1/*
2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
4 Copyright (C) 2008-2015 Marco Costalba, Joona Kiiski, Tord Romstad
5 Copyright (C) 2015-2019 Marco Costalba, Joona Kiiski, Gary Linscott, Tord Romstad
6
7 Stockfish is free software: you can redistribute it and/or modify
8 it under the terms of the GNU General Public License as published by
9 the Free Software Foundation, either version 3 of the License, or
10 (at your option) any later version.
11
12 Stockfish is distributed in the hope that it will be useful,
13 but WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 GNU General Public License for more details.
16
17 You should have received a copy of the GNU General Public License
18 along with this program. If not, see <http://www.gnu.org/licenses/>.
19*/
20
21#include <cassert>
22
23#include "bitboard.h"
24#include "endgame.h"
25#include "movegen.h"
26
27using std::string;
28
29namespace {
30
31 // Table used to drive the king towards the edge of the board
32 // in KX vs K and KQ vs KR endgames.
33 constexpr int PushToEdges[SQUARE_NB] = {
34 100, 90, 80, 70, 70, 80, 90, 100,
35 90, 70, 60, 50, 50, 60, 70, 90,
36 80, 60, 40, 30, 30, 40, 60, 80,
37 70, 50, 30, 20, 20, 30, 50, 70,
38 70, 50, 30, 20, 20, 30, 50, 70,
39 80, 60, 40, 30, 30, 40, 60, 80,
40 90, 70, 60, 50, 50, 60, 70, 90,
41 100, 90, 80, 70, 70, 80, 90, 100
42 };
43
44 // Table used to drive the king towards a corner square of the
45 // right color in KBN vs K endgames.
46 constexpr int PushToCorners[SQUARE_NB] = {
47 6400, 6080, 5760, 5440, 5120, 4800, 4480, 4160,
48 6080, 5760, 5440, 5120, 4800, 4480, 4160, 4480,
49 5760, 5440, 4960, 4480, 4480, 4000, 4480, 4800,
50 5440, 5120, 4480, 3840, 3520, 4480, 4800, 5120,
51 5120, 4800, 4480, 3520, 3840, 4480, 5120, 5440,
52 4800, 4480, 4000, 4480, 4480, 4960, 5440, 5760,
53 4480, 4160, 4480, 4800, 5120, 5440, 5760, 6080,
54 4160, 4480, 4800, 5120, 5440, 5760, 6080, 6400
55 };
56
57 // Tables used to drive a piece towards or away from another piece
58 constexpr int PushClose[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
59 constexpr int PushAway [8] = { 0, 5, 20, 40, 60, 80, 90, 100 };
60
61 // Pawn Rank based scaling factors used in KRPPKRP endgame
62 constexpr int KRPPKRPScaleFactors[RANK_NB] = { 0, 9, 10, 14, 21, 44, 0, 0 };
63
64#ifndef NDEBUG
65 bool verify_material(const Position& pos, Color c, Value npm, int pawnsCnt) {
66 return pos.non_pawn_material(c) == npm && pos.count<PAWN>(c) == pawnsCnt;
67 }
68#endif
69
70 // Map the square as if strongSide is white and strongSide's only pawn
71 // is on the left half of the board.
72 Square normalize(const Position& pos, Color strongSide, Square sq) {
73
74 assert(pos.count<PAWN>(strongSide) == 1);
75
76 if (file_of(pos.square<PAWN>(strongSide)) >= FILE_E)
77 sq = Square(sq ^ 7); // Mirror SQ_H1 -> SQ_A1
78
79 return strongSide == WHITE ? sq : ~sq;
80 }
81
82} // namespace
83
84
85namespace Endgames {
86
87 std::pair<Map<Value>, Map<ScaleFactor>> maps;
88
89 void init() {
90
91 add<KPK>("KPK");
92 add<KNNK>("KNNK");
93 add<KBNK>("KBNK");
94 add<KRKP>("KRKP");
95 add<KRKB>("KRKB");
96 add<KRKN>("KRKN");
97 add<KQKP>("KQKP");
98 add<KQKR>("KQKR");
99 add<KNNKP>("KNNKP");
100
101 add<KNPK>("KNPK");
102 add<KNPKB>("KNPKB");
103 add<KRPKR>("KRPKR");
104 add<KRPKB>("KRPKB");
105 add<KBPKB>("KBPKB");
106 add<KBPKN>("KBPKN");
107 add<KBPPKB>("KBPPKB");
108 add<KRPPKRP>("KRPPKRP");
109 }
110}
111
112
113/// Mate with KX vs K. This function is used to evaluate positions with
114/// king and plenty of material vs a lone king. It simply gives the
115/// attacking side a bonus for driving the defending king towards the edge
116/// of the board, and for keeping the distance between the two kings small.
