksq);
928 bksq = flop_square(bksq);
929 wpsq = flop_square(wpsq);
932 // If the pawn has advanced to the fifth rank or further, and is not a
933 // rook pawn, it's too dangerous to assume that it's at least a draw.
934 if ( square_rank(wpsq) >= RANK_5
935 && square_file(wpsq) != FILE_A)
936 return SCALE_FACTOR_NONE;
938 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a
939 // draw, it's probably at least a draw even with the pawn.
940 return probe_kpk_bitbase(wksq, wpsq, bksq, stm) ? SCALE_FACTOR_NONE : SCALE_FACTOR_ZERO;