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stockfish/src/endgame.cpp

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/*
Stockfish, a UCI chess playing engine derived from Glaurung 2.1
Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
Copyright (C) 2008-2013 Marco Costalba, Joona Kiiski, Tord Romstad
Stockfish is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
Stockfish is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include <algorithm>
#include <cassert>
#include "bitboard.h"
#include "bitcount.h"
#include "endgame.h"
#include "movegen.h"
using std::string;
namespace {
// Table used to drive the king towards the edge of the board
// in KX vs K and KQ vs KR endgames.
const int PushToEdges[SQUARE_NB] = {
100, 90, 80, 70, 70, 80, 90, 100,
90, 70, 60, 50, 50, 60, 70, 90,
80, 60, 40, 30, 30, 40, 60, 80,
70, 50, 30, 20, 20, 30, 50, 70,
70, 50, 30, 20, 20, 30, 50, 70,
80, 60, 40, 30, 30, 40, 60, 80,
90, 70, 60, 50, 50, 60, 70, 90,
100, 90, 80, 70, 70, 80, 90, 100,
};
// Table used to drive the king towards a corner square of the
// right color in KBN vs K endgames.
const int PushToCorners[SQUARE_NB] = {
200, 190, 180, 170, 160, 150, 140, 130,
190, 180, 170, 160, 150, 140, 130, 140,
180, 170, 155, 140, 140, 125, 140, 150,
170, 160, 140, 120, 110, 140, 150, 160,
160, 150, 140, 110, 120, 140, 160, 170,
150, 140, 125, 140, 140, 155, 170, 180,
140, 130, 140, 150, 160, 170, 180, 190,
130, 140, 150, 160, 170, 180, 190, 200
};
// Tables used to drive a piece towards or away from another piece
const int PushClose[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
const int PushAway [8] = { 0, 5, 20, 40, 60, 80, 90, 100 };
#ifndef NDEBUG
bool verify_material(const Position& pos, Color c, Value npm, int num_pawns) {
return pos.non_pawn_material(c) == npm && pos.count<PAWN>(c) == num_pawns;
}
#endif
// Map the square as if strongSide is white and strongSide's only pawn
// is on the left half of the board.
Square normalize(const Position& pos, Color strongSide, Square sq) {
assert(pos.count<PAWN>(strongSide) == 1);
if (file_of(pos.list<PAWN>(strongSide)[0]) >= FILE_E)
sq = Square(sq ^ 7); // Mirror SQ_H1 -> SQ_A1
if (strongSide == BLACK)
sq = ~sq;
return sq;
}
// Get the material key of a 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 to do the work for us. Note that the
// fen string could correspond to an illegal position.
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('0' + int(8 - code.length()))
+ sides[1] + "/8/8/8/8/8/8/8 w - - 0 10";
return Position(fen, false, NULL).material_key();
}
template<typename M>
void delete_endgame(const typename M::value_type& p) { delete p.second; }
} // 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<KBBKN>("KBBKN");
add<KNPK>("KNPK");
add<KNPKB>("KNPKB");
add<KRPKR>("KRPKR");
add<KRPKB>("KRPKB");
add<KBPKB>("KBPKB");
add<KBPKN>("KBPKN");
add<KBPPKB>("KBPPKB");
add<KRPPKRP>("KRPPKRP");
}
Endgames::~Endgames() {
for_each(m1.begin(), m1.end(), delete_endgame<M1>);
for_each(m2.begin(), m2.end(), delete_endgame<M2>);
}
template<EndgameType E>
void Endgames::add(const string& code) {
map((Endgame<E>*)0)[key(code, WHITE)] = new Endgame<E>(WHITE);
map((Endgame<E>*)0)[key(code, BLACK)] = 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.king_square(strongSide);
Square loserKSq = pos.king_square(weakSide);
Value result = pos.non_pawn_material(strongSide)
+ pos.count<PAWN>(strongSide) * PawnValueEg
+ PushToEdges[loserKSq]
+ PushClose[square_distance(winnerKSq, loserKSq)];
if ( pos.count<QUEEN>(strongSide)
|| pos.count<ROOK>(strongSide)
|| pos.bishop_pair(strongSide))
result += VALUE_KNOWN_WIN;
return strongSide == pos.side_to_move() ? result : -result;
}
/// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
/// defending king towards a corner square of the right color.