117template<>
118Value Endgame<KXK>::operator()(const Position& pos) const {
119
120 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
121 assert(!pos.checkers()); // Eval is never called when in check
122
123 // Stalemate detection with lone king
124 if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
125 return VALUE_DRAW;
126
127 Square winnerKSq = pos.square<KING>(strongSide);
128 Square loserKSq = pos.square<KING>(weakSide);
129
130 Value result = pos.non_pawn_material(strongSide)
131 + pos.count<PAWN>(strongSide) * PawnValueEg
132 + PushToEdges[loserKSq]
133 + PushClose[distance(winnerKSq, loserKSq)];
134
135 if ( pos.count<QUEEN>(strongSide)
136 || pos.count<ROOK>(strongSide)
137 ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
138 || ( (pos.pieces(strongSide, BISHOP) & ~DarkSquares)
139 && (pos.pieces(strongSide, BISHOP) & DarkSquares)))
140 result = std::min(result + VALUE_KNOWN_WIN, VALUE_MATE_IN_MAX_PLY - 1);
141
142 return strongSide == pos.side_to_move() ? result : -result;
143}
144
145
146/// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
147/// defending king towards a corner square that our bishop attacks.
148template<>
149Value Endgame<KBNK>::operator()(const Position& pos) const {
150
151 assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
152 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
153
154 Square winnerKSq = pos.square<KING>(strongSide);
155 Square loserKSq = pos.square<KING>(weakSide);
156 Square bishopSq = pos.square<BISHOP>(strongSide);
157
158 // If our Bishop does not attack A1/H8, we flip the enemy king square
159 // to drive to opposite corners (A8/H1).
160
161 Value result = VALUE_KNOWN_WIN
162 + PushClose[distance(winnerKSq, loserKSq)]
163 + PushToCorners[opposite_colors(bishopSq, SQ_A1) ? ~loserKSq : loserKSq];
164
165 assert(abs(result) < VALUE_MATE_IN_MAX_PLY);
166 return strongSide == pos.side_to_move() ? result : -result;
167}
168
169
170/// KP vs K. This endgame is evaluated with the help of a bitbase.
171template<>
172Value Endgame<KPK>::operator()(const Position& pos) const {
173
174 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
175 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
176
177 // Assume strongSide is white and the pawn is on files A-D
178 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
179 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
180 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
181
182 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
183
184 if (!Bitbases::probe(wksq, psq, bksq, us))
185 return VALUE_DRAW;
186
187 Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
188
189 return strongSide == pos.side_to_move() ? result : -result;
190}
191
192
193/// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
194/// a bitbase. The function below returns drawish scores when the pawn is
195/// far advanced with support of the king, while the attacking king is far
196/// away.
197template<>
198Value Endgame<KRKP>::operator()(const Position& pos) const {
199
200 assert(verify_material(pos, strongSide, RookValueMg, 0));
201 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
202
203 Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
204 Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
205 Square rsq = relative_square(strongSide, pos.square<ROOK>(strongSide));
206 Square psq = relative_square(strongSide, pos.square<PAWN>(weakSide));
207
208 Square queeningSq = make_square(file_of(psq), RANK_1);
209 Value result;
210
211 // If the stronger side's king is in front of the pawn, it's a win
212 if (forward_file_bb(WHITE, wksq) & psq)
213 result = RookValueEg - distance(wksq, psq);
214
215 // If the weaker side's king is too far from the pawn and the rook,
216 // it's a win.
