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/>.
33 //// Local definitions
38 // Table used to drive the defending king towards the edge of the board
39 // in KX vs K and KQ vs KR endgames.
40 const uint8_t MateTable[64] = {
41 100, 90, 80, 70, 70, 80, 90, 100,
42 90, 70, 60, 50, 50, 60, 70, 90,
43 80, 60, 40, 30, 30, 40, 60, 80,
44 70, 50, 30, 20, 20, 30, 50, 70,
45 70, 50, 30, 20, 20, 30, 50, 70,
46 80, 60, 40, 30, 30, 40, 60, 80,
47 90, 70, 60, 50, 50, 60, 70, 90,
48 100, 90, 80, 70, 70, 80, 90, 100,
51 // Table used to drive the defending king towards a corner square of the
52 // right color in KBN vs K endgames.
53 const uint8_t KBNKMateTable[64] = {
54 200, 190, 180, 170, 160, 150, 140, 130,
55 190, 180, 170, 160, 150, 140, 130, 140,
56 180, 170, 155, 140, 140, 125, 140, 150,
57 170, 160, 140, 120, 110, 140, 150, 160,
58 160, 150, 140, 110, 120, 140, 160, 170,
59 150, 140, 125, 140, 140, 155, 170, 180,
60 140, 130, 140, 150, 160, 170, 180, 190,
61 130, 140, 150, 160, 170, 180, 190, 200
64 // The attacking side is given a descending bonus based on distance between
65 // the two kings in basic endgames.
66 const int DistanceBonus[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
68 // Penalty for big distance between king and knight for the defending king
69 // and knight in KR vs KN endgames.
70 const int KRKNKingKnightDistancePenalty[8] = { 0, 0, 4, 10, 20, 32, 48, 70 };
72 // Bitbase for KP vs K
73 uint8_t KPKBitbase[24576];
75 // Various inline functions for accessing the above arrays
76 inline Value mate_table(Square s) {
77 return Value(MateTable[s]);
80 inline Value kbnk_mate_table(Square s) {
81 return Value(KBNKMateTable[s]);
84 inline Value distance_bonus(int d) {
85 return Value(DistanceBonus[d]);
88 inline Value krkn_king_knight_distance_penalty(int d) {
89 return Value(KRKNKingKnightDistancePenalty[d]);
92 // Function for probing the KP vs K bitbase
93 int probe_kpk(Square wksq, Square wpsq, Square bksq, Color stm);
102 /// init_bitbases() is called during program initialization, and simply loads
103 /// bitbases from disk into memory. At the moment, there is only the bitbase
104 /// for KP vs K, but we may decide to add other bitbases later.
105 extern void generate_kpk_bitbase(uint8_t bitbase[]);
107 void init_bitbases() {
108 generate_kpk_bitbase(KPKBitbase);
112 /// Mate with KX vs K. This function is used to evaluate positions with
113 /// King and plenty of material vs a lone king. It simply gives the
114 /// attacking side a bonus for driving the defending king towards the edge
115 /// of the board, and for keeping the distance between the two kings small.
117 Value EvaluationFunction<KXK>::apply(const Position& pos) const {
119 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
120 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
122 Square winnerKSq = pos.king_square(strongerSide);
123 Square loserKSq = pos.king_square(weakerSide);
125 Value result = pos.non_pawn_material(strongerSide)
126 + pos.piece_count(strongerSide, PAWN) * PawnValueEndgame
127 + mate_table(loserKSq)
128 + distance_bonus(square_distance(winnerKSq, loserKSq));
130 if ( pos.piece_count(strongerSide, QUEEN)
131 || pos.piece_count(strongerSide, ROOK)
132 || pos.piece_count(strongerSide, BISHOP) > 1)
133 // TODO: check for two equal-colored bishops!
134 result += VALUE_KNOWN_WIN;
136 return strongerSide == pos.side_to_move() ? result : -result;
140 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
141 /// defending king towards a corner square of the right color.
