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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) 2004-2021 The Stockfish developers (see AUTHORS file)
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 <cassert>
#include "bitboard.h"
#include "endgame.h"
#include "movegen.h"
namespace Stockfish {
namespace {
// Used to drive the king towards the edge of the board
// in KX vs K and KQ vs KR endgames.
// Values range from 27 (center squares) to 90 (in the corners)
inline int push_to_edge(Square s) {
int rd = edge_distance(rank_of(s)), fd = edge_distance(file_of(s));
return 90 - (7 * fd * fd / 2 + 7 * rd * rd / 2);
}
// Used to drive the king towards A1H8 corners in KBN vs K endgames.
// Values range from 0 on A8H1 diagonal to 7 in A1H8 corners
inline int push_to_corner(Square s) {
return abs(7 - rank_of(s) - file_of(s));
}
// Drive a piece close to or away from another piece
inline int push_close(Square s1, Square s2) { return 140 - 20 * distance(s1, s2); }
inline int push_away(Square s1, Square s2) { return 120 - push_close(s1, s2); }
#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 = flip_file(sq);
return strongSide == WHITE ? sq : flip_rank(sq);
}
} // namespace
namespace Endgames {
std::pair<Map<Value>, Map<ScaleFactor>> maps;
void init() {
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<KNNKP>("KNNKP");
add<KRPKR>("KRPKR");
add<KRPKB>("KRPKB");
add<KBPKB>("KBPKB");
add<KBPKN>("KBPKN");
add<KBPPKB>("KBPPKB");
add<KRPPKRP>("KRPPKRP");
}
}
/// 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 strongKing = pos.square<KING>(strongSide);
Square weakKing = pos.square<KING>(weakSide);
Value result = pos.non_pawn_material(strongSide)
+ pos.count<PAWN>(strongSide) * PawnValueEg
+ push_to_edge(weakKing)
+ push_close(strongKing, weakKing);
if ( pos.count<QUEEN>(strongSide)
|| pos.count<ROOK>(strongSide)
||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
|| ( (pos.pieces(strongSide, BISHOP) & ~DarkSquares)
&& (pos.pieces(strongSide, BISHOP) & DarkSquares)))
result = std::min(result + VALUE_KNOWN_WIN, VALUE_TB_WIN_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 that our bishop attacks.
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 strongKing = pos.square<KING>(strongSide);
Square strongBishop = pos.square<BISHOP>(strongSide);
Square weakKing = pos.square<KING>(weakSide);
// If our bishop does not attack A1/H8, we flip the enemy king square
// to drive to opposite corners (A8/H1).
Value result = (VALUE_KNOWN_WIN + 3520)
+ push_close(strongKing, weakKing)
+ 420 * push_to_corner(opposite_colors(strongBishop, SQ_A1) ? flip_file(weakKing) : weakKing);
assert(abs(result) < VALUE_TB_WIN_IN_MAX_PLY);
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 strongKing = normalize(pos, strongSide, pos.square<KING>(strongSide));
Square strongPawn = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
Square weakKing = normalize(pos, strongSide, pos.square<KING>(weakSide));
Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
if (!Bitbases::probe(strongKing, strongPawn, weakKing, us))
return VALUE_DRAW;
Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(strongPawn));
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 strongKing = pos.square<KING>(strongSide);
Square weakKing = pos.square<KING>(weakSide);
Square strongRook = pos.square<ROOK>(strongSide);
Square weakPawn = pos.square<PAWN>(weakSide);
Square queeningSquare = make_square(file_of(weakPawn), relative_rank(weakSide, RANK_8));
Value result;
// If the stronger side's king is in front of the pawn, it's a win
if (forward_file_bb(strongSide, strongKing) & weakPawn)
result = RookValueEg - distance(strongKing, weakPawn);
// If the weaker side's king is too far from the pawn and the rook,
// it's a win.
