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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) 2015-2018 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.   const 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.   const 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.   const int PushClose[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
  60.   const int PushAway [8] = { 0, 5, 20, 40, 60, 80, 90, 100 };
  61.  
  62.   // Pawn Rank based scaling factors used in KRPPKRP endgame
  63.   const 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. /// Endgames members definitions
  90.  
  91. Endgames::Endgames() {
  92.  
  93.   add<KPK>("KPK");
  94.   add<KNNK>("KNNK");
  95.   add<KBNK>("KBNK");
  96.   add<KRKP>("KRKP");
  97.   add<KRKB>("KRKB");
  98.   add<KRKN>("KRKN");
  99.   add<KQKP>("KQKP");
  100.   add<KQKR>("KQKR");
  101.  
  102.   add<KNPK>("KNPK");
  103.   add<KNPKB>("KNPKB");
  104.   add<KRPKR>("KRPKR");
  105.   add<KRPKB>("KRPKB");
  106.   add<KBPKB>("KBPKB");
  107.   add<KBPKN>("KBPKN");
  108.   add<KBPPKB>("KBPPKB");
  109.   add<KRPPKRP>("KRPPKRP");
  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.
  117. template<>
  118. Value 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 of the right color.
  148. template<>
  149. Value 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.   // kbnk_mate_table() tries to drive toward corners A1 or H8. If we have a
  159.   // bishop that cannot reach the above squares, we flip the kings in order
  160.   // to drive the enemy toward corners A8 or H1.
  161.   if (opposite_colors(bishopSq, SQ_A1))
  162.   {
  163.       winnerKSq = ~winnerKSq;
  164.       loserKSq  = ~loserKSq;
  165.   }
  166.  
  167.   Value result =  VALUE_KNOWN_WIN
  168.                 + PushClose[distance(winnerKSq, loserKSq)]
  169.                 + PushToCorners[loserKSq];
  170.  
  171.   return strongSide == pos.side_to_move() ? result : -result;
  172. }
  173.  
  174.  
  175. /// KP vs K. This endgame is evaluated with the help of a bitbase.
  176. template<>
  177. Value Endgame<KPK>::operator()(const Position& pos) const {
  178.  
  179.   assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
  180.   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  181.  
  182.   // Assume strongSide is white and the pawn is on files A-D
  183.   Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
  184.   Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
  185.   Square psq  = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  186.  
  187.   Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
  188.  
  189.   if (!Bitbases::probe(wksq, psq, bksq, us))
  190.       return VALUE_DRAW;
  191.  
  192.   Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
  193.  
  194.   return strongSide == pos.side_to_move() ? result : -result;
  195. }
  196.  
  197.  
  198. /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
  199. /// a bitbase. The function below returns drawish scores when the pawn is
  200. /// far advanced with support of the king, while the attacking king is far
  201. /// away.
  202. template<>
  203. Value Endgame<KRKP>::operator()(const Position& pos) const {
  204.  
  205.   assert(verify_material(pos, strongSide, RookValueMg, 0));
  206.   assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
  207.  
  208.   Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
  209.   Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
  210.   Square rsq  = relative_square(strongSide, pos.square<ROOK>(strongSide));
  211.   Square psq  = relative_square(strongSide, pos.square<PAWN>(weakSide));
  212.  
  213.   Square queeningSq = make_square(file_of(psq), RANK_1);
  214.   Value result;
  215.  
  216.   // If the stronger side's king is in front of the pawn, it's a win
  217.   if (wksq < psq && file_of(wksq) == file_of(psq))
  218.       result = RookValueEg - distance(wksq, psq);
  219.  
  220.   // If the weaker side's king is too far from the pawn and the rook,
  221.   // it's a win.
  222.   else if (   distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
  223.            && distance(bksq, rsq) >= 3)
  224.       result = RookValueEg - distance(wksq, psq);
  225.  
  226.   // If the pawn is far advanced and supported by the defending king,
  227.   // the position is drawish
  228.   else if (   rank_of(bksq) <= RANK_3
  229.            && distance(bksq, psq) == 1
  230.            && rank_of(wksq) >= RANK_4
  231.            && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
  232.       result = Value(80) - 8 * distance(wksq, psq);
  233.  
