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  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 <algorithm>
  22. #include <cassert>
  23.  
  24. #include "bitboard.h"
  25. #include "endgame.h"
  26. #include "movegen.h"
  27.  
  28. using std::string;
  29.  
  30. namespace {
  31.  
  32.   // Table used to drive the king towards the edge of the board
  33.   // in KX vs K and KQ vs KR endgames.
  34.   constexpr int PushToEdges[SQUARE_NB] = {
  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
  43.   };
  44.  
  45.   // Table used to drive the king towards a corner square of the
  46.   // right color in KBN vs K endgames.
  47.   constexpr int PushToCorners[SQUARE_NB] = {
  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
  56.   };
  57.  
  58.   // Tables used to drive a piece towards or away from another piece
  59.   constexpr int PushClose[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
  60.   constexpr int PushAway [8] = { 0, 5, 20, 40, 60, 80, 90, 100 };
  61.  
  62.   // Pawn Rank based scaling factors used in KRPPKRP endgame
  63.   constexpr int KRPPKRPScaleFactors[RANK_NB] = { 0, 9, 10, 14, 21, 44, 0, 0 };
  64.  
  65. #ifndef NDEBUG
  66.   bool verify_material(const Position& pos, Color c, Value npm, int pawnsCnt) {
  67.     return pos.non_pawn_material(c) == npm && pos.count<PAWN>(c) == pawnsCnt;
  68.   }
  69. #endif
  70.  
  71.   // Map the square as if strongSide is white and strongSide's only pawn
  72.   // is on the left half of the board.
  73.   Square normalize(const Position& pos, Color strongSide, Square sq) {
  74.  
  75.     assert(pos.count<PAWN>(strongSide) == 1);
  76.  
  77.     if (file_of(pos.square<PAWN>(strongSide)) >= FILE_E)
  78.         sq = Square(sq ^ 7); // Mirror SQ_H1 -> SQ_A1
  79.  
  80.     if (strongSide == BLACK)
  81.         sq = ~sq;
  82.  
  83.     return sq;
  84.   }
  85.  
  86. } // namespace
  87.  
  88.  
  89. /// Mate with KX vs K. This function is used to evaluate positions with
  90. /// king and plenty of material vs a lone king. It simply gives the
  91. /// attacking side a bonus for driving the defending king towards the edge
  92. /// of the board, and for keeping the distance between the two kings small.
  93. template<>
  94. Value Endgame<KXK>::operator()(const Position& pos) const {
  95.  
  96.   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  97.   assert(!pos.checkers()); // Eval is never called when in check
  98.  
  99.   // Stalemate detection with lone king
  100.   if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
  101.       return VALUE_DRAW;
  102.  
  103.   Square winnerKSq = pos.square<KING>(strongSide);
  104.   Square loserKSq = pos.square<KING>(weakSide);
  105.  
  106.   Value result =  pos.non_pawn_material(strongSide)
  107.                 + pos.count<PAWN>(strongSide) * PawnValueEg
  108.                 + PushToEdges[loserKSq]
  109.                 + PushClose[distance(winnerKSq, loserKSq)];
  110.  
  111.   if (   pos.count<QUEEN>(strongSide)
  112.       || pos.count<ROOK>(strongSide)
  113.       ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
  114.       || (   (pos.pieces(strongSide, BISHOP) & ~DarkSquares)
  115.           && (pos.pieces(strongSide, BISHOP) &  DarkSquares)))
  116.       result = std::min(result + VALUE_KNOWN_WIN, VALUE_MATE_IN_MAX_PLY - 1);
  117.  
  118.   return strongSide == pos.side_to_move() ? result : -result;
  119. }
  120.  
  121.  
  122. /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
  123. /// defending king towards a corner square of the right color.
  124. template<>
  125. Value Endgame<KBNK>::operator()(const Position& pos) const {
  126.  
  127.   assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
  128.   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  129.  
  130.   Square winnerKSq = pos.square<KING>(strongSide);
  131.   Square loserKSq = pos.square<KING>(weakSide);
  132.   Square bishopSq = pos.square<BISHOP>(strongSide);
  133.  
  134.   // kbnk_mate_table() tries to drive toward corners A1 or H8. If we have a
  135.   // bishop that cannot reach the above squares, we flip the kings in order
  136.   // to drive the enemy toward corners A8 or H1.