else if ( distance(weakKing, weakPawn) >= 3 + (pos.side_to_move() == weakSide)
&& distance(weakKing, strongRook) >= 3)
result = RookValueEg - distance(strongKing, weakPawn);
// If the pawn is far advanced and supported by the defending king,
// the position is drawish
else if ( relative_rank(strongSide, weakKing) <= RANK_3
&& distance(weakKing, weakPawn) == 1
&& relative_rank(strongSide, strongKing) >= RANK_4
&& distance(strongKing, weakPawn) > 2 + (pos.side_to_move() == strongSide))
result = Value(80) - 8 * distance(strongKing, weakPawn);
else
result = Value(200) - 8 * ( distance(strongKing, weakPawn + pawn_push(weakSide))
- distance(weakKing, weakPawn + pawn_push(weakSide))
- distance(weakPawn, queeningSquare));
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(push_to_edge(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 weakKing = pos.square<KING>(weakSide);
Square weakKnight = pos.square<KNIGHT>(weakSide);
Value result = Value(push_to_edge(weakKing) + push_away(weakKing, weakKnight));
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 strongKing = pos.square<KING>(strongSide);
Square weakKing = pos.square<KING>(weakSide);
Square weakPawn = pos.square<PAWN>(weakSide);
Value result = Value(push_close(strongKing, weakKing));
if ( relative_rank(weakSide, weakPawn) != RANK_7
|| distance(weakKing, weakPawn) != 1
|| ((FileBBB | FileDBB | FileEBB | FileGBB) & weakPawn))
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 strongKing = pos.square<KING>(strongSide);
Square weakKing = pos.square<KING>(weakSide);
Value result = QueenValueEg
- RookValueEg
+ push_to_edge(weakKing)
+ push_close(strongKing, weakKing);
return strongSide == pos.side_to_move() ? result : -result;
}
/// KNN vs KP. Very drawish, but there are some mate opportunities if we can
/// press the weakSide King to a corner before the pawn advances too much.
template<>
Value Endgame<KNNKP>::operator()(const Position& pos) const {
assert(verify_material(pos, strongSide, 2 * KnightValueMg, 0));
assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
Square weakKing = pos.square<KING>(weakSide);
Square weakPawn = pos.square<PAWN>(weakSide);
Value result = PawnValueEg
+ 2 * push_to_edge(weakKing)
- 10 * relative_rank(weakSide, weakPawn);
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 strongPawns = pos.pieces(strongSide, PAWN);
Bitboard allPawns = pos.pieces(PAWN);
Square strongBishop = pos.square<BISHOP>(strongSide);
Square weakKing = pos.square<KING>(weakSide);
Square strongKing = pos.square<KING>(strongSide);
// All strongSide pawns are on a single rook file?
if (!(strongPawns & ~FileABB) || !(strongPawns & ~FileHBB))
{
Square queeningSquare = relative_square(strongSide, make_square(file_of(lsb(strongPawns)), RANK_8));
if ( opposite_colors(queeningSquare, strongBishop)
&& distance(queeningSquare, weakKing) <= 1)
return SCALE_FACTOR_DRAW;
}
// If all the pawns are on the same B or G file, then it's potentially a draw
if ((!(allPawns & ~FileBBB) || !(allPawns & ~FileGBB))
&& pos.non_pawn_material(weakSide) == 0
&& pos.count<PAWN>(weakSide) >= 1)
{
// Get the least advanced weakSide pawn
Square weakPawn = frontmost_sq(strongSide, pos.pieces(weakSide, PAWN));
// 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, weakPawn) == RANK_7
&& (strongPawns & (weakPawn + pawn_push(weakSide)))
&& (opposite_colors(strongBishop, weakPawn) || !more_than_one(strongPawns)))
{
int strongKingDist = distance(weakPawn, strongKing);
int weakKingDist = distance(weakPawn, weakKing);
// 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, weakKing) >= 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 strongKing = pos.square<KING>(strongSide);
Square weakKing = pos.square<KING>(weakSide);
Square weakRook = pos.square<ROOK>(weakSide);
if ( relative_rank(weakSide, weakKing) <= RANK_2
&& relative_rank(weakSide, strongKing) >= RANK_4
&& relative_rank(weakSide, weakRook) == RANK_3
&& ( pos.pieces(weakSide, PAWN)
& attacks_bb<KING>(weakKing)
& pawn_attacks_bb(strongSide, weakRook)))
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 strongKing = normalize(pos, strongSide, pos.square<KING>(strongSide));
Square strongRook = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
Square strongPawn = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
Square weakKing = normalize(pos, strongSide, pos.square<KING>(weakSide));
Square weakRook = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