  234.   else
  235.       result =  Value(200) - 8 * (  distance(wksq, psq + SOUTH)
  236.                                   - distance(bksq, psq + SOUTH)
  237.                                   - distance(psq, queeningSq));
  238.  
  239.   return strongSide == pos.side_to_move() ? result : -result;
  240. }
  241.  
  242.  
  243. /// KR vs KB. This is very simple, and always returns drawish scores.  The
  244. /// score is slightly bigger when the defending king is close to the edge.
  245. template<>
  246. Value Endgame<KRKB>::operator()(const Position& pos) const {
  247.  
  248.   assert(verify_material(pos, strongSide, RookValueMg, 0));
  249.   assert(verify_material(pos, weakSide, BishopValueMg, 0));
  250.  
  251.   Value result = Value(PushToEdges[pos.square<KING>(weakSide)]);
  252.   return strongSide == pos.side_to_move() ? result : -result;
  253. }
  254.  
  255.  
  256. /// KR vs KN. The attacking side has slightly better winning chances than
  257. /// in KR vs KB, particularly if the king and the knight are far apart.
  258. template<>
  259. Value Endgame<KRKN>::operator()(const Position& pos) const {
  260.  
  261.   assert(verify_material(pos, strongSide, RookValueMg, 0));
  262.   assert(verify_material(pos, weakSide, KnightValueMg, 0));
  263.  
  264.   Square bksq = pos.square<KING>(weakSide);
  265.   Square bnsq = pos.square<KNIGHT>(weakSide);
  266.   Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
  267.   return strongSide == pos.side_to_move() ? result : -result;
  268. }
  269.  
  270.  
  271. /// KQ vs KP. In general, this is a win for the stronger side, but there are a
  272. /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
  273. /// with a king positioned next to it can be a draw, so in that case, we only
  274. /// use the distance between the kings.
  275. template<>
  276. Value Endgame<KQKP>::operator()(const Position& pos) const {
  277.  
  278.   assert(verify_material(pos, strongSide, QueenValueMg, 0));
  279.   assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
  280.  
  281.   Square winnerKSq = pos.square<KING>(strongSide);
  282.   Square loserKSq = pos.square<KING>(weakSide);
  283.   Square pawnSq = pos.square<PAWN>(weakSide);
  284.  
  285.   Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
  286.  
  287.   if (   relative_rank(weakSide, pawnSq) != RANK_7
  288.       || distance(loserKSq, pawnSq) != 1
  289.       || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
  290.       result += QueenValueEg - PawnValueEg;
  291.  
  292.   return strongSide == pos.side_to_move() ? result : -result;
  293. }
  294.  
  295.  
  296. /// KQ vs KR.  This is almost identical to KX vs K:  We give the attacking
  297. /// king a bonus for having the kings close together, and for forcing the
  298. /// defending king towards the edge. If we also take care to avoid null move for
  299. /// the defending side in the search, this is usually sufficient to win KQ vs KR.
  300. template<>
  301. Value Endgame<KQKR>::operator()(const Position& pos) const {
  302.  
  303.   assert(verify_material(pos, strongSide, QueenValueMg, 0));
  304.   assert(verify_material(pos, weakSide, RookValueMg, 0));
  305.  
  306.   Square winnerKSq = pos.square<KING>(strongSide);
  307.   Square loserKSq = pos.square<KING>(weakSide);
  308.  
  309.   Value result =  QueenValueEg
  310.                 - RookValueEg
  311.                 + PushToEdges[loserKSq]
  312.                 + PushClose[distance(winnerKSq, loserKSq)];
  313.  
  314.   return strongSide == pos.side_to_move() ? result : -result;
  315. }
  316.  
  317.  
  318. /// Some cases of trivial draws
  319. template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
  320.  
  321.  
  322. /// KB and one or more pawns vs K. It checks for draws with rook pawns and
  323. /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
  324. /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
  325. /// will be used.
  326. template<>
  327. ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
  328.  
  329.   assert(pos.non_pawn_material(strongSide) == BishopValueMg);
  330.   assert(pos.count<PAWN>(strongSide) >= 1);
  331.  
