/*
Stockfish, a UCI chess playing engine derived from Glaurung 2.1
Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
- Copyright (C) 2008-2009 Marco Costalba
+ Copyright (C) 2008-2010 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
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
-
-////
-//// Includes
-////
-
#include <cassert>
-#include <sstream>
-#include <map>
+#include <cstring>
#include "material.h"
using namespace std;
+namespace {
-////
-//// Local definitions
-////
+ // Values modified by Joona Kiiski
+ const Value MidgameLimit = Value(15581);
+ const Value EndgameLimit = Value(3998);
-namespace {
+ // Scale factors used when one side has no more pawns
+ const int NoPawnsSF[4] = { 6, 12, 32 };
// Polynomial material balance parameters
const Value RedundantQueenPenalty = Value(320);
const Value RedundantRookPenalty = Value(554);
- const int LinearCoefficients[6] = { 1617, -162, -1172, -190, 105, 26 };
- const int QuadraticCoefficientsSameColor[][6] = {
+ const int LinearCoefficients[6] = { 1617, -162, -1172, -190, 105, 26 };
+
+ const int QuadraticCoefficientsSameColor[][8] = {
{ 7, 7, 7, 7, 7, 7 }, { 39, 2, 7, 7, 7, 7 }, { 35, 271, -4, 7, 7, 7 },
{ 7, 25, 4, 7, 7, 7 }, { -27, -2, 46, 100, 56, 7 }, { 58, 29, 83, 148, -3, -25 } };
- const int QuadraticCoefficientsOppositeColor[][6] = {
+ const int QuadraticCoefficientsOppositeColor[][8] = {
{ 41, 41, 41, 41, 41, 41 }, { 37, 41, 41, 41, 41, 41 }, { 10, 62, 41, 41, 41, 41 },
{ 57, 64, 39, 41, 41, 41 }, { 50, 40, 23, -22, 41, 41 }, { 106, 101, 3, 151, 171, 41 } };
- // Named endgame evaluation and scaling functions, these
- // are accessed direcly and not through the function maps.
- EvaluationFunction<KmmKm> EvaluateKmmKm(WHITE);
- EvaluationFunction<KXK> EvaluateKXK(WHITE), EvaluateKKX(BLACK);
- ScalingFunction<KBPsK> ScaleKBPsK(WHITE), ScaleKKBPs(BLACK);
- ScalingFunction<KQKRPs> ScaleKQKRPs(WHITE), ScaleKRPsKQ(BLACK);
- ScalingFunction<KPsK> ScaleKPsK(WHITE), ScaleKKPs(BLACK);
- ScalingFunction<KPKP> ScaleKPKPw(WHITE), ScaleKPKPb(BLACK);
-
- typedef EndgameEvaluationFunctionBase EF;
- typedef EndgameScalingFunctionBase SF;
-}
-
-
-////
-//// Classes
-////
-
-/// EndgameFunctions class stores endgame evaluation and scaling functions
-/// in two std::map. Because STL library is not guaranteed to be thread
-/// safe even for read access, the maps, although with identical content,
-/// are replicated for each thread. This is faster then using locks.
-
-class EndgameFunctions {
-public:
- EndgameFunctions();
- ~EndgameFunctions();
- template<class T> T* get(Key key) const;
-
-private:
- template<class T> void add(const string& keyCode);
-
- static Key buildKey(const string& keyCode);
- static const string swapColors(const string& keyCode);
-
- // Here we store two maps, for evaluate and scaling functions
- pair<map<Key, EF*>, map<Key, SF*> > maps;
-
- // Maps accessing functions returning const and non-const references
- template<typename T> const map<Key, T*>& get() const { return maps.first; }
- template<typename T> map<Key, T*>& get() { return maps.first; }
-};
-
-// Explicit specializations of a member function shall be declared in
-// the namespace of which the class template is a member.
-template<> const map<Key, SF*>&
-EndgameFunctions::get<SF>() const { return maps.second; }
-
-template<> map<Key, SF*>&
-EndgameFunctions::get<SF>() { return maps.second; }
-
-
-////
-//// Functions
-////
+ // Endgame evaluation and scaling functions accessed direcly and not through
+ // the function maps because correspond to more then one material hash key.