template<>
Value Endgame<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.king_square(strongSide);
Square loserKSq = pos.king_square(weakSide);
Square bishopSq = pos.list<BISHOP>(strongSide)[0];
// kbnk_mate_table() tries to drive toward corners A1 or H8, if we have a
// bishop that cannot reach the above squares we flip the kings in order
// to drive the enemy toward corners A8 or H1.
if (opposite_colors(bishopSq, SQ_A1))
{
winnerKSq = ~winnerKSq;
loserKSq = ~loserKSq;
}
Value result = VALUE_KNOWN_WIN
+ PushClose[square_distance(winnerKSq, loserKSq)]
+ PushToCorners[loserKSq];
return strongSide == pos.side_to_move() ? result : -result;
}
/// KP vs K. This endgame is evaluated with the help of a bitbase.
template<>
Value Endgame<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.king_square(strongSide));
Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
Square psq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
if (!Bitbases::probe_kpk(wksq, psq, bksq, us))
return VALUE_DRAW;
Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
return strongSide == pos.side_to_move() ? result : -result;
}
/// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
/// a bitbase. The function below returns drawish scores when the pawn is
/// far advanced with support of the king, while the attacking king is far
/// away.
template<>
Value Endgame<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.king_square(strongSide));
Square bksq = relative_square(strongSide, pos.king_square(weakSide));
Square rsq = relative_square(strongSide, pos.list<ROOK>(strongSide)[0]);
Square psq = relative_square(strongSide, pos.list<PAWN>(weakSide)[0]);
Square queeningSq = 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 - Value(square_distance(wksq, psq));
// If the weaker side's king is too far from the pawn and the rook,
// it's a win.
else if ( square_distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
&& square_distance(bksq, rsq) >= 3)
result = RookValueEg - Value(square_distance(wksq, psq));
// If the pawn is far advanced and supported by the defending king,
// the position is drawish
else if ( rank_of(bksq) <= RANK_3
&& square_distance(bksq, psq) == 1
&& rank_of(wksq) >= RANK_4
&& square_distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
result = Value(80 - square_distance(wksq, psq) * 8);
else
result = Value(200)
- Value(square_distance(wksq, psq + DELTA_S) * 8)
+ Value(square_distance(bksq, psq + DELTA_S) * 8)
+ Value(square_distance(psq, queeningSq) * 8);
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.king_square(weakSide)]);
return strongSide == pos.side_to_move() ? result : -result;
}
/// KR vs KN. The attacking side has slightly better winning chances than
/// in KR vs KB, particularly if the king and the knight are far apart.
template<>
Value Endgame<KRKN>::operator()(const Position& pos) const {
assert(verify_material(pos, strongSide, RookValueMg, 0));
assert(verify_material(pos, weakSide, KnightValueMg, 0));
Square bksq = pos.king_square(weakSide);
Square bnsq = pos.list<KNIGHT>(weakSide)[0];
Value result = Value(PushToEdges[bksq] + PushAway[square_distance(bksq, bnsq)]);
return strongSide == pos.side_to_move() ? result : -result;
}
/// KQ vs KP. In general, this is a win for the stronger side, but there are a
/// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
/// with a king positioned next to it can be a draw, so in that case, we only
/// use the distance between the kings.