217 else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
218 && distance(bksq, rsq) >= 3)
219 result = RookValueEg - distance(wksq, psq);
220
221 // If the pawn is far advanced and supported by the defending king,
222 // the position is drawish
223 else if ( rank_of(bksq) <= RANK_3
224 && distance(bksq, psq) == 1
225 && rank_of(wksq) >= RANK_4
226 && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
227 result = Value(80) - 8 * distance(wksq, psq);
228
229 else
230 result = Value(200) - 8 * ( distance(wksq, psq + SOUTH)
231 - distance(bksq, psq + SOUTH)
232 - distance(psq, queeningSq));
233
234 return strongSide == pos.side_to_move() ? result : -result;
235}
236
237
238/// KR vs KB. This is very simple, and always returns drawish scores. The
239/// score is slightly bigger when the defending king is close to the edge.
240template<>
241Value Endgame<KRKB>::operator()(const Position& pos) const {
242
243 assert(verify_material(pos, strongSide, RookValueMg, 0));
244 assert(verify_material(pos, weakSide, BishopValueMg, 0));
245
246 Value result = Value(PushToEdges[pos.square<KING>(weakSide)]);
247 return strongSide == pos.side_to_move() ? result : -result;
248}
249
250
251/// KR vs KN. The attacking side has slightly better winning chances than
252/// in KR vs KB, particularly if the king and the knight are far apart.
253template<>
254Value Endgame<KRKN>::operator()(const Position& pos) const {
255
256 assert(verify_material(pos, strongSide, RookValueMg, 0));
257 assert(verify_material(pos, weakSide, KnightValueMg, 0));
258
259 Square bksq = pos.square<KING>(weakSide);
260 Square bnsq = pos.square<KNIGHT>(weakSide);
261 Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
262 return strongSide == pos.side_to_move() ? result : -result;
263}
264
265
266/// KQ vs KP. In general, this is a win for the stronger side, but there are a
267/// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
268/// with a king positioned next to it can be a draw, so in that case, we only
269/// use the distance between the kings.
270template<>
271Value Endgame<KQKP>::operator()(const Position& pos) const {
272
273 assert(verify_material(pos, strongSide, QueenValueMg, 0));
274 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
275
276 Square winnerKSq = pos.square<KING>(strongSide);
277 Square loserKSq = pos.square<KING>(weakSide);
278 Square pawnSq = pos.square<PAWN>(weakSide);
279
280 Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
281
282 if ( relative_rank(weakSide, pawnSq) != RANK_7
283 || distance(loserKSq, pawnSq) != 1
284 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
285 result += QueenValueEg - PawnValueEg;
286
287 return strongSide == pos.side_to_move() ? result : -result;
288}
289
290
291/// KQ vs KR. This is almost identical to KX vs K: We give the attacking
292/// king a bonus for having the kings close together, and for forcing the
293/// defending king towards the edge. If we also take care to avoid null move for
294/// the defending side in the search, this is usually sufficient to win KQ vs KR.
295template<>
296Value Endgame<KQKR>::operator()(const Position& pos) const {
297
298 assert(verify_material(pos, strongSide, QueenValueMg, 0));
299 assert(verify_material(pos, weakSide, RookValueMg, 0));
300
301 Square winnerKSq = pos.square<KING>(strongSide);
302 Square loserKSq = pos.square<KING>(weakSide);
303
304 Value result = QueenValueEg
305 - RookValueEg
306 + PushToEdges[loserKSq]
307 + PushClose[distance(winnerKSq, loserKSq)];
308
309 return strongSide == pos.side_to_move() ? result : -result;
310}
311
312
313/// KNN vs KP. Simply push the opposing king to the corner
314template<>
315Value Endgame<KNNKP>::operator()(const Position& pos) const {
316
317 assert(verify_material(pos, strongSide, 2 * KnightValueMg, 0));
318 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
319
320 Value result = 2 * KnightValueEg
321 - PawnValueEg
322 + PushToEdges[pos.square<KING>(weakSide)];
323
324 return strongSide == pos.side_to_move() ? result : -result;
325}
326
327
328/// Some cases of trivial draws
329template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
330
331
332/// KB and one or more pawns vs K. It checks for draws with rook pawns and
333/// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
334/// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
335/// will be used.
336template<>
337ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
338
339 assert(pos.non_pawn_material(strongSide) == BishopValueMg);
340 assert(pos.count<PAWN>(strongSide) >= 1);
341
342 // No assertions about the material of weakSide, because we want draws to
343 // be detected even when the weaker side has some pawns.