  137.   if (opposite_colors(bishopSq, SQ_A1))
  138.   {
  139.       winnerKSq = ~winnerKSq;
  140.       loserKSq  = ~loserKSq;
  141.   }
  142.  
  143.   Value result =  VALUE_KNOWN_WIN
  144.                 + PushClose[distance(winnerKSq, loserKSq)]
  145.                 + PushToCorners[loserKSq];
  146.  
  147.   return strongSide == pos.side_to_move() ? result : -result;
  148. }
  149.  
  150.  
  151. /// KP vs K. This endgame is evaluated with the help of a bitbase.
  152. template<>
  153. Value Endgame<KPK>::operator()(const Position& pos) const {
  154.  
  155.   assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
  156.   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  157.  
  158.   // Assume strongSide is white and the pawn is on files A-D
  159.   Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
  160.   Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
  161.   Square psq  = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  162.  
  163.   Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
  164.  
  165.   if (!Bitbases::probe(wksq, psq, bksq, us))
  166.       return VALUE_DRAW;
  167.  
  168.   Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
  169.  
  170.   return strongSide == pos.side_to_move() ? result : -result;
  171. }
  172.  
  173.  
  174. /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
  175. /// a bitbase. The function below returns drawish scores when the pawn is
  176. /// far advanced with support of the king, while the attacking king is far
  177. /// away.
  178. template<>
  179. Value Endgame<KRKP>::operator()(const Position& pos) const {
  180.  
  181.   assert(verify_material(pos, strongSide, RookValueMg, 0));
  182.   assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
  183.  
  184.   Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
  185.   Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
  186.   Square rsq  = relative_square(strongSide, pos.square<ROOK>(strongSide));
  187.   Square psq  = relative_square(strongSide, pos.square<PAWN>(weakSide));
  188.  
  189.   Square queeningSq = make_square(file_of(psq), RANK_1);
  190.   Value result;
  191.  
  192.   // If the stronger side's king is in front of the pawn, it's a win
  193.   if (forward_file_bb(WHITE, wksq) & psq)
  194.       result = RookValueEg - distance(wksq, psq);
  195.  
  196.   // If the weaker side's king is too far from the pawn and the rook,
  197.   // it's a win.
  198.   else if (   distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
  199.            && distance(bksq, rsq) >= 3)
  200.       result = RookValueEg - distance(wksq, psq);
  201.  
  202.   // If the pawn is far advanced and supported by the defending king,
  203.   // the position is drawish
  204.   else if (   rank_of(bksq) <= RANK_3
  205.            && distance(bksq, psq) == 1
  206.            && rank_of(wksq) >= RANK_4
  207.            && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
  208.       result = Value(80) - 8 * distance(wksq, psq);
  209.  
  210.   else
  211.       result =  Value(200) - 8 * (  distance(wksq, psq + SOUTH)
  212.                                   - distance(bksq, psq + SOUTH)
  213.                                   - distance(psq, queeningSq));
  214.  
  215.   return strongSide == pos.side_to_move() ? result : -result;
  216. }
  217.  
  218.  
  219. /// KR vs KB. This is very simple, and always returns drawish scores. The
  220. /// score is slightly bigger when the defending king is close to the edge.
  221. template<>
  222. Value Endgame<KRKB>::operator()(const Position& pos) const {
  223.  
  224.   assert(verify_material(pos, strongSide, RookValueMg, 0));
  225.   assert(verify_material(pos, weakSide, BishopValueMg, 0));
  226.  
  227.   Value result = Value(PushToEdges[pos.square<KING>(weakSide)]);
  228.   return strongSide == pos.side_to_move() ? result : -result;
  229. }
  230.  
  231.  
  232. /// KR vs KN. The attacking side has slightly better winning chances than
  233. /// in KR vs KB, particularly if the king and the knight are far apart.
  234. template<>
  235. Value Endgame<KRKN>::operator()(const Position& pos) const {
  236.  
  237.   assert(verify_material(pos, strongSide, RookValueMg, 0));
  238.   assert(verify_material(pos, weakSide, KnightValueMg, 0));
  239.  
  240.   Square bksq = pos.square<KING>(weakSide);
  241.   Square bnsq = pos.square<KNIGHT>(weakSide);
  242.   Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
  243.   return strongSide == pos.side_to_move() ? result : -result;
  244. }
  245.  
  246.  
