Subversion Repositories Games.Chess Giants

/*

  Stockfish, a UCI chess playing engine derived from Glaurung 2.1

  Copyright (C) 2004-2008 Tord Romstad (Glaurung author)

  Copyright (C) 2008-2015 Marco Costalba, Joona Kiiski, Tord Romstad

  Copyright (C) 2015-2016 Marco Costalba, Joona Kiiski, Gary Linscott, 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 <http://www.gnu.org/licenses/>.

*/

#include <algorithm>

#include <cassert>

#include "bitboard.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 };

  // Pawn Rank based scaling factors used in KRPPKRP endgame

  const int KRPPKRPScaleFactors[RANK_NB] = { 0, 9, 10, 14, 21, 44, 0, 0 };

#ifndef NDEBUG

  bool verify_material(const Position& pos, Color c, Value npm, int pawnsCnt) {

    return pos.non_pawn_material(c) == npm && pos.count<PAWN>(c) == pawnsCnt;

  }

#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<PAWN>(strongSide) == 1);

    if (file_of(pos.square<PAWN>(strongSide)) >= 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";

    StateInfo st;

    return Position().set(fen, false, &st, nullptr).material_key();

  }

} // namespace

/// Endgames members definitions

Endgames::Endgames() {

  add<KPK>("KPK");

  add<KNNK>("KNNK");

  add<KBNK>("KBNK");

  add<KRKP>("KRKP");

  add<KRKB>("KRKB");

  add<KRKN>("KRKN");

  add<KQKP>("KQKP");

  add<KQKR>("KQKR");

  add<KNPK>("KNPK");

  add<KNPKB>("KNPKB");

  add<KRPKR>("KRPKR");

  add<KRPKB>("KRPKB");

  add<KBPKB>("KBPKB");

  add<KBPKN>("KBPKN");

  add<KBPPKB>("KBPPKB");

  add<KRPPKRP>("KRPPKRP");

}

template<EndgameType E, typename T>

void Endgames::add(const string& code) {

  map<T>()[key(code, WHITE)] = std::unique_ptr<EndgameBase<T>>(new Endgame<E>(WHITE));

  map<T>()[key(code, BLACK)] = std::unique_ptr<EndgameBase<T>>(new Endgame<E>(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<KXK>::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<LEGAL>(pos).size())

      return VALUE_DRAW;

  Square winnerKSq = pos.square<KING>(strongSide);

  Square loserKSq = pos.square<KING>(weakSide);

  Value result =  pos.non_pawn_material(strongSide)

                + pos.count<PAWN>(strongSide) * PawnValueEg

                + PushToEdges[loserKSq]

                + PushClose[distance(winnerKSq, loserKSq)];

  if (   pos.count<QUEEN>(strongSide)

      || pos.count<ROOK>(strongSide)

      ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))

      ||(pos.count<BISHOP>(strongSide) > 1 && opposite_colors(pos.squares<BISHOP>(strongSide)[0],

                                                              pos.squares<BISHOP>(strongSide)[1])))

      result = std::min(result + VALUE_KNOWN_WIN, VALUE_MATE_IN_MAX_PLY - 1);

  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<KBNK>::operator()(const Position& pos) const {

  assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));

  assert(verify_material(pos, weakSide, VALUE_ZERO, 0));

  Square winnerKSq = pos.square<KING>(strongSide);

  Square loserKSq = pos.square<KING>(weakSide);

  Square bishopSq = pos.square<BISHOP>(strongSide);

  // 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[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<KPK>::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.square<KING>(strongSide));

  Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));

  Square psq  = normalize(pos, strongSide, pos.square<PAWN>(strongSide));

  Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;

  if (!Bitbases::probe(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<KRKP>::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.square<KING>(strongSide));

  Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));

  Square rsq  = relative_square(strongSide, pos.square<ROOK>(strongSide));

  Square psq  = relative_square(strongSide, pos.square<PAWN>(weakSide));

  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 - distance(wksq, psq);

  // If the weaker side's king is too far from the pawn and the rook,

  // it's a win.

  else if (   distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)

