/* Stockfish, a UCI chess playing engine derived from Glaurung 2.1 Copyright (C) 2004-2008 Tord Romstad (Glaurung author) Copyright (C) 2008-2014 Marco Costalba, Joona Kiiski, Tord Romstad Stockfish is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. Stockfish is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . */ #include #include #include "bitboard.h" #include "bitcount.h" #include "endgame.h" #include "movegen.h" using std::string; namespace { // Table used to drive the king towards the edge of the board // in KX vs K and KQ vs KR endgames. const int PushToEdges[SQUARE_NB] = { 100, 90, 80, 70, 70, 80, 90, 100, 90, 70, 60, 50, 50, 60, 70, 90, 80, 60, 40, 30, 30, 40, 60, 80, 70, 50, 30, 20, 20, 30, 50, 70, 70, 50, 30, 20, 20, 30, 50, 70, 80, 60, 40, 30, 30, 40, 60, 80, 90, 70, 60, 50, 50, 60, 70, 90, 100, 90, 80, 70, 70, 80, 90, 100, }; // Table used to drive the king towards a corner square of the // right color in KBN vs K endgames. const int PushToCorners[SQUARE_NB] = { 200, 190, 180, 170, 160, 150, 140, 130, 190, 180, 170, 160, 150, 140, 130, 140, 180, 170, 155, 140, 140, 125, 140, 150, 170, 160, 140, 120, 110, 140, 150, 160, 160, 150, 140, 110, 120, 140, 160, 170, 150, 140, 125, 140, 140, 155, 170, 180, 140, 130, 140, 150, 160, 170, 180, 190, 130, 140, 150, 160, 170, 180, 190, 200 }; // Tables used to drive a piece towards or away from another piece const int PushClose[8] = { 0, 0, 100, 80, 60, 40, 20, 10 }; const int PushAway [8] = { 0, 5, 20, 40, 60, 80, 90, 100 }; #ifndef NDEBUG bool verify_material(const Position& pos, Color c, Value npm, int num_pawns) { return pos.non_pawn_material(c) == npm && pos.count(c) == num_pawns; } #endif // Map the square as if strongSide is white and strongSide's only pawn // is on the left half of the board. Square normalize(const Position& pos, Color strongSide, Square sq) { assert(pos.count(strongSide) == 1); if (file_of(pos.list(strongSide)[0]) >= FILE_E) sq = Square(sq ^ 7); // Mirror SQ_H1 -> SQ_A1 if (strongSide == BLACK) sq = ~sq; return sq; } // Get the material key of Position out of the given endgame key code // like "KBPKN". The trick here is to first forge an ad-hoc FEN string // and then let a Position object do the work for us. Key key(const string& code, Color c) { assert(code.length() > 0 && code.length() < 8); assert(code[0] == 'K'); string sides[] = { code.substr(code.find('K', 1)), // Weak code.substr(0, code.find('K', 1)) }; // Strong std::transform(sides[c].begin(), sides[c].end(), sides[c].begin(), tolower); string fen = sides[0] + char(8 - sides[0].length() + '0') + "/8/8/8/8/8/8/" + sides[1] + char(8 - sides[1].length() + '0') + " w - - 0 10"; return Position(fen, false, NULL).material_key(); } template void delete_endgame(const typename M::value_type& p) { delete p.second; } } // namespace /// Endgames members definitions Endgames::Endgames() { add("KPK"); add("KNNK"); add("KBNK"); add("KRKP"); add("KRKB"); add("KRKN"); add("KQKP"); add("KQKR"); add("KNPK"); add("KNPKB"); add("KRPKR"); add("KRPKB"); add("KBPKB"); add("KBPKN"); add("KBPPKB"); add("KRPPKRP"); } Endgames::~Endgames() { for_each(m1.begin(), m1.end(), delete_endgame); for_each(m2.begin(), m2.end(), delete_endgame); } template void Endgames::add(const string& code) { map((Endgame*)0)[key(code, WHITE)] = new Endgame(WHITE); map((Endgame*)0)[key(code, BLACK)] = new Endgame(BLACK); } /// Mate with KX vs K. This function is used to evaluate positions with /// king and plenty of material vs a lone king. It simply gives the /// attacking side a bonus for driving the defending king towards the edge /// of the board, and for keeping the distance between the two kings small. template<> Value Endgame::operator()(const Position& pos) const { assert(verify_material(pos, weakSide, VALUE_ZERO, 0)); assert(!pos.checkers()); // Eval is never called when in check // Stalemate detection with lone king if (pos.side_to_move() == weakSide && !MoveList(pos).size()) return VALUE_DRAW; Square winnerKSq = pos.king_square(strongSide); Square loserKSq = pos.king_square(weakSide); Value result = pos.non_pawn_material(strongSide) + pos.count(strongSide) * PawnValueEg + PushToEdges[loserKSq] + PushClose[square_distance(winnerKSq, loserKSq)]; if ( pos.count(strongSide) || pos.count(strongSide) ||(pos.count(strongSide) && pos.count(strongSide)) || pos.bishop_pair(strongSide)) result += VALUE_KNOWN_WIN; return strongSide == pos.side_to_move() ? result : -result; } /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the /// defending king towards a corner square of the right color. template<> Value Endgame::operator()(const Position& pos) const { assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0)); assert(verify_material(pos, weakSide, VALUE_ZERO, 0)); Square winnerKSq = pos.king_square(strongSide); Square loserKSq = pos.king_square(weakSide); Square bishopSq = pos.list(strongSide)[0]; // kbnk_mate_table() tries to drive toward corners A1 or H8. If we have a // bishop that cannot reach the above squares, we flip the kings in order // to drive the enemy toward corners A8 or H1. if (opposite_colors(bishopSq, SQ_A1)) { winnerKSq = ~winnerKSq; loserKSq = ~loserKSq; } Value result = VALUE_KNOWN_WIN + PushClose[square_distance(winnerKSq, loserKSq)] + PushToCorners[loserKSq]; return strongSide == pos.side_to_move() ? result : -result; } /// KP vs K. This endgame is evaluated with the help of a bitbase. template<> Value Endgame::operator()(const Position& pos) const { assert(verify_material(pos, strongSide, VALUE_ZERO, 1)); assert(verify_material(pos, weakSide, VALUE_ZERO, 0)); // Assume strongSide is white and the pawn is on files A-D Square wksq = normalize(pos, strongSide, pos.king_square(strongSide)); Square bksq = normalize(pos, strongSide, pos.king_square(weakSide)); Square psq = normalize(pos, strongSide, pos.list(strongSide)[0]); Color us = strongSide == pos.side_to_move() ? WHITE : BLACK; if (!Bitbases::probe_kpk(wksq, psq, bksq, us)) return VALUE_DRAW; Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq)); return strongSide == pos.side_to_move() ? result : -result; } /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without /// a bitbase. The function below returns drawish scores when the pawn is /// far advanced with support of the king, while the attacking king is far /// away. template<> Value Endgame::operator()(const Position& pos) const { assert(verify_material(pos, strongSide, RookValueMg, 0)); assert(verify_material(pos, weakSide, VALUE_ZERO, 1)); Square wksq = relative_square(strongSide, pos.king_square(strongSide)); Square bksq = relative_square(strongSide, pos.king_square(weakSide)); Square rsq = relative_square(strongSide, pos.list(strongSide)[0]); Square psq = relative_square(strongSide, pos.list(weakSide)[0]); Square queeningSq = make_square(file_of(psq), RANK_1); Value result; // If the stronger side's king is in front of the pawn, it's a win if (wksq < psq && file_of(wksq) == file_of(psq)) result = RookValueEg - square_distance(wksq, psq); // If the weaker side's king is too far from the pawn and the rook, // it's a win. else if ( square_distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide) && square_distance(bksq, rsq) >= 3) result = RookValueEg - square_distance(wksq, psq); // If the pawn is far advanced and supported by the defending king, // the position is drawish else if ( rank_of(bksq) <= RANK_3 && square_distance(bksq, psq) == 1 && rank_of(wksq) >= RANK_4 && square_distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide)) result = Value(80) - 8 * square_distance(wksq, psq); else result = Value(200) - 8 * ( square_distance(wksq, psq + DELTA_S) - square_distance(bksq, psq + DELTA_S) - square_distance(psq, queeningSq)); return strongSide == pos.side_to_move() ? result : -result; } /// KR vs KB. This is very simple, and always returns drawish scores. The /// score is slightly bigger when the defending king is close to the edge. template<> Value Endgame::operator()(const Position& pos) const { assert(verify_material(pos, strongSide, RookValueMg, 0)); assert(verify_material(pos, weakSide, BishopValueMg, 0)); Value result = Value(PushToEdges[pos.king_square(weakSide)]); return strongSide == pos.side_to_move() ? result : -result; } /// KR vs KN. The attacking side has slightly better winning chances than /// in KR vs KB, particularly if the king and the knight are far apart. template<> Value Endgame::operator()(const Position& pos) const { assert(verify_material(pos, strongSide, RookValueMg, 0)); assert(verify_material(pos, weakSide, KnightValueMg, 0)); Square bksq = pos.king_square(weakSide); Square bnsq = pos.list(weakSide)[0]; Value result = Value(PushToEdges[bksq] + PushAway[square_distance(bksq, bnsq)]); return strongSide == pos.side_to_move() ? result : -result; } /// KQ vs KP. In general, this is a win for the stronger side, but there are a /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files /// with a king positioned next to it can be a draw, so in that case, we only /// use the distance between the kings. template<> Value Endgame::operator()(const Position& pos) const { assert(verify_material(pos, strongSide, QueenValueMg, 0)); assert(verify_material(pos, weakSide, VALUE_ZERO, 1)); Square winnerKSq = pos.king_square(strongSide); Square loserKSq = pos.king_square(weakSide); Square pawnSq = pos.list(weakSide)[0]; Value result = Value(PushClose[square_distance(winnerKSq, loserKSq)]); if ( relative_rank(weakSide, pawnSq) != RANK_7 || square_distance(loserKSq, pawnSq) != 1 || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq)) result += QueenValueEg - PawnValueEg; return strongSide == pos.side_to_move() ? result : -result; } /// KQ vs KR. This is almost identical to KX vs K: We give the attacking /// king a bonus for having the kings close together, and for forcing the /// defending king towards the edge. If we also take care to avoid null move for /// the defending side in the search, this is usually sufficient to win KQ vs KR. template<> Value Endgame::operator()(const Position& pos) const { assert(verify_material(pos, strongSide, QueenValueMg, 0)); assert(verify_material(pos, weakSide, RookValueMg, 0)); Square winnerKSq = pos.king_square(strongSide); Square loserKSq = pos.king_square(weakSide); Value result = QueenValueEg - RookValueEg + PushToEdges[loserKSq] + PushClose[square_distance(winnerKSq, loserKSq)]; return strongSide == pos.side_to_move() ? result : -result; } /// Some cases of trivial draws template<> Value Endgame::operator()(const Position&) const { return VALUE_DRAW; } /// KB and one or more pawns vs K. It checks for draws with rook pawns and /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling /// will be used. template<> ScaleFactor Endgame::operator()(const Position& pos) const { assert(pos.non_pawn_material(strongSide) == BishopValueMg); assert(pos.count(strongSide) >= 1); // No assertions about the material of weakSide, because we want draws to // be detected even when the weaker side has some pawns. Bitboard pawns = pos.pieces(strongSide, PAWN); File pawnFile = file_of(pos.list(strongSide)[0]); // All pawns are on a single rook file ? if ( (pawnFile == FILE_A || pawnFile == FILE_H) && !(pawns & ~file_bb(pawnFile))) { Square bishopSq = pos.list(strongSide)[0]; Square queeningSq = relative_square(strongSide, make_square(pawnFile, RANK_8)); Square kingSq = pos.king_square(weakSide); if ( opposite_colors(queeningSq, bishopSq) && square_distance(queeningSq, kingSq) <= 1) return SCALE_FACTOR_DRAW; } // If all the pawns are on the same B or G file, then it's potentially a draw if ( (pawnFile == FILE_B || pawnFile == FILE_G) && !