  247. /// KQ vs KP. In general, this is a win for the stronger side, but there are a
  248. /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
  249. /// with a king positioned next to it can be a draw, so in that case, we only
  250. /// use the distance between the kings.
  251. template<>
  252. Value Endgame<KQKP>::operator()(const Position& pos) const {
  253.  
  254.   assert(verify_material(pos, strongSide, QueenValueMg, 0));
  255.   assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
  256.  
  257.   Square winnerKSq = pos.square<KING>(strongSide);
  258.   Square loserKSq = pos.square<KING>(weakSide);
  259.   Square pawnSq = pos.square<PAWN>(weakSide);
  260.  
  261.   Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
  262.  
  263.   if (   relative_rank(weakSide, pawnSq) != RANK_7
  264.       || distance(loserKSq, pawnSq) != 1
  265.       || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
  266.       result += QueenValueEg - PawnValueEg;
  267.  
  268.   return strongSide == pos.side_to_move() ? result : -result;
  269. }
  270.  
  271.  
  272. /// KQ vs KR.  This is almost identical to KX vs K:  We give the attacking
  273. /// king a bonus for having the kings close together, and for forcing the
  274. /// defending king towards the edge. If we also take care to avoid null move for
  275. /// the defending side in the search, this is usually sufficient to win KQ vs KR.
  276. template<>
  277. Value Endgame<KQKR>::operator()(const Position& pos) const {
  278.  
  279.   assert(verify_material(pos, strongSide, QueenValueMg, 0));
  280.   assert(verify_material(pos, weakSide, RookValueMg, 0));
  281.  
  282.   Square winnerKSq = pos.square<KING>(strongSide);
  283.   Square loserKSq = pos.square<KING>(weakSide);
  284.  
  285.   Value result =  QueenValueEg
  286.                 - RookValueEg
  287.                 + PushToEdges[loserKSq]
  288.                 + PushClose[distance(winnerKSq, loserKSq)];
  289.  
  290.   return strongSide == pos.side_to_move() ? result : -result;
  291. }
  292.  
  293.  
  294. /// Some cases of trivial draws
  295. template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
  296.  
  297.  
  298. /// KB and one or more pawns vs K. It checks for draws with rook pawns and
  299. /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
  300. /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
  301. /// will be used.
  302. template<>
  303. ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
  304.  
  305.   assert(pos.non_pawn_material(strongSide) == BishopValueMg);
  306.   assert(pos.count<PAWN>(strongSide) >= 1);
  307.  
  308.   // No assertions about the material of weakSide, because we want draws to
  309.   // be detected even when the weaker side has some pawns.
  310.  
  311.   Bitboard pawns = pos.pieces(strongSide, PAWN);
  312.   File pawnsFile = file_of(lsb(pawns));
  313.  
  314.   // All pawns are on a single rook file?
  315.   if (    (pawnsFile == FILE_A || pawnsFile == FILE_H)
  316.       && !(pawns & ~file_bb(pawnsFile)))
  317.   {
  318.       Square bishopSq = pos.square<BISHOP>(strongSide);
  319.       Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
  320.       Square kingSq = pos.square<KING>(weakSide);
  321.  
  322.       if (   opposite_colors(queeningSq, bishopSq)
  323.           && distance(queeningSq, kingSq) <= 1)
  324.           return SCALE_FACTOR_DRAW;
  325.   }
  326.  
  327.   // If all the pawns are on the same B or G file, then it's potentially a draw
  328.   if (    (pawnsFile == FILE_B || pawnsFile == FILE_G)
  329.       && !(pos.pieces(PAWN) & ~file_bb(pawnsFile))
  330.       && pos.non_pawn_material(weakSide) == 0
  331.       && pos.count<PAWN>(weakSide) >= 1)
  332.   {
  333.       // Get weakSide pawn that is closest to the home rank
  334.       Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
  335.  
  336.       Square strongKingSq = pos.square<KING>(strongSide);
  337.       Square weakKingSq = pos.square<KING>(weakSide);
  338.       Square bishopSq = pos.square<BISHOP>(strongSide);
  339.  
  340.       // There's potential for a draw if our pawn is blocked on the 7th rank,
  341.       // the bishop cannot attack it or they only have one pawn left
  342.       if (   relative_rank(strongSide, weakPawnSq) == RANK_7
  343.           && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
  344.           && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
  345.       {
  346.           int strongKingDist = distance(weakPawnSq, strongKingSq);
  347.           int weakKingDist = distance(weakPawnSq, weakKingSq);
  348.  