143 Value EvaluationFunction<KBNK>::apply(const Position& pos) const {
145 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
146 assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
147 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame + BishopValueMidgame);
148 assert(pos.piece_count(strongerSide, BISHOP) == 1);
149 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
150 assert(pos.piece_count(strongerSide, PAWN) == 0);
152 Square winnerKSq = pos.king_square(strongerSide);
153 Square loserKSq = pos.king_square(weakerSide);
154 Square bishopSquare = pos.piece_list(strongerSide, BISHOP, 0);
156 // kbnk_mate_table() tries to drive toward corners A1 or H8,
157 // if we have a bishop that cannot reach the above squares we
158 // mirror the kings so to drive enemy toward corners A8 or H1.
159 if (opposite_color_squares(bishopSquare, SQ_A1))
161 winnerKSq = flop_square(winnerKSq);
162 loserKSq = flop_square(loserKSq);
165 Value result = VALUE_KNOWN_WIN
166 + distance_bonus(square_distance(winnerKSq, loserKSq))
167 + kbnk_mate_table(loserKSq);
169 return strongerSide == pos.side_to_move() ? result : -result;
173 /// KP vs K. This endgame is evaluated with the help of a bitbase.
175 Value EvaluationFunction<KPK>::apply(const Position& pos) const {
177 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
178 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
179 assert(pos.piece_count(strongerSide, PAWN) == 1);
180 assert(pos.piece_count(weakerSide, PAWN) == 0);
182 Square wksq, bksq, wpsq;
185 if (strongerSide == WHITE)
187 wksq = pos.king_square(WHITE);
188 bksq = pos.king_square(BLACK);
189 wpsq = pos.piece_list(WHITE, PAWN, 0);
190 stm = pos.side_to_move();
194 wksq = flip_square(pos.king_square(BLACK));
195 bksq = flip_square(pos.king_square(WHITE));
196 wpsq = flip_square(pos.piece_list(BLACK, PAWN, 0));
197 stm = opposite_color(pos.side_to_move());
200 if (square_file(wpsq) >= FILE_E)
202 wksq = flop_square(wksq);
203 bksq = flop_square(bksq);
204 wpsq = flop_square(wpsq);
207 if (!probe_kpk(wksq, wpsq, bksq, stm))
210 Value result = VALUE_KNOWN_WIN
212 + Value(square_rank(wpsq));
214 return strongerSide == pos.side_to_move() ? result : -result;
218 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
219 /// a bitbase. The function below returns drawish scores when the pawn is
220 /// far advanced with support of the king, while the attacking king is far
223 Value EvaluationFunction<KRKP>::apply(const Position& pos) const {
225 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
226 assert(pos.piece_count(strongerSide, PAWN) == 0);
227 assert(pos.non_pawn_material(weakerSide) == 0);
228 assert(pos.piece_count(weakerSide, PAWN) == 1);
230 Square wksq, wrsq, bksq, bpsq;
231 int tempo = (pos.side_to_move() == strongerSide);
233 wksq = pos.king_square(strongerSide);
234 wrsq = pos.piece_list(strongerSide, ROOK, 0);
235 bksq = pos.king_square(weakerSide);
236 bpsq = pos.piece_list(weakerSide, PAWN, 0);
238 if (strongerSide == BLACK)
240 wksq = flip_square(wksq);
241 wrsq = flip_square(wrsq);
242 bksq = flip_square(bksq);
243 bpsq = flip_square(bpsq);
246 Square queeningSq = make_square(square_file(bpsq), RANK_1);
249 // If the stronger side's king is in front of the pawn, it's a win
250 if (wksq < bpsq && square_file(wksq) == square_file(bpsq))
251 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
253 // If the weaker side's king is too far from the pawn and the rook,
255 else if ( square_distance(bksq, bpsq) - (tempo ^ 1) >= 3
256 && square_distance(bksq, wrsq) >= 3)
257 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
259 // If the pawn is far advanced and supported by the defending king,
260 // the position is drawish
261 else if ( square_rank(bksq) <= RANK_3
262 && square_distance(bksq, bpsq) == 1
263 && square_rank(wksq) >= RANK_4
264 && square_distance(wksq, bpsq) - tempo > 2)
265 result = Value(80 - square_distance(wksq, bpsq) * 8);
269 - Value(square_distance(wksq, bpsq + DELTA_S) * 8)
270 + Value(square_distance(bksq, bpsq + DELTA_S) * 8)
271 + Value(square_distance(bpsq, queeningSq) * 8);
273 return strongerSide == pos.side_to_move() ? result : -result;
277 /// KR vs KB. This is very simple, and always returns drawish scores. The
278 /// score is slightly bigger when the defending king is close to the edge.