template<>
Value Endgame<KQKP>::operator()(const Position& pos) const {
assert(verify_material(pos, strongSide, QueenValueMg, 0));
assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
Square winnerKSq = pos.king_square(strongSide);
Square loserKSq = pos.king_square(weakSide);
Square pawnSq = pos.list<PAWN>(weakSide)[0];
Value result = Value(PushClose[square_distance(winnerKSq, loserKSq)]);
if ( relative_rank(weakSide, pawnSq) != RANK_7
|| square_distance(loserKSq, pawnSq) != 1
|| !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
result += QueenValueEg - PawnValueEg;
return strongSide == pos.side_to_move() ? result : -result;
}
/// KQ vs KR. This is almost identical to KX vs K: We give the attacking
/// king a bonus for having the kings close together, and for forcing the
/// defending king towards the edge. If we also take care to avoid null move
/// for the defending side in the search, this is usually sufficient to be
/// able 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.king_square(strongSide);
Square loserKSq = pos.king_square(weakSide);
Value result = QueenValueEg
- RookValueEg
+ PushToEdges[loserKSq]
+ PushClose[square_distance(winnerKSq, loserKSq)];
return strongSide == pos.side_to_move() ? result : -result;
}
/// KBB vs KN. This is almost always a win. We try to push enemy king to a corner
/// and away from his knight. For a reference of this difficult endgame see:
/// en.wikipedia.org/wiki/Chess_endgame#Effect_of_tablebases_on_endgame_theory
template<>
Value Endgame<KBBKN>::operator()(const Position& pos) const {
assert(verify_material(pos, strongSide, 2 * BishopValueMg, 0));
assert(verify_material(pos, weakSide, KnightValueMg, 0));
Square winnerKSq = pos.king_square(strongSide);
Square loserKSq = pos.king_square(weakSide);
Square knightSq = pos.list<KNIGHT>(weakSide)[0];
Value result = VALUE_KNOWN_WIN
+ PushToCorners[loserKSq]
+ PushClose[square_distance(winnerKSq, loserKSq)]
+ PushAway[square_distance(loserKSq, knightSq)];
return strongSide == pos.side_to_move() ? result : -result;
}
/// Some cases of trivial draws
template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
template<> Value Endgame<KmmKm>::operator()(const Position&) const { return VALUE_DRAW; }
/// K, bishop 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 pawnFile = file_of(pos.list<PAWN>(strongSide)[0]);
// All pawns are on a single rook file ?
if ( (pawnFile == FILE_A || pawnFile == FILE_H)
&& !(pawns & ~file_bb(pawnFile)))
{
Square bishopSq = pos.list<BISHOP>(strongSide)[0];
Square queeningSq = relative_square(strongSide, pawnFile | RANK_8);
Square kingSq = pos.king_square(weakSide);
if ( opposite_colors(queeningSq, bishopSq)
&& square_distance(queeningSq, kingSq) <= 1)
return SCALE_FACTOR_DRAW;
}
// If all the pawns are on the same B or G file, then it's potentially a draw
if ( (pawnFile == FILE_B || pawnFile == FILE_G)
&& !(pos.pieces(PAWN) & ~file_bb(pawnFile))
&& pos.non_pawn_material(weakSide) == 0
&& pos.count<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.king_square(strongSide);
Square weakKingSq = pos.king_square(weakSide);
Square bishopSq = pos.list<BISHOP>(strongSide)[0];
// There's potential for a draw if our pawn is blocked on the 7th rank
// the bishop cannot attack it or they only have one pawn left
if ( relative_rank(strongSide, weakPawnSq) == RANK_7
&& (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
&& (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
{
int strongKingDist = square_distance(weakPawnSq, strongKingSq);
int weakKingDist = square_distance(weakPawnSq, weakKingSq);
// It's a draw if the weak king is on its back two ranks, within 2
// squares of the blocking pawn and the strong king is not
// closer. (I think this rule only fails in practically
// unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
// and positions where qsearch will immediately correct the
// problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
if ( relative_rank(strongSide, weakKingSq) >= RANK_7
&& weakKingDist <= 2
&& weakKingDist <= strongKingDist)
return SCALE_FACTOR_DRAW;
}
}
return SCALE_FACTOR_NONE;
}
/// K and queen vs K, rook 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.king_square(weakSide);
Square rsq = pos.list<ROOK>(weakSide)[0];
if ( relative_rank(weakSide, kingSq) <= RANK_2
&& relative_rank(weakSide, pos.king_square(strongSide)) >= RANK_4
&& relative_rank(weakSide, rsq) == RANK_3
&& ( pos.pieces(weakSide, PAWN)
& pos.attacks_from<KING>(kingSq)
& pos.attacks_from<PAWN>(rsq, strongSide)))
return SCALE_FACTOR_DRAW;
return SCALE_FACTOR_NONE;
}
/// K, rook and one pawn vs K and a rook. 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.king_square(strongSide));
Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
Square wrsq = normalize(pos, strongSide, pos.list<ROOK>(strongSide)[0]);
Square wpsq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
Square brsq = normalize(pos, strongSide, pos.list<ROOK>(weakSide)[0]);
File f = file_of(wpsq);
Rank r = rank_of(wpsq);
Square queeningSq = f | RANK_8;
int tempo = (pos.side_to_move() == strongSide);
// If the pawn is not too far advanced and the defending king defends the
// queening square, use the third-rank defence.