  332.   // No assertions about the material of weakSide, because we want draws to
  333.   // be detected even when the weaker side has some pawns.
  334.  
  335.   Bitboard pawns = pos.pieces(strongSide, PAWN);
  336.   File pawnsFile = file_of(lsb(pawns));
  337.  
  338.   // All pawns are on a single rook file?
  339.   if (    (pawnsFile == FILE_A || pawnsFile == FILE_H)
  340.       && !(pawns & ~file_bb(pawnsFile)))
  341.   {
  342.       Square bishopSq = pos.square<BISHOP>(strongSide);
  343.       Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
  344.       Square kingSq = pos.square<KING>(weakSide);
  345.  
  346.       if (   opposite_colors(queeningSq, bishopSq)
  347.           && distance(queeningSq, kingSq) <= 1)
  348.           return SCALE_FACTOR_DRAW;
  349.   }
  350.  
  351.   // If all the pawns are on the same B or G file, then it's potentially a draw
  352.   if (    (pawnsFile == FILE_B || pawnsFile == FILE_G)
  353.       && !(pos.pieces(PAWN) & ~file_bb(pawnsFile))
  354.       && pos.non_pawn_material(weakSide) == 0
  355.       && pos.count<PAWN>(weakSide) >= 1)
  356.   {
  357.       // Get weakSide pawn that is closest to the home rank
  358.       Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
  359.  
  360.       Square strongKingSq = pos.square<KING>(strongSide);
  361.       Square weakKingSq = pos.square<KING>(weakSide);
  362.       Square bishopSq = pos.square<BISHOP>(strongSide);
  363.  
  364.       // There's potential for a draw if our pawn is blocked on the 7th rank,
  365.       // the bishop cannot attack it or they only have one pawn left
  366.       if (   relative_rank(strongSide, weakPawnSq) == RANK_7
  367.           && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
  368.           && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
  369.       {
  370.           int strongKingDist = distance(weakPawnSq, strongKingSq);
  371.           int weakKingDist = distance(weakPawnSq, weakKingSq);
  372.  
  373.           // It's a draw if the weak king is on its back two ranks, within 2
  374.           // squares of the blocking pawn and the strong king is not
  375.           // closer. (I think this rule only fails in practically
  376.           // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
  377.           // and positions where qsearch will immediately correct the
  378.           // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
  379.           if (   relative_rank(strongSide, weakKingSq) >= RANK_7
  380.               && weakKingDist <= 2
  381.               && weakKingDist <= strongKingDist)
  382.               return SCALE_FACTOR_DRAW;
  383.       }
  384.   }
  385.  
  386.   return SCALE_FACTOR_NONE;
  387. }
  388.  
  389.  
  390. /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
  391. /// the third rank defended by a pawn.
  392. template<>
  393. ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
  394.  
  395.   assert(verify_material(pos, strongSide, QueenValueMg, 0));
  396.   assert(pos.count<ROOK>(weakSide) == 1);
  397.   assert(pos.count<PAWN>(weakSide) >= 1);
  398.  
  399.   Square kingSq = pos.square<KING>(weakSide);
  400.   Square rsq = pos.square<ROOK>(weakSide);
  401.  
  402.   if (    relative_rank(weakSide, kingSq) <= RANK_2
  403.       &&  relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
  404.       &&  relative_rank(weakSide, rsq) == RANK_3
  405.       && (  pos.pieces(weakSide, PAWN)
  406.           & pos.attacks_from<KING>(kingSq)
  407.           & pos.attacks_from<PAWN>(rsq, strongSide)))
  408.           return SCALE_FACTOR_DRAW;
  409.  
  410.   return SCALE_FACTOR_NONE;
  411. }
  412.  
  413.  
  414. /// KRP vs KR. This function knows a handful of the most important classes of
  415. /// drawn positions, but is far from perfect. It would probably be a good idea
  416. /// to add more knowledge in the future.
  417. ///
  418. /// It would also be nice to rewrite the actual code for this function,
  419. /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
  420. template<>
  421. ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
  422.  