344
345 Bitboard pawns = pos.pieces(strongSide, PAWN);
346 File pawnsFile = file_of(lsb(pawns));
347
348 // All pawns are on a single rook file?
349 if ( (pawnsFile == FILE_A || pawnsFile == FILE_H)
350 && !(pawns & ~file_bb(pawnsFile)))
351 {
352 Square bishopSq = pos.square<BISHOP>(strongSide);
353 Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
354 Square kingSq = pos.square<KING>(weakSide);
355
356 if ( opposite_colors(queeningSq, bishopSq)
357 && distance(queeningSq, kingSq) <= 1)
358 return SCALE_FACTOR_DRAW;
359 }
360
361 // If all the pawns are on the same B or G file, then it's potentially a draw
362 if ( (pawnsFile == FILE_B || pawnsFile == FILE_G)
363 && !(pos.pieces(PAWN) & ~file_bb(pawnsFile))
364 && pos.non_pawn_material(weakSide) == 0
365 && pos.count<PAWN>(weakSide) >= 1)
366 {
367 // Get weakSide pawn that is closest to the home rank
368 Square weakPawnSq = frontmost_sq(strongSide, pos.pieces(weakSide, PAWN));
369
370 Square strongKingSq = pos.square<KING>(strongSide);
371 Square weakKingSq = pos.square<KING>(weakSide);
372 Square bishopSq = pos.square<BISHOP>(strongSide);
373
374 // There's potential for a draw if our pawn is blocked on the 7th rank,
375 // the bishop cannot attack it or they only have one pawn left
376 if ( relative_rank(strongSide, weakPawnSq) == RANK_7
377 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
378 && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
379 {
380 int strongKingDist = distance(weakPawnSq, strongKingSq);
381 int weakKingDist = distance(weakPawnSq, weakKingSq);
382
383 // It's a draw if the weak king is on its back two ranks, within 2
384 // squares of the blocking pawn and the strong king is not
385 // closer. (I think this rule only fails in practically
386 // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
387 // and positions where qsearch will immediately correct the
388 // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
389 if ( relative_rank(strongSide, weakKingSq) >= RANK_7
390 && weakKingDist <= 2
391 && weakKingDist <= strongKingDist)
392 return SCALE_FACTOR_DRAW;
393 }
394 }
395
396 return SCALE_FACTOR_NONE;
397}
398
399
400/// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
401/// the third rank defended by a pawn.
402template<>
403ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
404
405 assert(verify_material(pos, strongSide, QueenValueMg, 0));
406 assert(pos.count<ROOK>(weakSide) == 1);
407 assert(pos.count<PAWN>(weakSide) >= 1);
408
409 Square kingSq = pos.square<KING>(weakSide);
410 Square rsq = pos.square<ROOK>(weakSide);
411
412 if ( relative_rank(weakSide, kingSq) <= RANK_2
413 && relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
414 && relative_rank(weakSide, rsq) == RANK_3
415 && ( pos.pieces(weakSide, PAWN)
416 & pos.attacks_from<KING>(kingSq)
417 & pos.attacks_from<PAWN>(rsq, strongSide)))
418 return SCALE_FACTOR_DRAW;
419
420 return SCALE_FACTOR_NONE;
421}
422
423
424/// KRP vs KR. This function knows a handful of the most important classes of
425/// drawn positions, but is far from perfect. It would probably be a good idea
426/// to add more knowledge in the future.
427///
428/// It would also be nice to rewrite the actual code for this function,
429/// which is mostly copied from Glaurung 1.x, and isn't very pretty.
430template<>
431ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
432
433 assert(verify_material(pos, strongSide, RookValueMg, 1));
434 assert(verify_material(pos, weakSide, RookValueMg, 0));
435
436 // Assume strongSide is white and the pawn is on files A-D
437 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
438 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
439 Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
440 Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
441 Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
442
443 File f = file_of(wpsq);
444 Rank r = rank_of(wpsq);
445 Square queeningSq = make_square(f, RANK_8);
446 int tempo = (pos.side_to_move() == strongSide);
447
448 // If the pawn is not too far advanced and the defending king defends the
449 // queening square, use the third-rank defence.