  349.           // It's a draw if the weak king is on its back two ranks, within 2
  350.           // squares of the blocking pawn and the strong king is not
  351.           // closer. (I think this rule only fails in practically
  352.           // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
  353.           // and positions where qsearch will immediately correct the
  354.           // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
  355.           if (   relative_rank(strongSide, weakKingSq) >= RANK_7
  356.               && weakKingDist <= 2
  357.               && weakKingDist <= strongKingDist)
  358.               return SCALE_FACTOR_DRAW;
  359.       }
  360.   }
  361.  
  362.   return SCALE_FACTOR_NONE;
  363. }
  364.  
  365.  
  366. /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
  367. /// the third rank defended by a pawn.
  368. template<>
  369. ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
  370.  
  371.   assert(verify_material(pos, strongSide, QueenValueMg, 0));
  372.   assert(pos.count<ROOK>(weakSide) == 1);
  373.   assert(pos.count<PAWN>(weakSide) >= 1);
  374.  
  375.   Square kingSq = pos.square<KING>(weakSide);
  376.   Square rsq = pos.square<ROOK>(weakSide);
  377.  
  378.   if (    relative_rank(weakSide, kingSq) <= RANK_2
  379.       &&  relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
  380.       &&  relative_rank(weakSide, rsq) == RANK_3
  381.       && (  pos.pieces(weakSide, PAWN)
  382.           & pos.attacks_from<KING>(kingSq)
  383.           & pos.attacks_from<PAWN>(rsq, strongSide)))
  384.           return SCALE_FACTOR_DRAW;
  385.  
  386.   return SCALE_FACTOR_NONE;
  387. }
  388.  
  389.  
  390. /// KRP vs KR. This function knows a handful of the most important classes of
  391. /// drawn positions, but is far from perfect. It would probably be a good idea
  392. /// to add more knowledge in the future.
  393. ///
  394. /// It would also be nice to rewrite the actual code for this function,
  395. /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
  396. template<>
  397. ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
  398.  
  399.   assert(verify_material(pos, strongSide, RookValueMg, 1));
  400.   assert(verify_material(pos, weakSide,   RookValueMg, 0));
  401.  
  402.   // Assume strongSide is white and the pawn is on files A-D
  403.   Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
  404.   Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
  405.   Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
  406.   Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  407.   Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
  408.  
  409.   File f = file_of(wpsq);
  410.   Rank r = rank_of(wpsq);
  411.   Square queeningSq = make_square(f, RANK_8);
  412.   int tempo = (pos.side_to_move() == strongSide);
  413.  
  414.   // If the pawn is not too far advanced and the defending king defends the
  415.   // queening square, use the third-rank defence.
  416.   if (   r <= RANK_5
  417.       && distance(bksq, queeningSq) <= 1
  418.       && wksq <= SQ_H5
  419.       && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
  420.       return SCALE_FACTOR_DRAW;
  421.  
  422.   // The defending side saves a draw by checking from behind in case the pawn
  423.   // has advanced to the 6th rank with the king behind.
  424.   if (   r == RANK_6
  425.       && distance(bksq, queeningSq) <= 1
  426.       && rank_of(wksq) + tempo <= RANK_6
  427.       && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
  428.       return SCALE_FACTOR_DRAW;
  429.  
  430.   if (   r >= RANK_6
  431.       && bksq == queeningSq
  432.       && rank_of(brsq) == RANK_1
  433.       && (!tempo || distance(wksq, wpsq) >= 2))
  434.       return SCALE_FACTOR_DRAW;
  435.  
  436.   // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
  437.   // and the black rook is behind the pawn.
  438.   if (   wpsq == SQ_A7
  439.       && wrsq == SQ_A8
  440.       && (bksq == SQ_H7 || bksq == SQ_G7)
  441.       && file_of(brsq) == FILE_A
  442.       && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
  443.       return SCALE_FACTOR_DRAW;
  444.  
  445.   // If the defending king blocks the pawn and the attacking king is too far
  446.   // away, it's a draw.
  447.   if (   r <= RANK_5
  448.       && bksq == wpsq + NORTH
  449.       && distance(wksq, wpsq) - tempo >= 2
  450.       && distance(wksq, brsq) - tempo >= 2)
  451.       return SCALE_FACTOR_DRAW;
  452.  