(pos.pieces(PAWN) & ~file_bb(pawnFile)) && pos.non_pawn_material(weakSide) == 0 && pos.count(weakSide) >= 1) { // Get weakSide pawn that is closest to the home rank Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN)); Square strongKingSq = pos.king_square(strongSide); Square weakKingSq = pos.king_square(weakSide); Square bishopSq = pos.list(strongSide)[0]; // There's potential for a draw if our pawn is blocked on the 7th rank, // the bishop cannot attack it or they only have one pawn left if ( relative_rank(strongSide, weakPawnSq) == RANK_7 && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide))) && (opposite_colors(bishopSq, weakPawnSq) || pos.count(strongSide) == 1)) { int strongKingDist = square_distance(weakPawnSq, strongKingSq); int weakKingDist = square_distance(weakPawnSq, weakKingSq); // It's a draw if the weak king is on its back two ranks, within 2 // squares of the blocking pawn and the strong king is not // closer. (I think this rule only fails in practically // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w // and positions where qsearch will immediately correct the // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w) if ( relative_rank(strongSide, weakKingSq) >= RANK_7 && weakKingDist <= 2 && weakKingDist <= strongKingDist) return SCALE_FACTOR_DRAW; } } return SCALE_FACTOR_NONE; } /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on /// the third rank defended by a pawn. template<> ScaleFactor Endgame::operator()(const Position& pos) const { assert(verify_material(pos, strongSide, QueenValueMg, 0)); assert(pos.count(weakSide) == 1); assert(pos.count(weakSide) >= 1); Square kingSq = pos.king_square(weakSide); Square rsq = pos.list(weakSide)[0]; if ( relative_rank(weakSide, kingSq) <= RANK_2 && relative_rank(weakSide, pos.king_square(strongSide)) >= RANK_4 && relative_rank(weakSide, rsq) == RANK_3 && ( pos.pieces(weakSide, PAWN) & pos.attacks_from(kingSq) & pos.attacks_from(rsq, strongSide))) return SCALE_FACTOR_DRAW; return SCALE_FACTOR_NONE; } /// KRP vs KR. This function knows a handful of the most important classes of /// drawn positions, but is far from perfect. It would probably be a good idea /// to add more knowledge in the future. /// /// It would also be nice to rewrite the actual code for this function, /// which is mostly copied from Glaurung 1.x, and isn't very pretty. template<> ScaleFactor Endgame::operator()(const Position& pos) const { assert(verify_material(pos, strongSide, RookValueMg, 1)); assert(verify_material(pos, weakSide, RookValueMg, 0)); // Assume strongSide is white and the pawn is on files A-D Square wksq = normalize(pos, strongSide, pos.king_square(strongSide)); Square bksq = normalize(pos, strongSide, pos.king_square(weakSide)); Square wrsq = normalize(pos, strongSide, pos.list(strongSide)[0]); Square wpsq = normalize(pos, strongSide, pos.list(strongSide)[0]); Square brsq = normalize(pos, strongSide, pos.list(weakSide)[0]); File f = file_of(wpsq); Rank r = rank_of(wpsq); Square queeningSq = make_square(f, RANK_8); int tempo = (pos.side_to_move() == strongSide); // If the pawn is not too far advanced and the defending king defends the // queening square, use the third-rank defence. if ( r <= RANK_5 && square_distance(bksq, queeningSq) <= 1 && wksq <= SQ_H5 && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6))) return SCALE_FACTOR_DRAW; // The defending side saves a draw by checking from behind in case the pawn // has advanced to the 6th rank with the king behind. if ( r == RANK_6 && square_distance(bksq, queeningSq) <= 1 && rank_of(wksq) + tempo <= RANK_6 && (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3))) return SCALE_FACTOR_DRAW; if ( r >= RANK_6 && bksq == queeningSq && rank_of(brsq) == RANK_1 && (!tempo || square_distance(wksq, wpsq) >= 2)) return SCALE_FACTOR_DRAW; // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7 // and the black rook is behind the pawn. if ( wpsq == SQ_A7 && wrsq == SQ_A8 && (bksq == SQ_H7 || bksq == SQ_G7) && file_of(brsq) == FILE_A && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5)) return