450 if ( r <= RANK_5
451 && distance(bksq, queeningSq) <= 1
452 && wksq <= SQ_H5
453 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
454 return SCALE_FACTOR_DRAW;
455
456 // The defending side saves a draw by checking from behind in case the pawn
457 // has advanced to the 6th rank with the king behind.
458 if ( r == RANK_6
459 && distance(bksq, queeningSq) <= 1
460 && rank_of(wksq) + tempo <= RANK_6
461 && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
462 return SCALE_FACTOR_DRAW;
463
464 if ( r >= RANK_6
465 && bksq == queeningSq
466 && rank_of(brsq) == RANK_1
467 && (!tempo || distance(wksq, wpsq) >= 2))
468 return SCALE_FACTOR_DRAW;
469
470 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
471 // and the black rook is behind the pawn.
472 if ( wpsq == SQ_A7
473 && wrsq == SQ_A8
474 && (bksq == SQ_H7 || bksq == SQ_G7)
475 && file_of(brsq) == FILE_A
476 && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
477 return SCALE_FACTOR_DRAW;
478
479 // If the defending king blocks the pawn and the attacking king is too far
480 // away, it's a draw.
481 if ( r <= RANK_5
482 && bksq == wpsq + NORTH
483 && distance(wksq, wpsq) - tempo >= 2
484 && distance(wksq, brsq) - tempo >= 2)
485 return SCALE_FACTOR_DRAW;
486
487 // Pawn on the 7th rank supported by the rook from behind usually wins if the
488 // attacking king is closer to the queening square than the defending king,
489 // and the defending king cannot gain tempi by threatening the attacking rook.
490 if ( r == RANK_7
491 && f != FILE_A
492 && file_of(wrsq) == f
493 && wrsq != queeningSq
494 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
495 && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
496 return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
497
498 // Similar to the above, but with the pawn further back
499 if ( f != FILE_A
500 && file_of(wrsq) == f
501 && wrsq < wpsq
502 && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
503 && (distance(wksq, wpsq + NORTH) < distance(bksq, wpsq + NORTH) - 2 + tempo)
504 && ( distance(bksq, wrsq) + tempo >= 3
505 || ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
506 && (distance(wksq, wpsq + NORTH) < distance(bksq, wrsq) + tempo))))
507 return ScaleFactor( SCALE_FACTOR_MAX
508 - 8 * distance(wpsq, queeningSq)
509 - 2 * distance(wksq, queeningSq));
510
511 // If the pawn is not far advanced and the defending king is somewhere in
512 // the pawn's path, it's probably a draw.
513 if (r <= RANK_4 && bksq > wpsq)
514 {
515 if (file_of(bksq) == file_of(wpsq))
516 return ScaleFactor(10);
517 if ( distance<File>(bksq, wpsq) == 1
518 && distance(wksq, bksq) > 2)
519 return ScaleFactor(24 - 2 * distance(wksq, bksq));
520 }
521 return SCALE_FACTOR_NONE;
522}
523
524template<>
525ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
526
527 assert(verify_material(pos, strongSide, RookValueMg, 1));
528 assert(verify_material(pos, weakSide, BishopValueMg, 0));
529
530 // Test for a rook pawn
531 if (pos.pieces(PAWN) & (FileABB | FileHBB))
532 {
533 Square ksq = pos.square<KING>(weakSide);
534 Square bsq = pos.square<BISHOP>(weakSide);
535 Square psq = pos.square<PAWN>(strongSide);
536 Rank rk = relative_rank(strongSide, psq);
537 Direction push = pawn_push(strongSide);
538
539 // If the pawn is on the 5th rank and the pawn (currently) is on
540 // the same color square as the bishop then there is a chance of
541 // a fortress. Depending on the king position give a moderate
542 // reduction or a stronger one if the defending king is near the
543 // corner but not trapped there.
544 if (rk == RANK_5 && !opposite_colors(bsq, psq))
545 {
546 int d = distance(psq + 3 * push, ksq);
547
548 if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
549 return ScaleFactor(24);
550 else
551 return ScaleFactor(48);
552 }
553
554 // When the pawn has moved to the 6th rank we can be fairly sure
555 // it's drawn if the bishop attacks the square in front of the
556 // pawn from a reasonable distance and the defending king is near
557 // the corner
558 if ( rk == RANK_6
559 && distance(psq + 2 * push, ksq) <= 1
560 && (PseudoAttacks[BISHOP][bsq] & (psq + push))
561 && distance<File>(bsq, psq) >= 2)
562 return ScaleFactor(8);
563 }
564
565 return SCALE_FACTOR_NONE;
566}
567
568/// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
569/// pawns and the defending king is actively placed, the position is drawish.