  423.   assert(verify_material(pos, strongSide, RookValueMg, 1));
  424.   assert(verify_material(pos, weakSide,   RookValueMg, 0));
  425.  
  426.   // Assume strongSide is white and the pawn is on files A-D
  427.   Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
  428.   Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
  429.   Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
  430.   Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  431.   Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
  432.  
  433.   File f = file_of(wpsq);
  434.   Rank r = rank_of(wpsq);
  435.   Square queeningSq = make_square(f, RANK_8);
  436.   int tempo = (pos.side_to_move() == strongSide);
  437.  
  438.   // If the pawn is not too far advanced and the defending king defends the
  439.   // queening square, use the third-rank defence.
  440.   if (   r <= RANK_5
  441.       && distance(bksq, queeningSq) <= 1
  442.       && wksq <= SQ_H5
  443.       && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
  444.       return SCALE_FACTOR_DRAW;
  445.  
  446.   // The defending side saves a draw by checking from behind in case the pawn
  447.   // has advanced to the 6th rank with the king behind.
  448.   if (   r == RANK_6
  449.       && distance(bksq, queeningSq) <= 1
  450.       && rank_of(wksq) + tempo <= RANK_6
  451.       && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
  452.       return SCALE_FACTOR_DRAW;
  453.  
  454.   if (   r >= RANK_6
  455.       && bksq == queeningSq
  456.       && rank_of(brsq) == RANK_1
  457.       && (!tempo || distance(wksq, wpsq) >= 2))
  458.       return SCALE_FACTOR_DRAW;
  459.  
  460.   // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
  461.   // and the black rook is behind the pawn.
  462.   if (   wpsq == SQ_A7
  463.       && wrsq == SQ_A8
  464.       && (bksq == SQ_H7 || bksq == SQ_G7)
  465.       && file_of(brsq) == FILE_A
  466.       && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
  467.       return SCALE_FACTOR_DRAW;
  468.  
  469.   // If the defending king blocks the pawn and the attacking king is too far
  470.   // away, it's a draw.
  471.   if (   r <= RANK_5
  472.       && bksq == wpsq + NORTH
  473.       && distance(wksq, wpsq) - tempo >= 2
  474.       && distance(wksq, brsq) - tempo >= 2)
  475.       return SCALE_FACTOR_DRAW;
  476.  
  477.   // Pawn on the 7th rank supported by the rook from behind usually wins if the
  478.   // attacking king is closer to the queening square than the defending king,
  479.   // and the defending king cannot gain tempi by threatening the attacking rook.
  480.   if (   r == RANK_7
  481.       && f != FILE_A
  482.       && file_of(wrsq) == f
  483.       && wrsq != queeningSq
  484.       && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
  485.       && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
  486.       return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
  487.  
  488.   // Similar to the above, but with the pawn further back
  489.   if (   f != FILE_A
  490.       && file_of(wrsq) == f
  491.       && wrsq < wpsq
  492.       && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
  493.       && (distance(wksq, wpsq + NORTH) < distance(bksq, wpsq + NORTH) - 2 + tempo)
  494.       && (  distance(bksq, wrsq) + tempo >= 3
  495.           || (    distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
  496.               && (distance(wksq, wpsq + NORTH) < distance(bksq, wrsq) + tempo))))
  497.       return ScaleFactor(  SCALE_FACTOR_MAX
  498.                          - 8 * distance(wpsq, queeningSq)
  499.                          - 2 * distance(wksq, queeningSq));
  500.  
  501.   // If the pawn is not far advanced and the defending king is somewhere in
  502.   // the pawn's path, it's probably a draw.
  503.   if (r <= RANK_4 && bksq > wpsq)
  504.   {
  505.       if (file_of(bksq) == file_of(wpsq))
  506.           return ScaleFactor(10);
  507.       if (   distance<File>(bksq, wpsq) == 1
  508.           && distance(wksq, bksq) > 2)
  509.           return ScaleFactor(24 - 2 * distance(wksq, bksq));
  510.   }
  511.   return SCALE_FACTOR_NONE;
  512. }
  513.  
  514. template<>
  515. ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
  516.  