if ( r <= RANK_5
&& square_distance(bksq, queeningSq) <= 1
&& wksq <= SQ_H5
&& (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
return SCALE_FACTOR_DRAW;
// The defending side saves a draw by checking from behind in case the pawn
// has advanced to the 6th rank with the king behind.
if ( r == RANK_6
&& square_distance(bksq, queeningSq) <= 1
&& rank_of(wksq) + tempo <= RANK_6
&& (rank_of(brsq) == RANK_1 || (!tempo && abs(file_of(brsq) - f) >= 3)))
return SCALE_FACTOR_DRAW;
if ( r >= RANK_6
&& bksq == queeningSq
&& rank_of(brsq) == RANK_1
&& (!tempo || square_distance(wksq, wpsq) >= 2))
return SCALE_FACTOR_DRAW;
// White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
// and the black rook is behind the pawn.
if ( wpsq == SQ_A7
&& wrsq == SQ_A8
&& (bksq == SQ_H7 || bksq == SQ_G7)
&& file_of(brsq) == FILE_A
&& (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
return SCALE_FACTOR_DRAW;
// If the defending king blocks the pawn and the attacking king is too far
// away, it's a draw.
if ( r <= RANK_5
&& bksq == wpsq + DELTA_N
&& square_distance(wksq, wpsq) - tempo >= 2
&& square_distance(wksq, brsq) - tempo >= 2)
return SCALE_FACTOR_DRAW;
// Pawn on the 7th rank supported by the rook from behind usually wins if the
// attacking king is closer to the queening square than the defending king,
// and the defending king cannot gain tempi by threatening the attacking rook.
if ( r == RANK_7
&& f != FILE_A
&& file_of(wrsq) == f
&& wrsq != queeningSq
&& (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
&& (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
// Similar to the above, but with the pawn further back
if ( f != FILE_A
&& file_of(wrsq) == f
&& wrsq < wpsq
&& (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
&& (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
&& ( square_distance(bksq, wrsq) + tempo >= 3
|| ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
&& (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
return ScaleFactor( SCALE_FACTOR_MAX
- 8 * square_distance(wpsq, queeningSq)
- 2 * square_distance(wksq, queeningSq));
// If the pawn is not far advanced, and the defending king is somewhere in
// the pawn's path, it's probably a draw.
if (r <= RANK_4 && bksq > wpsq)
{
if (file_of(bksq) == file_of(wpsq))
return ScaleFactor(10);
if ( abs(file_of(bksq) - file_of(wpsq)) == 1
&& square_distance(wksq, bksq) > 2)
return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
}
return SCALE_FACTOR_NONE;
}
template<>
ScaleFactor Endgame<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.king_square(weakSide);
Square bsq = pos.list<BISHOP>(weakSide)[0];
Square psq = pos.list<PAWN>(strongSide)[0];
Rank rk = relative_rank(strongSide, psq);
Square push = pawn_push(strongSide);
// If the pawn is on the 5th rank and the pawn (currently) is on
// the same color square as the bishop then there is a chance of
// a fortress. Depending on the king position give a moderate
// reduction or a stronger one if the defending king is near the
// corner but not trapped there.