570template<>
571ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
572
573 assert(verify_material(pos, strongSide, RookValueMg, 2));
574 assert(verify_material(pos, weakSide, RookValueMg, 1));
575
576 Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
577 Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
578 Square bksq = pos.square<KING>(weakSide);
579
580 // Does the stronger side have a passed pawn?
581 if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
582 return SCALE_FACTOR_NONE;
583
584 Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
585
586 if ( distance<File>(bksq, wpsq1) <= 1
587 && distance<File>(bksq, wpsq2) <= 1
588 && relative_rank(strongSide, bksq) > r)
589 {
590 assert(r > RANK_1 && r < RANK_7);
591 return ScaleFactor(KRPPKRPScaleFactors[r]);
592 }
593 return SCALE_FACTOR_NONE;
594}
595
596
597/// K and two or more pawns vs K. There is just a single rule here: If all pawns
598/// are on the same rook file and are blocked by the defending king, it's a draw.
599template<>
600ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
601
602 assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
603 assert(pos.count<PAWN>(strongSide) >= 2);
604 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
605
606 Square ksq = pos.square<KING>(weakSide);
607 Bitboard pawns = pos.pieces(strongSide, PAWN);
608
609 // If all pawns are ahead of the king, on a single rook file and
610 // the king is within one file of the pawns, it's a draw.
611 if ( !(pawns & ~forward_ranks_bb(weakSide, ksq))
612 && !((pawns & ~FileABB) && (pawns & ~FileHBB))
613 && distance<File>(ksq, lsb(pawns)) <= 1)
614 return SCALE_FACTOR_DRAW;
615
616 return SCALE_FACTOR_NONE;
617}
618
619
620/// KBP vs KB. There are two rules: if the defending king is somewhere along the
621/// path of the pawn, and the square of the king is not of the same color as the
622/// stronger side's bishop, it's a draw. If the two bishops have opposite color,
623/// it's almost always a draw.
624template<>
625ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
626
627 assert(verify_material(pos, strongSide, BishopValueMg, 1));
628 assert(verify_material(pos, weakSide, BishopValueMg, 0));
629
630 Square pawnSq = pos.square<PAWN>(strongSide);
631 Square strongBishopSq = pos.square<BISHOP>(strongSide);
632 Square weakBishopSq = pos.square<BISHOP>(weakSide);
633 Square weakKingSq = pos.square<KING>(weakSide);
634
635 // Case 1: Defending king blocks the pawn, and cannot be driven away
636 if ( file_of(weakKingSq) == file_of(pawnSq)
637 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
638 && ( opposite_colors(weakKingSq, strongBishopSq)
639 || relative_rank(strongSide, weakKingSq) <= RANK_6))
640 return SCALE_FACTOR_DRAW;
641
642 // Case 2: Opposite colored bishops
643 if (opposite_colors(strongBishopSq, weakBishopSq))
644 return SCALE_FACTOR_DRAW;
645
646 return SCALE_FACTOR_NONE;
647}
648
649
650/// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
651template<>
652ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
653
654 assert(verify_material(pos, strongSide, BishopValueMg, 2));
655 assert(verify_material(pos, weakSide, BishopValueMg, 0));
656
657 Square wbsq = pos.square<BISHOP>(strongSide);
658 Square bbsq = pos.square<BISHOP>(weakSide);
659
660 if (!opposite_colors(wbsq, bbsq))
661 return SCALE_FACTOR_NONE;
662
663 Square ksq = pos.square<KING>(weakSide);
664 Square psq1 = pos.squares<PAWN>(strongSide)[0];
665 Square psq2 = pos.squares<PAWN>(strongSide)[1];
666 Square blockSq1, blockSq2;
667
668 if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
669 {
670 blockSq1 = psq1 + pawn_push(strongSide);
671 blockSq2 = make_square(file_of(psq2), rank_of(psq1));
672 }
673 else
674 {
675 blockSq1 = psq2 + pawn_push(strongSide);
676 blockSq2 = make_square(file_of(psq1), rank_of(psq2));
677 }
678
679 switch (distance<File>(psq1, psq2))
680 {
681 case 0:
682 // Both pawns are on the same file. It's an easy draw if the defender firmly
683 // controls some square in the frontmost pawn's path.