  517.   assert(verify_material(pos, strongSide, RookValueMg, 1));
  518.   assert(verify_material(pos, weakSide, BishopValueMg, 0));
  519.  
  520.   // Test for a rook pawn
  521.   if (pos.pieces(PAWN) & (FileABB | FileHBB))
  522.   {
  523.       Square ksq = pos.square<KING>(weakSide);
  524.       Square bsq = pos.square<BISHOP>(weakSide);
  525.       Square psq = pos.square<PAWN>(strongSide);
  526.       Rank rk = relative_rank(strongSide, psq);
  527.       Direction push = pawn_push(strongSide);
  528.  
  529.       // If the pawn is on the 5th rank and the pawn (currently) is on
  530.       // the same color square as the bishop then there is a chance of
  531.       // a fortress. Depending on the king position give a moderate
  532.       // reduction or a stronger one if the defending king is near the
  533.       // corner but not trapped there.
  534.       if (rk == RANK_5 && !opposite_colors(bsq, psq))
  535.       {
  536.           int d = distance(psq + 3 * push, ksq);
  537.  
  538.           if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
  539.               return ScaleFactor(24);
  540.           else
  541.               return ScaleFactor(48);
  542.       }
  543.  
  544.       // When the pawn has moved to the 6th rank we can be fairly sure
  545.       // it's drawn if the bishop attacks the square in front of the
  546.       // pawn from a reasonable distance and the defending king is near
  547.       // the corner
  548.       if (   rk == RANK_6
  549.           && distance(psq + 2 * push, ksq) <= 1
  550.           && (PseudoAttacks[BISHOP][bsq] & (psq + push))
  551.           && distance<File>(bsq, psq) >= 2)
  552.           return ScaleFactor(8);
  553.   }
  554.  
  555.   return SCALE_FACTOR_NONE;
  556. }
  557.  
  558. /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
  559. /// pawns and the defending king is actively placed, the position is drawish.
  560. template<>
  561. ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
  562.  
  563.   assert(verify_material(pos, strongSide, RookValueMg, 2));
  564.   assert(verify_material(pos, weakSide,   RookValueMg, 1));
  565.  
  566.   Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
  567.   Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
  568.   Square bksq = pos.square<KING>(weakSide);
  569.  
  570.   // Does the stronger side have a passed pawn?
  571.   if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
  572.       return SCALE_FACTOR_NONE;
  573.  
  574.   Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
  575.  
  576.   if (   distance<File>(bksq, wpsq1) <= 1
  577.       && distance<File>(bksq, wpsq2) <= 1
  578.       && relative_rank(strongSide, bksq) > r)
  579.   {
  580.       assert(r > RANK_1 && r < RANK_7);
  581.       return ScaleFactor(KRPPKRPScaleFactors[r]);
  582.   }
  583.   return SCALE_FACTOR_NONE;
  584. }
  585.  
  586.  
  587. /// K and two or more pawns vs K. There is just a single rule here: If all pawns
  588. /// are on the same rook file and are blocked by the defending king, it's a draw.
  589. template<>
  590. ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
  591.  
  592.   assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
  593.   assert(pos.count<PAWN>(strongSide) >= 2);
  594.   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  595.  
  596.   Square ksq = pos.square<KING>(weakSide);
  597.   Bitboard pawns = pos.pieces(strongSide, PAWN);
  598.  
  599.   // If all pawns are ahead of the king, on a single rook file and
  600.   // the king is within one file of the pawns, it's a draw.
  601.   if (   !(pawns & ~forward_ranks_bb(weakSide, ksq))
  602.       && !((pawns & ~FileABB) && (pawns & ~FileHBB))
  603.       &&  distance<File>(ksq, lsb(pawns)) <= 1)
  604.       return SCALE_FACTOR_DRAW;
  605.  
  606.   return SCALE_FACTOR_NONE;
  607. }
  608.  
  609.  
  610. /// KBP vs KB. There are two rules: if the defending king is somewhere along the
  611. /// path of the pawn, and the square of the king is not of the same color as the
  612. /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
  613. /// it's almost always a draw.
  614. template<>
  615. ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
  616.  