  453.   // Pawn on the 7th rank supported by the rook from behind usually wins if the
  454.   // attacking king is closer to the queening square than the defending king,
  455.   // and the defending king cannot gain tempi by threatening the attacking rook.
  456.   if (   r == RANK_7
  457.       && f != FILE_A
  458.       && file_of(wrsq) == f
  459.       && wrsq != queeningSq
  460.       && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
  461.       && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
  462.       return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
  463.  
  464.   // Similar to the above, but with the pawn further back
  465.   if (   f != FILE_A
  466.       && file_of(wrsq) == f
  467.       && wrsq < wpsq
  468.       && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
  469.       && (distance(wksq, wpsq + NORTH) < distance(bksq, wpsq + NORTH) - 2 + tempo)
  470.       && (  distance(bksq, wrsq) + tempo >= 3
  471.           || (    distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
  472.               && (distance(wksq, wpsq + NORTH) < distance(bksq, wrsq) + tempo))))
  473.       return ScaleFactor(  SCALE_FACTOR_MAX
  474.                          - 8 * distance(wpsq, queeningSq)
  475.                          - 2 * distance(wksq, queeningSq));
  476.  
  477.   // If the pawn is not far advanced and the defending king is somewhere in
  478.   // the pawn's path, it's probably a draw.
  479.   if (r <= RANK_4 && bksq > wpsq)
  480.   {
  481.       if (file_of(bksq) == file_of(wpsq))
  482.           return ScaleFactor(10);
  483.       if (   distance<File>(bksq, wpsq) == 1
  484.           && distance(wksq, bksq) > 2)
  485.           return ScaleFactor(24 - 2 * distance(wksq, bksq));
  486.   }
  487.   return SCALE_FACTOR_NONE;
  488. }
  489.  
  490. template<>
  491. ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
  492.  
  493.   assert(verify_material(pos, strongSide, RookValueMg, 1));
  494.   assert(verify_material(pos, weakSide, BishopValueMg, 0));
  495.  
  496.   // Test for a rook pawn
  497.   if (pos.pieces(PAWN) & (FileABB | FileHBB))
  498.   {
  499.       Square ksq = pos.square<KING>(weakSide);
  500.       Square bsq = pos.square<BISHOP>(weakSide);
  501.       Square psq = pos.square<PAWN>(strongSide);
  502.       Rank rk = relative_rank(strongSide, psq);
  503.       Direction push = pawn_push(strongSide);
  504.  
  505.       // If the pawn is on the 5th rank and the pawn (currently) is on
  506.       // the same color square as the bishop then there is a chance of
  507.       // a fortress. Depending on the king position give a moderate
  508.       // reduction or a stronger one if the defending king is near the
  509.       // corner but not trapped there.
  510.       if (rk == RANK_5 && !opposite_colors(bsq, psq))
  511.       {
  512.           int d = distance(psq + 3 * push, ksq);
  513.  
  514.           if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
  515.               return ScaleFactor(24);
  516.           else
  517.               return ScaleFactor(48);
  518.       }
  519.  
  520.       // When the pawn has moved to the 6th rank we can be fairly sure
  521.       // it's drawn if the bishop attacks the square in front of the
  522.       // pawn from a reasonable distance and the defending king is near
  523.       // the corner
  524.       if (   rk == RANK_6
  525.           && distance(psq + 2 * push, ksq) <= 1
  526.           && (PseudoAttacks[BISHOP][bsq] & (psq + push))
  527.           && distance<File>(bsq, psq) >= 2)
  528.           return ScaleFactor(8);
  529.   }
  530.  
  531.   return SCALE_FACTOR_NONE;
  532. }
  533.  
  534. /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
  535. /// pawns and the defending king is actively placed, the position is drawish.
  536. template<>
  537. ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
  538.  
  539.   assert(verify_material(pos, strongSide, RookValueMg, 2));
  540.   assert(verify_material(pos, weakSide,   RookValueMg, 1));
  541.  
  542.   Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
  543.   Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
  544.   Square bksq = pos.square<KING>(weakSide);
  545.  
  546.   // Does the stronger side have a passed pawn?
  547.   if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
  548.       return SCALE_FACTOR_NONE;
  549.  
  550.   Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
  551.  