if (rk == RANK_5 && !opposite_colors(bsq, psq))
{
int d = square_distance(psq + 3 * push, ksq);
if (d <= 2 && !(d == 0 && ksq == pos.king_square(strongSide) + 2 * push))
return ScaleFactor(24);
else
return ScaleFactor(48);
}
// When the pawn has moved to the 6th rank we can be fairly sure
// it's drawn if the bishop attacks the square in front of the
// pawn from a reasonable distance and the defending king is near
// the corner
if ( rk == RANK_6
&& square_distance(psq + 2 * push, ksq) <= 1
&& (PseudoAttacks[BISHOP][bsq] & (psq + push))
&& file_distance(bsq, psq) >= 2)
return ScaleFactor(8);
}
return SCALE_FACTOR_NONE;
}
/// K, rook and two pawns vs K, rook and one pawn. There is only a single
/// pattern: 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.list<PAWN>(strongSide)[0];
Square wpsq2 = pos.list<PAWN>(strongSide)[1];
Square bksq = pos.king_square(weakSide);
// Does the stronger side have a passed pawn?
if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
return SCALE_FACTOR_NONE;
Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
if ( file_distance(bksq, wpsq1) <= 1
&& file_distance(bksq, wpsq2) <= 1
&& relative_rank(strongSide, bksq) > r)
{
switch (r) {
case RANK_2: return ScaleFactor(10);
case RANK_3: return ScaleFactor(10);
case RANK_4: return ScaleFactor(15);
case RANK_5: return ScaleFactor(20);
case RANK_6: return ScaleFactor(40);
default: assert(false);
}
}
return SCALE_FACTOR_NONE;
}
/// K and two or more pawns vs K. There is just a single rule here: If all pawns
/// are on the same rook file and are blocked by the defending king, it's a draw.
template<>
ScaleFactor Endgame<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.king_square(weakSide);
Bitboard pawns = pos.pieces(strongSide, PAWN);
Square psq = pos.list<PAWN>(strongSide)[0];
// If all pawns are ahead of the king, all pawns are on a single
// rook file and the king is within one file of the pawns then draw.
if ( !(pawns & ~in_front_bb(weakSide, rank_of(ksq)))
&& !((pawns & ~FileABB) && (pawns & ~FileHBB))
&& file_distance(ksq, psq) <= 1)
return SCALE_FACTOR_DRAW;
return SCALE_FACTOR_NONE;
}
/// K, bishop and a pawn vs K and a bishop. 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.list<PAWN>(strongSide)[0];
Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
Square weakBishopSq = pos.list<BISHOP>(weakSide)[0];
Square weakKingSq = pos.king_square(weakSide);
// Case 1: Defending king blocks the pawn, and cannot be driven away
if ( file_of(weakKingSq) == file_of(pawnSq)
&& relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
&& ( opposite_colors(weakKingSq, strongBishopSq)
|| relative_rank(strongSide, weakKingSq) <= RANK_6))
return SCALE_FACTOR_DRAW;
// Case 2: Opposite colored bishops
if (opposite_colors(strongBishopSq, weakBishopSq))
{
// We assume that the position is drawn in the following three situations:
//
// a. The pawn is on rank 5 or further back.
// b. The defending king is somewhere in the pawn's path.
// c. The defending bishop attacks some square along the pawn's path,
// and is at least three squares away from the pawn.
//
// These rules are probably not perfect, but in practice they work
// reasonably well.
if (relative_rank(strongSide, pawnSq) <= RANK_5)
return SCALE_FACTOR_DRAW;
else
{
Bitboard path = forward_bb(strongSide, pawnSq);
if (path & pos.pieces(weakSide, KING))
return SCALE_FACTOR_DRAW;
if ( (pos.attacks_from<BISHOP>(weakBishopSq) & path)
&& square_distance(weakBishopSq, pawnSq) >= 3)
return SCALE_FACTOR_DRAW;
}
}
return SCALE_FACTOR_NONE;
}
/// K, bishop and two pawns vs K and bishop. 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.list<BISHOP>(strongSide)[0];
Square bbsq = pos.list<BISHOP>(weakSide)[0];
if (!opposite_colors(wbsq, bbsq))
return SCALE_FACTOR_NONE;
Square ksq = pos.king_square(weakSide);
Square psq1 = pos.list<PAWN>(strongSide)[0];
Square psq2 = pos.list<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 = file_of(psq2) | rank_of(psq1);
}
else
{
blockSq1 = psq2 + pawn_push(strongSide);
blockSq2 = file_of(psq1) | rank_of(psq2);
}
switch (file_distance(psq1, psq2))
{
case 0:
// Both pawns are on the same file. It's an easy draw if the defender firmly
// controls some square in the frontmost pawn's path.