File pawnFile = file_of(strongPawn);
Rank pawnRank = rank_of(strongPawn);
Square queeningSquare = make_square(pawnFile, 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 ( pawnRank <= RANK_5
&& distance(weakKing, queeningSquare) <= 1
&& strongKing <= SQ_H5
&& (rank_of(weakRook) == RANK_6 || (pawnRank <= RANK_3 && rank_of(strongRook) != 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 ( pawnRank == RANK_6
&& distance(weakKing, queeningSquare) <= 1
&& rank_of(strongKing) + tempo <= RANK_6
&& (rank_of(weakRook) == RANK_1 || (!tempo && distance<File>(weakRook, strongPawn) >= 3)))
return SCALE_FACTOR_DRAW;
if ( pawnRank >= RANK_6
&& weakKing == queeningSquare
&& rank_of(weakRook) == RANK_1
&& (!tempo || distance(strongKing, strongPawn) >= 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 ( strongPawn == SQ_A7
&& strongRook == SQ_A8
&& (weakKing == SQ_H7 || weakKing == SQ_G7)
&& file_of(weakRook) == FILE_A
&& (rank_of(weakRook) <= RANK_3 || file_of(strongKing) >= FILE_D || rank_of(strongKing) <= 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 ( pawnRank <= RANK_5
&& weakKing == strongPawn + NORTH
&& distance(strongKing, strongPawn) - tempo >= 2
&& distance(strongKing, weakRook) - 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 ( pawnRank == RANK_7
&& pawnFile != FILE_A
&& file_of(strongRook) == pawnFile
&& strongRook != queeningSquare
&& (distance(strongKing, queeningSquare) < distance(weakKing, queeningSquare) - 2 + tempo)
&& (distance(strongKing, queeningSquare) < distance(weakKing, strongRook) + tempo))
return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(strongKing, queeningSquare));
// Similar to the above, but with the pawn further back
if ( pawnFile != FILE_A
&& file_of(strongRook) == pawnFile
&& strongRook < strongPawn
&& (distance(strongKing, queeningSquare) < distance(weakKing, queeningSquare) - 2 + tempo)
&& (distance(strongKing, strongPawn + NORTH) < distance(weakKing, strongPawn + NORTH) - 2 + tempo)
&& ( distance(weakKing, strongRook) + tempo >= 3
|| ( distance(strongKing, queeningSquare) < distance(weakKing, strongRook) + tempo
&& (distance(strongKing, strongPawn + NORTH) < distance(weakKing, strongPawn) + tempo))))
return ScaleFactor( SCALE_FACTOR_MAX
- 8 * distance(strongPawn, queeningSquare)
- 2 * distance(strongKing, queeningSquare));
// If the pawn is not far advanced and the defending king is somewhere in
// the pawn's path, it's probably a draw.
if (pawnRank <= RANK_4 && weakKing > strongPawn)
{
if (file_of(weakKing) == file_of(strongPawn))
return ScaleFactor(10);
if ( distance<File>(weakKing, strongPawn) == 1
&& distance(strongKing, weakKing) > 2)
return ScaleFactor(24 - 2 * distance(strongKing, weakKing));
}
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 weakKing = pos.square<KING>(weakSide);
Square weakBishop = pos.square<BISHOP>(weakSide);
Square strongKing = pos.square<KING>(strongSide);
Square strongPawn = pos.square<PAWN>(strongSide);
Rank pawnRank = relative_rank(strongSide, strongPawn);
Direction 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 (pawnRank == RANK_5 && !opposite_colors(weakBishop, strongPawn))
{
int d = distance(strongPawn + 3 * push, weakKing);
if (d <= 2 && !(d == 0 && weakKing == strongKing + 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 ( pawnRank == RANK_6
&& distance(strongPawn + 2 * push, weakKing) <= 1
&& (attacks_bb<BISHOP>(weakBishop) & (strongPawn + push))
&& distance<File>(weakBishop, strongPawn) >= 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 strongPawn1 = lsb(pos.pieces(strongSide, PAWN));
Square strongPawn2 = msb(pos.pieces(strongSide, PAWN));
Square weakKing = pos.square<KING>(weakSide);
// Does the stronger side have a passed pawn?
if (pos.pawn_passed(strongSide, strongPawn1) || pos.pawn_passed(strongSide, strongPawn2))
return SCALE_FACTOR_NONE;
Rank pawnRank = std::max(relative_rank(strongSide, strongPawn1), relative_rank(strongSide, strongPawn2));
if ( distance<File>(weakKing, strongPawn1) <= 1
&& distance<File>(weakKing, strongPawn2) <= 1
&& relative_rank(strongSide, weakKing) > pawnRank)
{
assert(pawnRank > RANK_1 && pawnRank < RANK_7);
return ScaleFactor(7 * pawnRank);
}
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 weakKing = pos.square<KING>(weakSide);
Bitboard strongPawns = pos.pieces(strongSide, PAWN);
// If all pawns are ahead of the king on a single rook file, it's a draw.