  617.   assert(verify_material(pos, strongSide, BishopValueMg, 1));
  618.   assert(verify_material(pos, weakSide,   BishopValueMg, 0));
  619.  
  620.   Square pawnSq = pos.square<PAWN>(strongSide);
  621.   Square strongBishopSq = pos.square<BISHOP>(strongSide);
  622.   Square weakBishopSq = pos.square<BISHOP>(weakSide);
  623.   Square weakKingSq = pos.square<KING>(weakSide);
  624.  
  625.   // Case 1: Defending king blocks the pawn, and cannot be driven away
  626.   if (   file_of(weakKingSq) == file_of(pawnSq)
  627.       && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
  628.       && (   opposite_colors(weakKingSq, strongBishopSq)
  629.           || relative_rank(strongSide, weakKingSq) <= RANK_6))
  630.       return SCALE_FACTOR_DRAW;
  631.  
  632.   // Case 2: Opposite colored bishops
  633.   if (opposite_colors(strongBishopSq, weakBishopSq))
  634.   {
  635.       // We assume that the position is drawn in the following three situations:
  636.       //
  637.       //   a. The pawn is on rank 5 or further back.
  638.       //   b. The defending king is somewhere in the pawn's path.
  639.       //   c. The defending bishop attacks some square along the pawn's path,
  640.       //      and is at least three squares away from the pawn.
  641.       //
  642.       // These rules are probably not perfect, but in practice they work
  643.       // reasonably well.
  644.  
  645.       if (relative_rank(strongSide, pawnSq) <= RANK_5)
  646.           return SCALE_FACTOR_DRAW;
  647.  
  648.       Bitboard path = forward_file_bb(strongSide, pawnSq);
  649.  
  650.       if (path & pos.pieces(weakSide, KING))
  651.           return SCALE_FACTOR_DRAW;
  652.  
  653.       if (  (pos.attacks_from<BISHOP>(weakBishopSq) & path)
  654.           && distance(weakBishopSq, pawnSq) >= 3)
  655.           return SCALE_FACTOR_DRAW;
  656.   }
  657.   return SCALE_FACTOR_NONE;
  658. }
  659.  
  660.  
  661. /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
  662. template<>
  663. ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
  664.  
  665.   assert(verify_material(pos, strongSide, BishopValueMg, 2));
  666.   assert(verify_material(pos, weakSide,   BishopValueMg, 0));
  667.  
  668.   Square wbsq = pos.square<BISHOP>(strongSide);
  669.   Square bbsq = pos.square<BISHOP>(weakSide);
  670.  
  671.   if (!opposite_colors(wbsq, bbsq))
  672.       return SCALE_FACTOR_NONE;
  673.  
  674.   Square ksq = pos.square<KING>(weakSide);
  675.   Square psq1 = pos.squares<PAWN>(strongSide)[0];
  676.   Square psq2 = pos.squares<PAWN>(strongSide)[1];
  677.   Rank r1 = rank_of(psq1);
  678.   Rank r2 = rank_of(psq2);
  679.   Square blockSq1, blockSq2;
  680.  
  681.   if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
  682.   {
  683.       blockSq1 = psq1 + pawn_push(strongSide);
  684.       blockSq2 = make_square(file_of(psq2), rank_of(psq1));
  685.   }
  686.   else
  687.   {
  688.       blockSq1 = psq2 + pawn_push(strongSide);
  689.       blockSq2 = make_square(file_of(psq1), rank_of(psq2));
  690.   }
  691.  
  692.   switch (distance<File>(psq1, psq2))
  693.   {
  694.   case 0:
  695.     // Both pawns are on the same file. It's an easy draw if the defender firmly
  696.     // controls some square in the frontmost pawn's path.
  697.     if (   file_of(ksq) == file_of(blockSq1)
  698.         && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
  699.         && opposite_colors(ksq, wbsq))
  700.         return SCALE_FACTOR_DRAW;
  701.     else
  702.         return SCALE_FACTOR_NONE;
  703.  
  704.   case 1:
  705.     // Pawns on adjacent files. It's a draw if the defender firmly controls the
  706.     // square in front of the frontmost pawn's path, and the square diagonally
  707.     // behind this square on the file of the other pawn.