280 Value EvaluationFunction<KRKB>::apply(const Position& pos) const {
282 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
283 assert(pos.piece_count(strongerSide, PAWN) == 0);
284 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
285 assert(pos.piece_count(weakerSide, PAWN) == 0);
286 assert(pos.piece_count(weakerSide, BISHOP) == 1);
288 Value result = mate_table(pos.king_square(weakerSide));
289 return strongerSide == pos.side_to_move() ? result : -result;
293 /// KR vs KN. The attacking side has slightly better winning chances than
294 /// in KR vs KB, particularly if the king and the knight are far apart.
296 Value EvaluationFunction<KRKN>::apply(const Position& pos) const {
298 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
299 assert(pos.piece_count(strongerSide, PAWN) == 0);
300 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
301 assert(pos.piece_count(weakerSide, PAWN) == 0);
302 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
304 Square defendingKSq = pos.king_square(weakerSide);
305 Square nSq = pos.piece_list(weakerSide, KNIGHT, 0);
307 int d = square_distance(defendingKSq, nSq);
308 Value result = Value(10)
309 + mate_table(defendingKSq)
310 + krkn_king_knight_distance_penalty(d);
312 return strongerSide == pos.side_to_move() ? result : -result;
316 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
317 /// king a bonus for having the kings close together, and for forcing the
318 /// defending king towards the edge. If we also take care to avoid null move
319 /// for the defending side in the search, this is usually sufficient to be
320 /// able to win KQ vs KR.
322 Value EvaluationFunction<KQKR>::apply(const Position& pos) const {
324 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
325 assert(pos.piece_count(strongerSide, PAWN) == 0);
326 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
327 assert(pos.piece_count(weakerSide, PAWN) == 0);
329 Square winnerKSq = pos.king_square(strongerSide);
330 Square loserKSq = pos.king_square(weakerSide);
332 Value result = QueenValueEndgame
334 + mate_table(loserKSq)
335 + distance_bonus(square_distance(winnerKSq, loserKSq));
337 return strongerSide == pos.side_to_move() ? result : -result;
341 Value EvaluationFunction<KBBKN>::apply(const Position& pos) const {
343 assert(pos.piece_count(strongerSide, BISHOP) == 2);
344 assert(pos.non_pawn_material(strongerSide) == 2*BishopValueMidgame);
345 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
346 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
347 assert(pos.pieces(PAWN) == EmptyBoardBB);
349 Value result = BishopValueEndgame;
350 Square wksq = pos.king_square(strongerSide);
351 Square bksq = pos.king_square(weakerSide);
352 Square nsq = pos.piece_list(weakerSide, KNIGHT, 0);
354 // Bonus for attacking king close to defending king
355 result += distance_bonus(square_distance(wksq, bksq));
357 // Bonus for driving the defending king and knight apart
358 result += Value(square_distance(bksq, nsq) * 32);
360 // Bonus for restricting the knight's mobility
361 result += Value((8 - count_1s<CNT32_MAX15>(pos.attacks_from<KNIGHT>(nsq))) * 8);
363 return strongerSide == pos.side_to_move() ? result : -result;
367 /// K and two minors vs K and one or two minors or K and two knights against
368 /// king alone are always draw.