           && distance(bksq, rsq) >= 3)

      result = RookValueEg - 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

           && distance(bksq, psq) == 1

           && rank_of(wksq) >= RANK_4

           && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))

      result = Value(80) - 8 * distance(wksq, psq);

  else

      result =  Value(200) - 8 * (  distance(wksq, psq + SOUTH)

                                  - distance(bksq, psq + SOUTH)

                                  - 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<KRKB>::operator()(const Position& pos) const {

  assert(verify_material(pos, strongSide, RookValueMg, 0));

  assert(verify_material(pos, weakSide, BishopValueMg, 0));

  Value result = Value(PushToEdges[pos.square<KING>(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<KRKN>::operator()(const Position& pos) const {

  assert(verify_material(pos, strongSide, RookValueMg, 0));

  assert(verify_material(pos, weakSide, KnightValueMg, 0));

  Square bksq = pos.square<KING>(weakSide);

  Square bnsq = pos.square<KNIGHT>(weakSide);

  Value result = Value(PushToEdges[bksq] + PushAway[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<KQKP>::operator()(const Position& pos) const {

  assert(verify_material(pos, strongSide, QueenValueMg, 0));

  assert(verify_material(pos, weakSide, VALUE_ZERO, 1));

  Square winnerKSq = pos.square<KING>(strongSide);

  Square loserKSq = pos.square<KING>(weakSide);

  Square pawnSq = pos.square<PAWN>(weakSide);

  Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);

  if (   relative_rank(weakSide, pawnSq) != RANK_7

      || 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<KQKR>::operator()(const Position& pos) const {

  assert(verify_material(pos, strongSide, QueenValueMg, 0));

  assert(verify_material(pos, weakSide, RookValueMg, 0));

  Square winnerKSq = pos.square<KING>(strongSide);

  Square loserKSq = pos.square<KING>(weakSide);

  Value result =  QueenValueEg

                - RookValueEg

                + PushToEdges[loserKSq]

                + PushClose[distance(winnerKSq, loserKSq)];

  return strongSide == pos.side_to_move() ? result : -result;

}

/// Some cases of trivial draws

template<> Value Endgame<KNNK>::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<KBPsK>::operator()(const Position& pos) const {

  assert(pos.non_pawn_material(strongSide) == BishopValueMg);

  assert(pos.count<PAWN>(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 pawnsFile = file_of(lsb(pawns));

  // All pawns are on a single rook file?

  if (    (pawnsFile == FILE_A || pawnsFile == FILE_H)

      && !(pawns & ~file_bb(pawnsFile)))

  {

      Square bishopSq = pos.square<BISHOP>(strongSide);

      Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));

      Square kingSq = pos.square<KING>(weakSide);

      if (   opposite_colors(queeningSq, bishopSq)

          && 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 (    (pawnsFile == FILE_B || pawnsFile == FILE_G)

      && !(pos.pieces(PAWN) & ~file_bb(pawnsFile))

      && pos.non_pawn_material(weakSide) == 0

      && pos.count<PAWN>(weakSide) >= 1)

  {

      // Get weakSide pawn that is closest to the home rank

      Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));

      Square strongKingSq = pos.square<KING>(strongSide);

      Square weakKingSq = pos.square<KING>(weakSide);

      Square bishopSq = pos.square<BISHOP>(strongSide);

      // 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<PAWN>(strongSide) == 1))

      {

          int strongKingDist = distance(weakPawnSq, strongKingSq);

          int weakKingDist = 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<KQKRPs>::operator()(const Position& pos) const {

  assert(verify_material(pos, strongSide, QueenValueMg, 0));

  assert(pos.count<ROOK>(weakSide) == 1);

  assert(pos.count<PAWN>(weakSide) >= 1);

  Square kingSq = pos.square<KING>(weakSide);

  Square rsq = pos.square<ROOK>(weakSide);

  if (    relative_rank(weakSide, kingSq) <= RANK_2

      &&  relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4

      &&  relative_rank(weakSide, rsq) == RANK_3

      && (  pos.pieces(weakSide, PAWN)

          & pos.attacks_from<KING>(kingSq)

          & pos.attacks_from<PAWN>(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<KRPKR>::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.square<KING>(strongSide));

  Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));

  Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));

  Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));

  Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));