  552.   if (   distance<File>(bksq, wpsq1) <= 1
  553.       && distance<File>(bksq, wpsq2) <= 1
  554.       && relative_rank(strongSide, bksq) > r)
  555.   {
  556.       assert(r > RANK_1 && r < RANK_7);
  557.       return ScaleFactor(KRPPKRPScaleFactors[r]);
  558.   }
  559.   return SCALE_FACTOR_NONE;
  560. }
  561.  
  562.  
  563. /// K and two or more pawns vs K. There is just a single rule here: If all pawns
  564. /// are on the same rook file and are blocked by the defending king, it's a draw.
  565. template<>
  566. ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
  567.  
  568.   assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
  569.   assert(pos.count<PAWN>(strongSide) >= 2);
  570.   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  571.  
  572.   Square ksq = pos.square<KING>(weakSide);
  573.   Bitboard pawns = pos.pieces(strongSide, PAWN);
  574.  
  575.   // If all pawns are ahead of the king, on a single rook file and
  576.   // the king is within one file of the pawns, it's a draw.
  577.   if (   !(pawns & ~forward_ranks_bb(weakSide, ksq))
  578.       && !((pawns & ~FileABB) && (pawns & ~FileHBB))
  579.       &&  distance<File>(ksq, lsb(pawns)) <= 1)
  580.       return SCALE_FACTOR_DRAW;
  581.  
  582.   return SCALE_FACTOR_NONE;
  583. }
  584.  
  585.  
  586. /// KBP vs KB. There are two rules: if the defending king is somewhere along the
  587. /// path of the pawn, and the square of the king is not of the same color as the
  588. /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
  589. /// it's almost always a draw.
  590. template<>
  591. ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
  592.  
  593.   assert(verify_material(pos, strongSide, BishopValueMg, 1));
  594.   assert(verify_material(pos, weakSide,   BishopValueMg, 0));
  595.  
  596.   Square pawnSq = pos.square<PAWN>(strongSide);
  597.   Square strongBishopSq = pos.square<BISHOP>(strongSide);
  598.   Square weakBishopSq = pos.square<BISHOP>(weakSide);
  599.   Square weakKingSq = pos.square<KING>(weakSide);
  600.  
  601.   // Case 1: Defending king blocks the pawn, and cannot be driven away
  602.   if (   file_of(weakKingSq) == file_of(pawnSq)
  603.       && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
  604.       && (   opposite_colors(weakKingSq, strongBishopSq)
  605.           || relative_rank(strongSide, weakKingSq) <= RANK_6))
  606.       return SCALE_FACTOR_DRAW;
  607.  
  608.   // Case 2: Opposite colored bishops
  609.   if (opposite_colors(strongBishopSq, weakBishopSq))
  610.       return SCALE_FACTOR_DRAW;
  611.  
  612.   return SCALE_FACTOR_NONE;
  613. }
  614.  
  615.  
  616. /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
  617. template<>
  618. ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
  619.  
  620.   assert(verify_material(pos, strongSide, BishopValueMg, 2));
  621.   assert(verify_material(pos, weakSide,   BishopValueMg, 0));
  622.  
  623.   Square wbsq = pos.square<BISHOP>(strongSide);
  624.   Square bbsq = pos.square<BISHOP>(weakSide);
  625.  
  626.   if (!opposite_colors(wbsq, bbsq))
  627.       return SCALE_FACTOR_NONE;
  628.  
  629.   Square ksq = pos.square<KING>(weakSide);
  630.   Square psq1 = pos.squares<PAWN>(strongSide)[0];
  631.   Square psq2 = pos.squares<PAWN>(strongSide)[1];
  632.   Rank r1 = rank_of(psq1);
  633.   Rank r2 = rank_of(psq2);
  634.   Square blockSq1, blockSq2;
  635.  
  636.   if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
  637.   {
  638.       blockSq1 = psq1 + pawn_push(strongSide);
  639.       blockSq2 = make_square(file_of(psq2), rank_of(psq1));
  640.   }
  641.   else
  642.   {
  643.       blockSq1 = psq2 + pawn_push(strongSide);
  644.       blockSq2 = make_square(file_of(psq1), rank_of(psq2));
  645.   }
  646.  
  647.   switch (distance<File>(psq1, psq2))
  648.   {
  649.   case 0:
  650.     // Both pawns are on the same file. It's an easy draw if the defender firmly
  651.     // controls some square in the frontmost pawn's path.