370 Value EvaluationFunction<KmmKm>::apply(const Position&) const {
375 Value EvaluationFunction<KNNK>::apply(const Position&) const {
379 /// KBPKScalingFunction scales endgames where the stronger side has king,
380 /// bishop and one or more pawns. It checks for draws with rook pawns and a
381 /// bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_ZERO is
382 /// returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
385 ScaleFactor ScalingFunction<KBPsK>::apply(const Position& pos) const {
387 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
388 assert(pos.piece_count(strongerSide, BISHOP) == 1);
389 assert(pos.piece_count(strongerSide, PAWN) >= 1);
391 // No assertions about the material of weakerSide, because we want draws to
392 // be detected even when the weaker side has some pawns.
394 Bitboard pawns = pos.pieces(PAWN, strongerSide);
395 File pawnFile = square_file(pos.piece_list(strongerSide, PAWN, 0));
397 // All pawns are on a single rook file ?
398 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
399 && (pawns & ~file_bb(pawnFile)) == EmptyBoardBB)
401 Square bishopSq = pos.piece_list(strongerSide, BISHOP, 0);
402 Square queeningSq = relative_square(strongerSide, make_square(pawnFile, RANK_8));
403 Square kingSq = pos.king_square(weakerSide);
405 if ( opposite_color_squares(queeningSq, bishopSq)
406 && abs(square_file(kingSq) - pawnFile) <= 1)
408 // The bishop has the wrong color, and the defending king is on the
409 // file of the pawn(s) or the neighboring file. Find the rank of the
412 if (strongerSide == WHITE)
414 for (rank = RANK_7; (rank_bb(rank) & pawns) == EmptyBoardBB; rank--) {}
415 assert(rank >= RANK_2 && rank <= RANK_7);
419 for (rank = RANK_2; (rank_bb(rank) & pawns) == EmptyBoardBB; rank++) {}
420 rank = Rank(rank ^ 7); // HACK to get the relative rank
421 assert(rank >= RANK_2 && rank <= RANK_7);
423 // If the defending king has distance 1 to the promotion square or
424 // is placed somewhere in front of the pawn, it's a draw.
425 if ( square_distance(kingSq, queeningSq) <= 1
426 || relative_rank(strongerSide, kingSq) >= rank)
427 return SCALE_FACTOR_ZERO;
430 return SCALE_FACTOR_NONE;
434 /// KQKRPScalingFunction scales endgames where the stronger side has only
435 /// king and queen, while the weaker side has at least a rook and a pawn.
436 /// It tests for fortress draws with a rook on the third rank defended by
439 ScaleFactor ScalingFunction<KQKRPs>::apply(const Position& pos) const {
441 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
442 assert(pos.piece_count(strongerSide, QUEEN) == 1);
443 assert(pos.piece_count(strongerSide, PAWN) == 0);
444 assert(pos.piece_count(weakerSide, ROOK) == 1);
445 assert(pos.piece_count(weakerSide, PAWN) >= 1);
447 Square kingSq = pos.king_square(weakerSide);
448 if ( relative_rank(weakerSide, kingSq) <= RANK_2
449 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
450 && (pos.pieces(ROOK, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_3)))
451 && (pos.pieces(PAWN, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_2)))
452 && (pos.attacks_from<KING>(kingSq) & pos.pieces(PAWN, weakerSide)))
454 Square rsq = pos.piece_list(weakerSide, ROOK, 0);
455 if (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(PAWN, weakerSide))
456 return SCALE_FACTOR_ZERO;
458 return SCALE_FACTOR_NONE;
462 /// KRPKRScalingFunction scales KRP vs KR endgames. This function knows a
463 /// handful of the most important classes of drawn positions, but is far
464 /// from perfect. It would probably be a good idea to add more knowledge
467 /// It would also be nice to rewrite the actual code for this function,
468 /// which is mostly copied from Glaurung 1.x, and not very pretty.