SCALE_FACTOR_DRAW; // If the defending king blocks the pawn and the attacking king is too far // away, it's a draw. if ( r <= RANK_5 && bksq == wpsq + DELTA_N && square_distance(wksq, wpsq) - tempo >= 2 && square_distance(wksq, brsq) - tempo >= 2) return SCALE_FACTOR_DRAW; // Pawn on the 7th rank supported by the rook from behind usually wins if the // attacking king is closer to the queening square than the defending king, // and the defending king cannot gain tempi by threatening the attacking rook. if ( r == RANK_7 && f != FILE_A && file_of(wrsq) == f && wrsq != queeningSq && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo) && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo)) return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq)); // Similar to the above, but with the pawn further back if ( f != FILE_A && file_of(wrsq) == f && wrsq < wpsq && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo) && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo) && ( square_distance(bksq, wrsq) + tempo >= 3 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo)))) return ScaleFactor( SCALE_FACTOR_MAX - 8 * square_distance(wpsq, queeningSq) - 2 * square_distance(wksq, queeningSq)); // If the pawn is not far advanced and the defending king is somewhere in // the pawn's path, it's probably a draw. if (r <= RANK_4 && bksq > wpsq) { if (file_of(bksq) == file_of(wpsq)) return ScaleFactor(10); if ( abs(file_of(bksq) - file_of(wpsq)) == 1 && square_distance(wksq, bksq) > 2) return ScaleFactor(24 - 2 * square_distance(wksq, bksq)); } return SCALE_FACTOR_NONE; } template<> ScaleFactor Endgame::operator()(const Position& pos) const { assert(verify_material(pos, strongSide, RookValueMg, 1)); assert(verify_material(pos, weakSide, BishopValueMg, 0)); // Test for a rook pawn if (pos.pieces(PAWN) & (FileABB | FileHBB)) { Square ksq = pos.king_square(weakSide); Square bsq = pos.list(weakSide)[0]; Square psq = pos.list(strongSide)[0]; Rank rk = relative_rank(strongSide, psq); Square push = pawn_push(strongSide); // If the pawn is on the 5th rank and the pawn (currently) is on // the same color square as the bishop then there is a chance of // a fortress. Depending on the king position give a moderate // reduction or a stronger one if the defending king is near the // corner but not trapped there. if (rk == RANK_5 && !opposite_colors(bsq, psq)) { int d = square_distance(psq + 3 * push, ksq); if (d <= 2 && !(d == 0 && ksq == pos.king_square(strongSide) + 2 * push)) return ScaleFactor(24); else return ScaleFactor(48); } // When the pawn has moved to the 6th rank we can be fairly sure // it's drawn if the bishop attacks the square in front of the // pawn from a reasonable distance and the defending king is near // the corner if ( rk == RANK_6 && square_distance(psq + 2 * push, ksq) <= 1 && (PseudoAttacks[BISHOP][bsq] & (psq + push)) && file_distance(bsq, psq) >= 2) return ScaleFactor(8); } return SCALE_FACTOR_NONE; } /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed /// pawns and the defending king is actively placed, the position is drawish. template<> ScaleFactor Endgame::operator()(const Position& pos) const { assert(verify_material(pos, strongSide, RookValueMg, 2)); assert(verify_material(pos, weakSide, RookValueMg, 1)); Square wpsq1 = pos.list(strongSide)[0]; Square wpsq2 = pos.list(strongSide)[1]; Square bksq = pos.king_square(weakSide); // Does the stronger side have a passed pawn? if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2)) return SCALE_FACTOR_NONE; Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2)); if ( file_distance(bksq, wpsq1) <= 1 && file_distance(bksq, wpsq2) <= 1 && relative_rank(strongSide, bksq) > r) { switch (r) { case RANK_2: return ScaleFactor(10); case RANK_3: return ScaleFactor(10); case RANK_4: return ScaleFactor(15); case RANK_5: return ScaleFactor(20); case RANK_6: return ScaleFactor(40); default: assert(false); } } return SCALE_FACTOR_NONE; } /// K and two or more pawns vs K. There is just a single rule here: If all pawns /// are on the same rook file and are blocked by the defending king, it's a draw. template<> ScaleFactor Endgame::operator()(const Position& pos) const { assert(pos.non_pawn_material(strongSide) == VALUE_ZERO); assert(pos.count(strongSide) >= 2); assert(verify_material(pos, weakSide, VALUE_ZERO, 0)); Square ksq = pos.king_square(weakSide); Bitboard pawns = pos.pieces(strongSide, PAWN); Square psq = pos.list(strongSide)[0]; // If all pawns are ahead of the king, on a single rook file and // the king is within one file of the pawns, it's a draw. if ( !(pawns & ~in_front_bb(weakSide, rank_of(ksq))) && !((pawns & ~FileABB) && (pawns & ~FileHBB)) && file_distance(ksq, psq) <= 1) return SCALE_FACTOR_DRAW; return SCALE_FACTOR_NONE; } /// KBP vs KB. There are two rules: if the defending king is somewhere along the /// path of the pawn, and the square of the king is not of the same color as the /// stronger side's bishop, it's a draw. If the two bishops have opposite color, /// it's almost always a draw. template<> ScaleFactor Endgame::operator()(const Position& pos) const { assert(verify_material(pos, strongSide, BishopValueMg, 1)); assert(verify_material(pos, weakSide, BishopValueMg, 0)); Square pawnSq = pos.list(strongSide)[0]; Square strongBishopSq = pos.list(strongSide)[0]; Square weakBishopSq = pos.list(weakSide)[0]; Square weakKingSq = pos.king_square(weakSide); // Case 1: Defending king blocks the pawn, and cannot be driven away if ( file_of(weakKingSq) == file_of(pawnSq) && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq) && ( opposite_colors(weakKingSq, strongBishopSq) || relative_rank(strongSide, weakKingSq) <= RANK_6)) return SCALE_FACTOR_DRAW; // Case 2: Opposite colored bishops if (opposite_colors(strongBishopSq, weakBishopSq)) { // We assume that the position is drawn in the following three situations: // // a. The pawn is on rank 5 or further back. // b. The defending king is somewhere in the pawn's path. // c. The defending bishop attacks some square along the pawn's path, // and is at least three squares away from the pawn. // // These rules are probably not perfect, but in practice they work // reasonably well. if (relative_rank(strongSide, pawnSq) <= RANK_5) return SCALE_FACTOR_DRAW; else { Bitboard path = forward_bb(strongSide, pawnSq); if (path & pos.pieces(weakSide, KING)) return SCALE_FACTOR_DRAW; if ( (pos.attacks_from(weakBishopSq) & path) && square_distance(weakBishopSq, pawnSq) >= 3) return SCALE_FACTOR_DRAW; } } return SCALE_FACTOR_NONE; } /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops template<> ScaleFactor Endgame::operator()(const Position& pos) const { assert(verify_material(pos, strongSide, BishopValueMg, 2)); assert(verify_material(pos, weakSide, BishopValueMg, 0)); Square wbsq = pos.list(strongSide)[0]; Square bbsq = pos.list(weakSide)[0]; if (!opposite_colors(wbsq, bbsq)) return SCALE_FACTOR_NONE; Square ksq = pos.king_square(weakSide); Square psq1 = pos.list(strongSide)[0]; Square psq2 = pos.list(strongSide)[1]; Rank r1 = rank_of(psq1); Rank r2 = rank_of(psq2); Square blockSq1, blockSq2; if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2)) { blockSq1 = psq1 + pawn_push(strongSide); blockSq2 = make_square(file_of(psq2), rank_of(psq1)); } else { blockSq1 = psq2 + pawn_push(strongSide); blockSq2 = make_square(file_of(psq1), rank_of(psq2)); } switch (file_distance(psq1, psq2)) { case 0: // Both pawns are on the same file. It's an easy draw if the defender firmly // controls some square in the frontmost pawn's path. if ( file_of(ksq) == file_of(blockSq1) && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1) && opposite_colors(ksq, wbsq)) return SCALE_FACTOR_DRAW; else return SCALE_FACTOR_NONE; case 1: // Pawns on adjacent files. It's a draw if the defender firmly controls the // square in