  708.     if (   ksq == blockSq1
  709.         && opposite_colors(ksq, wbsq)
  710.         && (   bbsq == blockSq2
  711.             || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
  712.             || distance(r1, r2) >= 2))
  713.         return SCALE_FACTOR_DRAW;
  714.  
  715.     else if (   ksq == blockSq2
  716.              && opposite_colors(ksq, wbsq)
  717.              && (   bbsq == blockSq1
  718.                  || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
  719.         return SCALE_FACTOR_DRAW;
  720.     else
  721.         return SCALE_FACTOR_NONE;
  722.  
  723.   default:
  724.     // The pawns are not on the same file or adjacent files. No scaling.
  725.     return SCALE_FACTOR_NONE;
  726.   }
  727. }
  728.  
  729.  
  730. /// KBP vs KN. There is a single rule: If the defending king is somewhere along
  731. /// the path of the pawn, and the square of the king is not of the same color as
  732. /// the stronger side's bishop, it's a draw.
  733. template<>
  734. ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
  735.  
  736.   assert(verify_material(pos, strongSide, BishopValueMg, 1));
  737.   assert(verify_material(pos, weakSide, KnightValueMg, 0));
  738.  
  739.   Square pawnSq = pos.square<PAWN>(strongSide);
  740.   Square strongBishopSq = pos.square<BISHOP>(strongSide);
  741.   Square weakKingSq = pos.square<KING>(weakSide);
  742.  
  743.   if (   file_of(weakKingSq) == file_of(pawnSq)
  744.       && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
  745.       && (   opposite_colors(weakKingSq, strongBishopSq)
  746.           || relative_rank(strongSide, weakKingSq) <= RANK_6))
  747.       return SCALE_FACTOR_DRAW;
  748.  
  749.   return SCALE_FACTOR_NONE;
  750. }
  751.  
  752.  
  753. /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
  754. /// and the defending king prevents the pawn from advancing, the position is drawn.
  755. template<>
  756. ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
  757.  
  758.   assert(verify_material(pos, strongSide, KnightValueMg, 1));
  759.   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  760.  
  761.   // Assume strongSide is white and the pawn is on files A-D
  762.   Square pawnSq     = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  763.   Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
  764.  
  765.   if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
  766.       return SCALE_FACTOR_DRAW;
  767.  
  768.   return SCALE_FACTOR_NONE;
  769. }
  770.  
  771.  
  772. /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
  773. /// Otherwise the position is drawn.
  774. template<>
  775. ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
  776.  
  777.   Square pawnSq = pos.square<PAWN>(strongSide);
  778.   Square bishopSq = pos.square<BISHOP>(weakSide);
  779.   Square weakKingSq = pos.square<KING>(weakSide);
  780.  
  781.   // King needs to get close to promoting pawn to prevent knight from blocking.
  782.   // Rules for this are very tricky, so just approximate.
  783.   if (forward_file_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
  784.       return ScaleFactor(distance(weakKingSq, pawnSq));
  785.  
  786.   return SCALE_FACTOR_NONE;
  787. }
  788.  
  789.  
  790. /// KP vs KP. This is done by removing the weakest side's pawn and probing the
  791. /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
  792. /// has at least a draw with the pawn as well. The exception is when the stronger
  793. /// side's pawn is far advanced and not on a rook file; in this case it is often
  794. /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
  795. template<>
  796. ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
  797.  
  798.   assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
  799.   assert(verify_material(pos, weakSide,   VALUE_ZERO, 1));
  800.  
  801.   // Assume strongSide is white and the pawn is on files A-D
  802.   Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
  803.   Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
  804.   Square psq  = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  805.  
  806.   Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
  807.  
  808.   // If the pawn has advanced to the fifth rank or further, and is not a
  809.   // rook pawn, it's too dangerous to assume that it's at least a draw.
  810.   if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
  811.       return SCALE_FACTOR_NONE;
  812.  
  813.   // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
  814.   // it's probably at least a draw even with the pawn.
  815.   return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;
  816. }
  817.