470 ScaleFactor ScalingFunction<KRPKR>::apply(const Position& pos) const {
472 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
473 assert(pos.piece_count(strongerSide, PAWN) == 1);
474 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
475 assert(pos.piece_count(weakerSide, PAWN) == 0);
477 Square wksq = pos.king_square(strongerSide);
478 Square wrsq = pos.piece_list(strongerSide, ROOK, 0);
479 Square wpsq = pos.piece_list(strongerSide, PAWN, 0);
480 Square bksq = pos.king_square(weakerSide);
481 Square brsq = pos.piece_list(weakerSide, ROOK, 0);
483 // Orient the board in such a way that the stronger side is white, and the
484 // pawn is on the left half of the board.
485 if (strongerSide == BLACK)
487 wksq = flip_square(wksq);
488 wrsq = flip_square(wrsq);
489 wpsq = flip_square(wpsq);
490 bksq = flip_square(bksq);
491 brsq = flip_square(brsq);
493 if (square_file(wpsq) > FILE_D)
495 wksq = flop_square(wksq);
496 wrsq = flop_square(wrsq);
497 wpsq = flop_square(wpsq);
498 bksq = flop_square(bksq);
499 brsq = flop_square(brsq);
502 File f = square_file(wpsq);
503 Rank r = square_rank(wpsq);
504 Square queeningSq = make_square(f, RANK_8);
505 int tempo = (pos.side_to_move() == strongerSide);
507 // If the pawn is not too far advanced and the defending king defends the
508 // queening square, use the third-rank defence.
510 && square_distance(bksq, queeningSq) <= 1
512 && (square_rank(brsq) == RANK_6 || (r <= RANK_3 && square_rank(wrsq) != RANK_6)))
513 return SCALE_FACTOR_ZERO;
515 // The defending side saves a draw by checking from behind in case the pawn
516 // has advanced to the 6th rank with the king behind.
518 && square_distance(bksq, queeningSq) <= 1
519 && square_rank(wksq) + tempo <= RANK_6
520 && (square_rank(brsq) == RANK_1 || (!tempo && abs(square_file(brsq) - f) >= 3)))
521 return SCALE_FACTOR_ZERO;
524 && bksq == queeningSq
525 && square_rank(brsq) == RANK_1
526 && (!tempo || square_distance(wksq, wpsq) >= 2))
527 return SCALE_FACTOR_ZERO;
529 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
530 // and the black rook is behind the pawn.
533 && (bksq == SQ_H7 || bksq == SQ_G7)
534 && square_file(brsq) == FILE_A
535 && (square_rank(brsq) <= RANK_3 || square_file(wksq) >= FILE_D || square_rank(wksq) <= RANK_5))
536 return SCALE_FACTOR_ZERO;
538 // If the defending king blocks the pawn and the attacking king is too far
539 // away, it's a draw.
541 && bksq == wpsq + DELTA_N
542 && square_distance(wksq, wpsq) - tempo >= 2
543 && square_distance(wksq, brsq) - tempo >= 2)
544 return SCALE_FACTOR_ZERO;
546 // Pawn on the 7th rank supported by the rook from behind usually wins if the
547 // attacking king is closer to the queening square than the defending king,
548 // and the defending king cannot gain tempi by threatening the attacking rook.
551 && square_file(wrsq) == f
552 && wrsq != queeningSq
553 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
554 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
555 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
557 // Similar to the above, but with the pawn further back
559 && square_file(wrsq) == f
561 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
562 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
563 && ( square_distance(bksq, wrsq) + tempo >= 3
564 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
565 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
566 return ScaleFactor( SCALE_FACTOR_MAX
567 - 8 * square_distance(wpsq, queeningSq)
568 - 2 * square_distance(wksq, queeningSq));
570 // If the pawn is not far advanced, and the defending king is somewhere in
571 // the pawn's path, it's probably a draw.