front of the frontmost pawn's path, and the square diagonally // behind this square on the file of the other pawn. if ( ksq == blockSq1 && opposite_colors(ksq, wbsq) && ( bbsq == blockSq2 || (pos.attacks_from(blockSq2) & pos.pieces(weakSide, BISHOP)) || abs(r1 - r2) >= 2)) return SCALE_FACTOR_DRAW; else if ( ksq == blockSq2 && opposite_colors(ksq, wbsq) && ( bbsq == blockSq1 || (pos.attacks_from(blockSq1) & pos.pieces(weakSide, BISHOP)))) return SCALE_FACTOR_DRAW; else return SCALE_FACTOR_NONE; default: // The pawns are not on the same file or adjacent files. No scaling. return SCALE_FACTOR_NONE; } } /// KBP vs KN. There is a single rule: If the defending king is somewhere along /// the path of the pawn, and the square of the king is not of the same color as /// the stronger side's bishop, it's a draw. template<> ScaleFactor Endgame::operator()(const Position& pos) const { assert(verify_material(pos, strongSide, BishopValueMg, 1)); assert(verify_material(pos, weakSide, KnightValueMg, 0)); Square pawnSq = pos.list(strongSide)[0]; Square strongBishopSq = pos.list(strongSide)[0]; Square weakKingSq = pos.king_square(weakSide); if ( file_of(weakKingSq) == file_of(pawnSq) && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq) && ( opposite_colors(weakKingSq, strongBishopSq) || relative_rank(strongSide, weakKingSq) <= RANK_6)) return SCALE_FACTOR_DRAW; return SCALE_FACTOR_NONE; } /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank /// and the defending king prevents the pawn from advancing, the position is drawn. template<> ScaleFactor Endgame::operator()(const Position& pos) const { assert(verify_material(pos, strongSide, KnightValueMg, 1)); assert(verify_material(pos, weakSide, VALUE_ZERO, 0)); // Assume strongSide is white and the pawn is on files A-D Square pawnSq = normalize(pos, strongSide, pos.list(strongSide)[0]); Square weakKingSq = normalize(pos, strongSide, pos.king_square(weakSide)); if (pawnSq == SQ_A7 && square_distance(SQ_A8, weakKingSq) <= 1) return SCALE_FACTOR_DRAW; return SCALE_FACTOR_NONE; } /// KNP vs KB. If knight can block bishop from taking pawn, it's a win. /// Otherwise the position is drawn. template<> ScaleFactor Endgame::operator()(const Position& pos) const { Square pawnSq = pos.list(strongSide)[0]; Square bishopSq = pos.list(weakSide)[0]; Square weakKingSq = pos.king_square(weakSide); // King needs to get close to promoting pawn to prevent knight from blocking. // Rules for this are very tricky, so just approximate. if (forward_bb(strongSide, pawnSq) & pos.attacks_from(bishopSq)) return ScaleFactor(square_distance(weakKingSq, pawnSq)); return SCALE_FACTOR_NONE; } /// KP vs KP. This is done by removing the weakest side's pawn and probing the /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably /// has at least a draw with the pawn as well. The exception is when the stronger /// side's pawn is far advanced and not on a rook file; in this case it is often /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1). template<> ScaleFactor Endgame::operator()(const Position& pos) const { assert(verify_material(pos, strongSide, VALUE_ZERO, 1)); assert(verify_material(pos, weakSide, VALUE_ZERO, 1)); // Assume strongSide is white and the pawn is on files A-D Square wksq = normalize(pos, strongSide, pos.king_square(strongSide)); Square bksq = normalize(pos, strongSide, pos.king_square(weakSide)); Square psq = normalize(pos, strongSide, pos.list(strongSide)[0]); Color us = strongSide == pos.side_to_move() ? WHITE : BLACK; // If the pawn has advanced to the fifth rank or further, and is not a // rook pawn, it's too dangerous to assume that it's at least a draw. if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A) return SCALE_FACTOR_NONE; // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw, // it's probably at least a draw even with the pawn. return Bitbases::probe_kpk(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW; }