684 if ( file_of(ksq) == file_of(blockSq1)
685 && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
686 && opposite_colors(ksq, wbsq))
687 return SCALE_FACTOR_DRAW;
688 else
689 return SCALE_FACTOR_NONE;
690
691 case 1:
692 // Pawns on adjacent files. It's a draw if the defender firmly controls the
693 // square in front of the frontmost pawn's path, and the square diagonally
694 // behind this square on the file of the other pawn.
695 if ( ksq == blockSq1
696 && opposite_colors(ksq, wbsq)
697 && ( bbsq == blockSq2
698 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
699 || distance<Rank>(psq1, psq2) >= 2))
700 return SCALE_FACTOR_DRAW;
701
702 else if ( ksq == blockSq2
703 && opposite_colors(ksq, wbsq)
704 && ( bbsq == blockSq1
705 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
706 return SCALE_FACTOR_DRAW;
707 else
708 return SCALE_FACTOR_NONE;
709
710 default:
711 // The pawns are not on the same file or adjacent files. No scaling.
712 return SCALE_FACTOR_NONE;
713 }
714}
715
716
717/// KBP vs KN. There is a single rule: If the defending king is somewhere along
718/// the path of the pawn, and the square of the king is not of the same color as
719/// the stronger side's bishop, it's a draw.
720template<>
721ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
722
723 assert(verify_material(pos, strongSide, BishopValueMg, 1));
724 assert(verify_material(pos, weakSide, KnightValueMg, 0));
725
726 Square pawnSq = pos.square<PAWN>(strongSide);
727 Square strongBishopSq = pos.square<BISHOP>(strongSide);
728 Square weakKingSq = pos.square<KING>(weakSide);
729
730 if ( file_of(weakKingSq) == file_of(pawnSq)
731 && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
732 && ( opposite_colors(weakKingSq, strongBishopSq)
733 || relative_rank(strongSide, weakKingSq) <= RANK_6))
734 return SCALE_FACTOR_DRAW;
735
736 return SCALE_FACTOR_NONE;
737}
738
739
740/// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
741/// and the defending king prevents the pawn from advancing, the position is drawn.
742template<>
743ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
744
745 assert(verify_material(pos, strongSide, KnightValueMg, 1));
746 assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
747
748 // Assume strongSide is white and the pawn is on files A-D
749 Square pawnSq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
750 Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
751
752 if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
753 return SCALE_FACTOR_DRAW;
754
755 return SCALE_FACTOR_NONE;
756}
757
758
759/// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
760/// Otherwise the position is drawn.
761template<>
762ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
763
764 assert(verify_material(pos, strongSide, KnightValueMg, 1));
765 assert(verify_material(pos, weakSide, BishopValueMg, 0));
766
767 Square pawnSq = pos.square<PAWN>(strongSide);
768 Square bishopSq = pos.square<BISHOP>(weakSide);
769 Square weakKingSq = pos.square<KING>(weakSide);
770
771 // King needs to get close to promoting pawn to prevent knight from blocking.
772 // Rules for this are very tricky, so just approximate.
773 if (forward_file_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
774 return ScaleFactor(distance(weakKingSq, pawnSq));
775
776 return SCALE_FACTOR_NONE;
777}
778
779
780/// KP vs KP. This is done by removing the weakest side's pawn and probing the
781/// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
782/// has at least a draw with the pawn as well. The exception is when the stronger
783/// side's pawn is far advanced and not on a rook file; in this case it is often
784/// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
785template<>
786ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
787
788 assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
789 assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
790
791 // Assume strongSide is white and the pawn is on files A-D
792 Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
793 Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
794 Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
795
796 Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
797
798 // If the pawn has advanced to the fifth rank or further, and is not a
799 // rook pawn, it's too dangerous to assume that it's at least a draw.
800 if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
801 return SCALE_FACTOR_NONE;
802
803 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
804 // it's probably at least a draw even with the pawn.
805 return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;
806}
807