572 if (r <= RANK_4 && bksq > wpsq)
574 if (square_file(bksq) == square_file(wpsq))
575 return ScaleFactor(10);
576 if ( abs(square_file(bksq) - square_file(wpsq)) == 1
577 && square_distance(wksq, bksq) > 2)
578 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
580 return SCALE_FACTOR_NONE;
584 /// KRPPKRPScalingFunction scales KRPP vs KRP endgames. There is only a
585 /// single pattern: If the stronger side has no pawns and the defending king
586 /// is actively placed, the position is drawish.
588 ScaleFactor ScalingFunction<KRPPKRP>::apply(const Position& pos) const {
590 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
591 assert(pos.piece_count(strongerSide, PAWN) == 2);
592 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
593 assert(pos.piece_count(weakerSide, PAWN) == 1);
595 Square wpsq1 = pos.piece_list(strongerSide, PAWN, 0);
596 Square wpsq2 = pos.piece_list(strongerSide, PAWN, 1);
597 Square bksq = pos.king_square(weakerSide);
599 // Does the stronger side have a passed pawn?
600 if ( pos.pawn_is_passed(strongerSide, wpsq1)
601 || pos.pawn_is_passed(strongerSide, wpsq2))
602 return SCALE_FACTOR_NONE;
604 Rank r = Max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
606 if ( file_distance(bksq, wpsq1) <= 1
607 && file_distance(bksq, wpsq2) <= 1
608 && relative_rank(strongerSide, bksq) > r)
611 case RANK_2: return ScaleFactor(10);
612 case RANK_3: return ScaleFactor(10);
613 case RANK_4: return ScaleFactor(15);
614 case RANK_5: return ScaleFactor(20);
615 case RANK_6: return ScaleFactor(40);
616 default: assert(false);
619 return SCALE_FACTOR_NONE;
623 /// KPsKScalingFunction scales endgames with king and two or more pawns
624 /// against king. There is just a single rule here: If all pawns are on
625 /// the same rook file and are blocked by the defending king, it's a draw.
627 ScaleFactor ScalingFunction<KPsK>::apply(const Position& pos) const {
629 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
630 assert(pos.piece_count(strongerSide, PAWN) >= 2);
631 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
632 assert(pos.piece_count(weakerSide, PAWN) == 0);
634 Square ksq = pos.king_square(weakerSide);
635 Bitboard pawns = pos.pieces(PAWN, strongerSide);
637 // Are all pawns on the 'a' file?
638 if ((pawns & ~FileABB) == EmptyBoardBB)
640 // Does the defending king block the pawns?
641 if ( square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
642 || ( square_file(ksq) == FILE_A
643 && (in_front_bb(strongerSide, ksq) & pawns) == EmptyBoardBB))
644 return SCALE_FACTOR_ZERO;
646 // Are all pawns on the 'h' file?
647 else if ((pawns & ~FileHBB) == EmptyBoardBB)
649 // Does the defending king block the pawns?
650 if ( square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
651 || ( square_file(ksq) == FILE_H
652 && (in_front_bb(strongerSide, ksq) & pawns) == EmptyBoardBB))
653 return SCALE_FACTOR_ZERO;
655 return SCALE_FACTOR_NONE;
659 /// KBPKBScalingFunction scales KBP vs KB endgames. There are two rules:
660 /// If the defending king is somewhere along the path of the pawn, and the
661 /// square of the king is not of the same color as the stronger side's bishop,
662 /// it's a draw. If the two bishops have opposite color, it's almost always
665 ScaleFactor ScalingFunction<KBPKB>::apply(const Position& pos) const {
667 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
668 assert(pos.piece_count(strongerSide, BISHOP) == 1);
669 assert(pos.piece_count(strongerSide, PAWN) == 1);
670 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
671 assert(pos.piece_count(weakerSide, BISHOP) == 1);
672 assert(pos.piece_count(weakerSide, PAWN) == 0);
674 Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
675 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP, 0);
676 Square weakerBishopSq = pos.piece_list(weakerSide, BISHOP, 0);
677 Square weakerKingSq = pos.king_square(weakerSide);
679 // Case 1: Defending king blocks the pawn, and cannot be driven away
680 if ( square_file(weakerKingSq) == square_file(pawnSq)
681 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
682 && ( opposite_color_squares(weakerKingSq, strongerBishopSq)
683 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
684 return SCALE_FACTOR_ZERO;
686 // Case 2: Opposite colored bishops
687 if (opposite_color_squares(strongerBishopSq, weakerBishopSq))
689 // We assume that the position is drawn in the following three situations:
691 // a. The pawn is on rank 5 or further back.