if ( !(strongPawns & ~(FileABB | FileHBB))
&& !(strongPawns & ~passed_pawn_span(weakSide, weakKing)))
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 strongPawn = pos.square<PAWN>(strongSide);
Square strongBishop = pos.square<BISHOP>(strongSide);
Square weakBishop = pos.square<BISHOP>(weakSide);
Square weakKing = pos.square<KING>(weakSide);
// Case 1: Defending king blocks the pawn, and cannot be driven away
if ( (forward_file_bb(strongSide, strongPawn) & weakKing)
&& ( opposite_colors(weakKing, strongBishop)
|| relative_rank(strongSide, weakKing) <= RANK_6))
return SCALE_FACTOR_DRAW;
// Case 2: Opposite colored bishops
if (opposite_colors(strongBishop, weakBishop))
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 strongBishop = pos.square<BISHOP>(strongSide);
Square weakBishop = pos.square<BISHOP>(weakSide);
if (!opposite_colors(strongBishop, weakBishop))
return SCALE_FACTOR_NONE;
Square weakKing = pos.square<KING>(weakSide);
Square strongPawn1 = lsb(pos.pieces(strongSide, PAWN));
Square strongPawn2 = msb(pos.pieces(strongSide, PAWN));
Square blockSq1, blockSq2;
if (relative_rank(strongSide, strongPawn1) > relative_rank(strongSide, strongPawn2))
{
blockSq1 = strongPawn1 + pawn_push(strongSide);
blockSq2 = make_square(file_of(strongPawn2), rank_of(strongPawn1));
}
else
{
blockSq1 = strongPawn2 + pawn_push(strongSide);
blockSq2 = make_square(file_of(strongPawn1), rank_of(strongPawn2));
}
switch (distance<File>(strongPawn1, strongPawn2))
{
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(weakKing) == file_of(blockSq1)
&& relative_rank(strongSide, weakKing) >= relative_rank(strongSide, blockSq1)
&& opposite_colors(weakKing, strongBishop))
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 ( weakKing == blockSq1
&& opposite_colors(weakKing, strongBishop)
&& ( weakBishop == blockSq2
|| (attacks_bb<BISHOP>(blockSq2, pos.pieces()) & pos.pieces(weakSide, BISHOP))
|| distance<Rank>(strongPawn1, strongPawn2) >= 2))
return SCALE_FACTOR_DRAW;
else if ( weakKing == blockSq2
&& opposite_colors(weakKing, strongBishop)
&& ( weakBishop == blockSq1
|| (attacks_bb<BISHOP>(blockSq1, pos.pieces()) & pos.pieces(weakSide, BISHOP))))
return SCALE_FACTOR_DRAW;
else
return SCALE_FACTOR_NONE;
default:
// The pawns are not on the same file or adjacent files. No scaling.
return SCALE_FACTOR_NONE;
}
}
/// KBP vs KN. There is a single rule: if the defending king is somewhere along
/// the path of the pawn, and the square of the king is not of the same color as
/// the stronger side's bishop, it's a draw.
template<>
ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
assert(verify_material(pos, strongSide, BishopValueMg, 1));
assert(verify_material(pos, weakSide, KnightValueMg, 0));
Square strongPawn = pos.square<PAWN>(strongSide);
Square strongBishop = pos.square<BISHOP>(strongSide);
Square weakKing = pos.square<KING>(weakSide);
if ( file_of(weakKing) == file_of(strongPawn)
&& relative_rank(strongSide, strongPawn) < relative_rank(strongSide, weakKing)
&& ( opposite_colors(weakKing, strongBishop)
|| relative_rank(strongSide, weakKing) <= RANK_6))
return SCALE_FACTOR_DRAW;
return SCALE_FACTOR_NONE;
}
/// KP vs KP. This is done by removing the weakest side's pawn and probing the
/// KP vs K bitbase: if the weakest side has a draw without the pawn, it probably
/// has at least a draw with the pawn as well. The exception is when the stronger
/// side's pawn is far advanced and not on a rook file; in this case it is often
/// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
template<>
ScaleFactor Endgame<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 strongKing = normalize(pos, strongSide, pos.square<KING>(strongSide));
Square weakKing = normalize(pos, strongSide, pos.square<KING>(weakSide));
Square strongPawn = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
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(strongPawn) >= RANK_5 && file_of(strongPawn) != 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(strongKing, strongPawn, weakKing, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;
}
} // namespace Stockfish
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