if ( file_of(ksq) == file_of(blockSq1)
&& relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
&& opposite_colors(ksq, wbsq))
return SCALE_FACTOR_DRAW;
else
return SCALE_FACTOR_NONE;
case 1:
// Pawns on adjacent files. It's a draw if the defender firmly controls the
// square in front of the frontmost pawn's path, and the square diagonally
// behind this square on the file of the other pawn.
if ( ksq == blockSq1
&& opposite_colors(ksq, wbsq)
&& ( bbsq == blockSq2
|| (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
|| abs(r1 - r2) >= 2))
return SCALE_FACTOR_DRAW;
else if ( ksq == blockSq2
&& opposite_colors(ksq, wbsq)
&& ( bbsq == blockSq1
|| (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
return SCALE_FACTOR_DRAW;
else
return SCALE_FACTOR_NONE;
default:
// The pawns are not on the same file or adjacent files. No scaling.
return SCALE_FACTOR_NONE;
}
}
/// K, bisop and a pawn vs K and knight. There is a single rule: If the defending
/// king is somewhere along the path of the pawn, and the square of the king is
/// not of the same color as the stronger side's bishop, it's a draw.
template<>
ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
assert(verify_material(pos, strongSide, BishopValueMg, 1));
assert(verify_material(pos, weakSide, KnightValueMg, 0));
Square pawnSq = pos.list<PAWN>(strongSide)[0];
Square strongBishopSq = pos.list<BISHOP>(strongSide)[0];
Square weakKingSq = pos.king_square(weakSide);
if ( file_of(weakKingSq) == file_of(pawnSq)
&& relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
&& ( opposite_colors(weakKingSq, strongBishopSq)
|| relative_rank(strongSide, weakKingSq) <= RANK_6))
return SCALE_FACTOR_DRAW;
return SCALE_FACTOR_NONE;
}
/// K, knight and a pawn vs K. There is a single rule: If the pawn is a rook pawn
/// on the 7th rank and the defending king prevents the pawn from advancing, the
/// position is drawn.
template<>
ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
assert(verify_material(pos, strongSide, KnightValueMg, 1));
assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
// Assume strongSide is white and the pawn is on files A-D
Square pawnSq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
Square weakKingSq = normalize(pos, strongSide, pos.king_square(weakSide));
if (pawnSq == SQ_A7 && square_distance(SQ_A8, weakKingSq) <= 1)
return SCALE_FACTOR_DRAW;
return SCALE_FACTOR_NONE;
}
/// K, knight and a pawn vs K and bishop. If knight can block bishop from taking
/// pawn, it's a win. Otherwise, drawn.
template<>
ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
Square pawnSq = pos.list<PAWN>(strongSide)[0];
Square bishopSq = pos.list<BISHOP>(weakSide)[0];
Square weakKingSq = pos.king_square(weakSide);
// King needs to get close to promoting pawn to prevent knight from blocking.
// Rules for this are very tricky, so just approximate.
if (forward_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
return ScaleFactor(square_distance(weakKingSq, pawnSq));
return SCALE_FACTOR_NONE;
}
/// K and a pawn vs K and a pawn. This is done by removing the weakest side's
/// pawn and probing the KP vs K bitbase: If the weakest side has a draw without
/// the pawn, she probably has at least a draw with the pawn as well. The exception
/// is when the stronger side's pawn is far advanced and not on a rook file; in
/// this case it is often possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
template<>
ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
// Assume strongSide is white and the pawn is on files A-D
Square wksq = normalize(pos, strongSide, pos.king_square(strongSide));
Square bksq = normalize(pos, strongSide, pos.king_square(weakSide));
Square psq = normalize(pos, strongSide, pos.list<PAWN>(strongSide)[0]);
Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
// If the pawn has advanced to the fifth rank or further, and is not a
// rook pawn, it's too dangerous to assume that it's at least a draw.
if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
return SCALE_FACTOR_NONE;
// Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
// it's probably at least a draw even with the pawn.
return Bitbases::probe_kpk(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;
}
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