692 // b. The defending king is somewhere in the pawn's path.
693 // c. The defending bishop attacks some square along the pawn's path,
694 // and is at least three squares away from the pawn.
696 // These rules are probably not perfect, but in practice they work
699 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
700 return SCALE_FACTOR_ZERO;
703 Bitboard path = squares_in_front_of(strongerSide, pawnSq);
705 if (path & pos.pieces(KING, weakerSide))
706 return SCALE_FACTOR_ZERO;
708 if ( (pos.attacks_from<BISHOP>(weakerBishopSq) & path)
709 && square_distance(weakerBishopSq, pawnSq) >= 3)
710 return SCALE_FACTOR_ZERO;
713 return SCALE_FACTOR_NONE;
717 /// KBPPKBScalingFunction scales KBPP vs KB endgames. It detects a few basic
718 /// draws with opposite-colored bishops.
720 ScaleFactor ScalingFunction<KBPPKB>::apply(const Position& pos) const {
722 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
723 assert(pos.piece_count(strongerSide, BISHOP) == 1);
724 assert(pos.piece_count(strongerSide, PAWN) == 2);
725 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
726 assert(pos.piece_count(weakerSide, BISHOP) == 1);
727 assert(pos.piece_count(weakerSide, PAWN) == 0);
729 Square wbsq = pos.piece_list(strongerSide, BISHOP, 0);
730 Square bbsq = pos.piece_list(weakerSide, BISHOP, 0);
732 if (!opposite_color_squares(wbsq, bbsq))
733 return SCALE_FACTOR_NONE;
735 Square ksq = pos.king_square(weakerSide);
736 Square psq1 = pos.piece_list(strongerSide, PAWN, 0);
737 Square psq2 = pos.piece_list(strongerSide, PAWN, 1);
738 Rank r1 = square_rank(psq1);
739 Rank r2 = square_rank(psq2);
740 Square blockSq1, blockSq2;
742 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
744 blockSq1 = psq1 + pawn_push(strongerSide);
745 blockSq2 = make_square(square_file(psq2), square_rank(psq1));
749 blockSq1 = psq2 + pawn_push(strongerSide);
750 blockSq2 = make_square(square_file(psq1), square_rank(psq2));
753 switch (file_distance(psq1, psq2))
756 // Both pawns are on the same file. Easy draw if defender firmly controls
757 // some square in the frontmost pawn's path.
758 if ( square_file(ksq) == square_file(blockSq1)
759 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
760 && opposite_color_squares(ksq, wbsq))
761 return SCALE_FACTOR_ZERO;
763 return SCALE_FACTOR_NONE;
766 // Pawns on neighboring files. Draw if defender firmly controls the square
767 // in front of the frontmost pawn's path, and the square diagonally behind
768 // this square on the file of the other pawn.
770 && opposite_color_squares(ksq, wbsq)
771 && ( bbsq == blockSq2
772 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(BISHOP, weakerSide))
773 || abs(r1 - r2) >= 2))
774 return SCALE_FACTOR_ZERO;
776 else if ( ksq == blockSq2
777 && opposite_color_squares(ksq, wbsq)
778 && ( bbsq == blockSq1
779 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(BISHOP, weakerSide))))
780 return SCALE_FACTOR_ZERO;
782 return SCALE_FACTOR_NONE;
785 // The pawns are not on the same file or adjacent files. No scaling.