  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

      && 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

      && distance(bksq, queeningSq) <= 1

      && rank_of(wksq) + tempo <= RANK_6

      && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))

      return SCALE_FACTOR_DRAW;

  if (   r >= RANK_6

      && bksq == queeningSq

      && rank_of(brsq) == RANK_1

      && (!tempo || 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 + NORTH

      && distance(wksq, wpsq) - tempo >= 2

      && 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

      && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)

      && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))

      return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));

  // Similar to the above, but with the pawn further back

  if (   f != FILE_A

      && file_of(wrsq) == f

      && wrsq < wpsq

      && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)

      && (distance(wksq, wpsq + NORTH) < distance(bksq, wpsq + NORTH) - 2 + tempo)

      && (  distance(bksq, wrsq) + tempo >= 3

          || (    distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo

              && (distance(wksq, wpsq + NORTH) < distance(bksq, wrsq) + tempo))))

      return ScaleFactor(  SCALE_FACTOR_MAX

                         - 8 * distance(wpsq, queeningSq)

                         - 2 * 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 (   distance<File>(bksq, wpsq) == 1

          && distance(wksq, bksq) > 2)

          return ScaleFactor(24 - 2 * distance(wksq, bksq));

  }

  return SCALE_FACTOR_NONE;

}

template<>

ScaleFactor Endgame<KRPKB>::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.square<KING>(weakSide);

      Square bsq = pos.square<BISHOP>(weakSide);

      Square psq = pos.square<PAWN>(strongSide);

      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 = distance(psq + 3 * push, ksq);

          if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(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

          && distance(psq + 2 * push, ksq) <= 1

          && (PseudoAttacks[BISHOP][bsq] & (psq + push))

          && distance<File>(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<KRPPKRP>::operator()(const Position& pos) const {

  assert(verify_material(pos, strongSide, RookValueMg, 2));

  assert(verify_material(pos, weakSide,   RookValueMg, 1));

  Square wpsq1 = pos.squares<PAWN>(strongSide)[0];

  Square wpsq2 = pos.squares<PAWN>(strongSide)[1];

  Square bksq = pos.square<KING>(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 (   distance<File>(bksq, wpsq1) <= 1

      && distance<File>(bksq, wpsq2) <= 1

      && relative_rank(strongSide, bksq) > r)

  {

      assert(r > RANK_1 && r < RANK_7);

      return ScaleFactor(KRPPKRPScaleFactors[r]);

  }

  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<KPsK>::operator()(const Position& pos) const {

  assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);

  assert(pos.count<PAWN>(strongSide) >= 2);

  assert(verify_material(pos, weakSide, VALUE_ZERO, 0));

  Square ksq = pos.square<KING>(weakSide);

  Bitboard pawns = pos.pieces(strongSide, PAWN);

  // 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))

      &&  distance<File>(ksq, lsb(pawns)) <= 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<KBPKB>::operator()(const Position& pos) const {

  assert(verify_material(pos, strongSide, BishopValueMg, 1));

  assert(verify_material(pos, weakSide,   BishopValueMg, 0));

  Square pawnSq = pos.square<PAWN>(strongSide);

  Square strongBishopSq = pos.square<BISHOP>(strongSide);

  Square weakBishopSq = pos.square<BISHOP>(weakSide);

  Square weakKingSq = pos.square<KING>(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<BISHOP>(weakBishopSq) & path)

              && 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<KBPPKB>::operator()(const Position& pos) const {

  assert(verify_material(pos, strongSide, BishopValueMg, 2));

  assert(verify_material(pos, weakSide,   BishopValueMg, 0));

  Square wbsq = pos.square<BISHOP>(strongSide);

  Square bbsq = pos.square<BISHOP>(weakSide);

  if (!opposite_colors(wbsq, bbsq))

      return SCALE_FACTOR_NONE;

  Square ksq = pos.square<KING>(weakSide);

  Square psq1 = pos.squares<PAWN>(strongSide)[0];

  Square psq2 = pos.squares<PAWN>(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 (distance<File>(psq1, psq2))

  {

  case 0:

    // Both pawns are on the same file. It's an easy draw if the defender firmly