  652.     if (   file_of(ksq) == file_of(blockSq1)
  653.         && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
  654.         && opposite_colors(ksq, wbsq))
  655.         return SCALE_FACTOR_DRAW;
  656.     else
  657.         return SCALE_FACTOR_NONE;
  658.  
  659.   case 1:
  660.     // Pawns on adjacent files. It's a draw if the defender firmly controls the
  661.     // square in front of the frontmost pawn's path, and the square diagonally
  662.     // behind this square on the file of the other pawn.
  663.     if (   ksq == blockSq1
  664.         && opposite_colors(ksq, wbsq)
  665.         && (   bbsq == blockSq2
  666.             || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
  667.             || distance(r1, r2) >= 2))
  668.         return SCALE_FACTOR_DRAW;
  669.  
  670.     else if (   ksq == blockSq2
  671.              && opposite_colors(ksq, wbsq)
  672.              && (   bbsq == blockSq1
  673.                  || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
  674.         return SCALE_FACTOR_DRAW;
  675.     else
  676.         return SCALE_FACTOR_NONE;
  677.  
  678.   default:
  679.     // The pawns are not on the same file or adjacent files. No scaling.
  680.     return SCALE_FACTOR_NONE;
  681.   }
  682. }
  683.  
  684.  
  685. /// KBP vs KN. There is a single rule: If the defending king is somewhere along
  686. /// the path of the pawn, and the square of the king is not of the same color as
  687. /// the stronger side's bishop, it's a draw.
  688. template<>
  689. ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
  690.  
  691.   assert(verify_material(pos, strongSide, BishopValueMg, 1));
  692.   assert(verify_material(pos, weakSide, KnightValueMg, 0));
  693.  
  694.   Square pawnSq = pos.square<PAWN>(strongSide);
  695.   Square strongBishopSq = pos.square<BISHOP>(strongSide);
  696.   Square weakKingSq = pos.square<KING>(weakSide);
  697.  
  698.   if (   file_of(weakKingSq) == file_of(pawnSq)
  699.       && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
  700.       && (   opposite_colors(weakKingSq, strongBishopSq)
  701.           || relative_rank(strongSide, weakKingSq) <= RANK_6))
  702.       return SCALE_FACTOR_DRAW;
  703.  
  704.   return SCALE_FACTOR_NONE;
  705. }
  706.  
  707.  
  708. /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
  709. /// and the defending king prevents the pawn from advancing, the position is drawn.
  710. template<>
  711. ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
  712.  
  713.   assert(verify_material(pos, strongSide, KnightValueMg, 1));
  714.   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  715.  
  716.   // Assume strongSide is white and the pawn is on files A-D
  717.   Square pawnSq     = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  718.   Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
  719.  
  720.   if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
  721.       return SCALE_FACTOR_DRAW;
  722.  
  723.   return SCALE_FACTOR_NONE;
  724. }
  725.  
  726.  
  727. /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
  728. /// Otherwise the position is drawn.
  729. template<>
  730. ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
  731.  
  732.   Square pawnSq = pos.square<PAWN>(strongSide);
  733.   Square bishopSq = pos.square<BISHOP>(weakSide);
  734.   Square weakKingSq = pos.square<KING>(weakSide);
  735.  
  736.   // King needs to get close to promoting pawn to prevent knight from blocking.
  737.   // Rules for this are very tricky, so just approximate.
  738.   if (forward_file_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
  739.       return ScaleFactor(distance(weakKingSq, pawnSq));
  740.  
  741.   return SCALE_FACTOR_NONE;
  742. }
  743.  
  744.  
  745. /// KP vs KP. This is done by removing the weakest side's pawn and probing the
  746. /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
  747. /// has at least a draw with the pawn as well. The exception is when the stronger
  748. /// side's pawn is far advanced and not on a rook file; in this case it is often
  749. /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
  750. template<>
  751. ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
  752.  
  753.   assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
  754.   assert(verify_material(pos, weakSide,   VALUE_ZERO, 1));
  755.  
  756.   // Assume strongSide is white and the pawn is on files A-D
  757.   Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
  758.   Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
  759.   Square psq  = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  760.  
  761.   Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
  762.  
  763.   // If the pawn has advanced to the fifth rank or further, and is not a
  764.   // rook pawn, it's too dangerous to assume that it's at least a draw.
  765.   if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
  766.       return SCALE_FACTOR_NONE;
  767.  
  768.   // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
  769.   // it's probably at least a draw even with the pawn.
  770.   return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;
  771. }
  772.