786 return SCALE_FACTOR_NONE;
791 /// KBPKNScalingFunction scales KBP vs KN endgames. There is a single rule:
792 /// If the defending king is somewhere along the path of the pawn, and the
793 /// square of the king is not of the same color as the stronger side's bishop,
796 ScaleFactor ScalingFunction<KBPKN>::apply(const Position& pos) const {
798 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
799 assert(pos.piece_count(strongerSide, BISHOP) == 1);
800 assert(pos.piece_count(strongerSide, PAWN) == 1);
801 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
802 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
803 assert(pos.piece_count(weakerSide, PAWN) == 0);
805 Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
806 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP, 0);
807 Square weakerKingSq = pos.king_square(weakerSide);
809 if ( square_file(weakerKingSq) == square_file(pawnSq)
810 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
811 && ( opposite_color_squares(weakerKingSq, strongerBishopSq)
812 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
813 return SCALE_FACTOR_ZERO;
815 return SCALE_FACTOR_NONE;
819 /// KNPKScalingFunction scales KNP vs K endgames. There is a single rule:
820 /// If the pawn is a rook pawn on the 7th rank and the defending king prevents
821 /// the pawn from advancing, the position is drawn.
823 ScaleFactor ScalingFunction<KNPK>::apply(const Position& pos) const {
825 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame);
826 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
827 assert(pos.piece_count(strongerSide, PAWN) == 1);
828 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
829 assert(pos.piece_count(weakerSide, PAWN) == 0);
831 Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
832 Square weakerKingSq = pos.king_square(weakerSide);
834 if ( pawnSq == relative_square(strongerSide, SQ_A7)
835 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
836 return SCALE_FACTOR_ZERO;
838 if ( pawnSq == relative_square(strongerSide, SQ_H7)
839 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
840 return SCALE_FACTOR_ZERO;
842 return SCALE_FACTOR_NONE;
846 /// KPKPScalingFunction scales KP vs KP endgames. This is done by removing
847 /// the weakest side's pawn and probing the KP vs K bitbase: If the weakest
848 /// side has a draw without the pawn, she probably has at least a draw with
849 /// the pawn as well. The exception is when the stronger side's pawn is far
850 /// advanced and not on a rook file; in this case it is often possible to win
851 /// (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
853 ScaleFactor ScalingFunction<KPKP>::apply(const Position& pos) const {
855 assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
856 assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
857 assert(pos.piece_count(WHITE, PAWN) == 1);
858 assert(pos.piece_count(BLACK, PAWN) == 1);
860 Square wksq, bksq, wpsq;
863 if (strongerSide == WHITE)
865 wksq = pos.king_square(WHITE);
866 bksq = pos.king_square(BLACK);
867 wpsq = pos.piece_list(WHITE, PAWN, 0);
868 stm = pos.side_to_move();
872 wksq = flip_square(pos.king_square(BLACK));
873 bksq = flip_square(pos.king_square(WHITE));
874 wpsq = flip_square(pos.piece_list(BLACK, PAWN, 0));
875 stm = opposite_color(pos.side_to_move());
878 if (square_file(wpsq) >= FILE_E)
880 wksq = flop_square(wksq);
881 bksq = flop_square(bksq);
882 wpsq = flop_square(wpsq);
885 // If the pawn has advanced to the fifth rank or further, and is not a
886 // rook pawn, it's too dangerous to assume that it's at least a draw.
887 if ( square_rank(wpsq) >= RANK_5
888 && square_file(wpsq) != FILE_A)
889 return SCALE_FACTOR_NONE;
891 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a
892 // draw, it's probably at least a draw even with the pawn.
893 return probe_kpk(wksq, wpsq, bksq, stm) ? SCALE_FACTOR_NONE : SCALE_FACTOR_ZERO;
899 // Probe the KP vs K bitbase
901 int probe_kpk(Square wksq, Square wpsq, Square bksq, Color stm) {
903 int wp = square_file(wpsq) + 4 * (square_rank(wpsq) - 1);
904 int index = int(stm) + 2 * bksq + 128 * wksq + 8192 * wp;
906 assert(index >= 0 && index < 24576 * 8);
908 return KPKBitbase[index / 8] & (1 << (index & 7));