+ Endgame<Value, KmmKm> EvaluateKmmKm[] = { Endgame<Value, KmmKm>(WHITE), Endgame<Value, KmmKm>(BLACK) };
+ Endgame<Value, KXK> EvaluateKXK[] = { Endgame<Value, KXK>(WHITE), Endgame<Value, KXK>(BLACK) };
+
+ Endgame<ScaleFactor, KBPsK> ScaleKBPsK[] = { Endgame<ScaleFactor, KBPsK>(WHITE), Endgame<ScaleFactor, KBPsK>(BLACK) };
+ Endgame<ScaleFactor, KQKRPs> ScaleKQKRPs[] = { Endgame<ScaleFactor, KQKRPs>(WHITE), Endgame<ScaleFactor, KQKRPs>(BLACK) };
+ Endgame<ScaleFactor, KPsK> ScaleKPsK[] = { Endgame<ScaleFactor, KPsK>(WHITE), Endgame<ScaleFactor, KPsK>(BLACK) };
+ Endgame<ScaleFactor, KPKP> ScaleKPKP[] = { Endgame<ScaleFactor, KPKP>(WHITE), Endgame<ScaleFactor, KPKP>(BLACK) };
+
+ // Helper templates used to detect a given material distribution
+ template<Color Us> bool is_KXK(const Position& pos) {
+ const Color Them = (Us == WHITE ? BLACK : WHITE);
+ return pos.non_pawn_material(Them) == VALUE_ZERO
+ && pos.piece_count(Them, PAWN) == 0
+ && pos.non_pawn_material(Us) >= RookValueMidgame;
+ }
-/// MaterialInfoTable c'tor and d'tor, called once by each thread
+ template<Color Us> bool is_KBPsKs(const Position& pos) {
+ return pos.non_pawn_material(Us) == BishopValueMidgame
+ && pos.piece_count(Us, BISHOP) == 1
+ && pos.piece_count(Us, PAWN) >= 1;
+ }
-MaterialInfoTable::MaterialInfoTable(unsigned int numOfEntries) {
+ template<Color Us> bool is_KQKRPs(const Position& pos) {
+ const Color Them = (Us == WHITE ? BLACK : WHITE);
+ return pos.piece_count(Us, PAWN) == 0
+ && pos.non_pawn_material(Us) == QueenValueMidgame
+ && pos.piece_count(Us, QUEEN) == 1
+ && pos.piece_count(Them, ROOK) == 1
+ && pos.piece_count(Them, PAWN) >= 1;
+ }
- size = numOfEntries;
- entries = new MaterialInfo[size];
- funcs = new EndgameFunctions();
+} // namespace
- if (!entries || !funcs)
- {
- cerr << "Failed to allocate " << numOfEntries * sizeof(MaterialInfo)
- << " bytes for material hash table." << endl;
- Application::exit_with_failure();
- }
-}
-MaterialInfoTable::~MaterialInfoTable() {
+/// MaterialInfoTable c'tor and d'tor allocate and free the space for Endgames
- delete funcs;
- delete [] entries;
-}
+void MaterialInfoTable::init() { Base::init(); if (!funcs) funcs = new Endgames(); }
+MaterialInfoTable::~MaterialInfoTable() { delete funcs; }
/// MaterialInfoTable::get_material_info() takes a position object as input,
/// is stored there, so we don't have to recompute everything when the
/// same material configuration occurs again.
-MaterialInfo* MaterialInfoTable::get_material_info(const Position& pos) {
+MaterialInfo* MaterialInfoTable::get_material_info(const Position& pos) const {
Key key = pos.get_material_key();
- int index = key & (size - 1);
- MaterialInfo* mi = entries + index;
+ MaterialInfo* mi = probe(key);
// If mi->key matches the position's material hash key, it means that we
// have analysed this material configuration before, and we can simply
if (mi->key == key)
return mi;
- // Clear the MaterialInfo object, and set its key
- mi->clear();
+ // Initialize MaterialInfo entry
+ memset(mi, 0, sizeof(MaterialInfo));
mi->key = key;
+ mi->factor[WHITE] = mi->factor[BLACK] = (uint8_t)SCALE_FACTOR_NORMAL;
+
+ // Store game phase
+ mi->gamePhase = MaterialInfoTable::game_phase(pos);
// Let's look if we have a specialized evaluation function for this
// particular material configuration. First we look for a fixed
// configuration one, then a generic one if previous search failed.
- if ((mi->evaluationFunction = funcs->get<EF>(key)) != NULL)
+ if ((mi->evaluationFunction = funcs->get<EndgameBase<Value> >(key)) != NULL)
return mi;
- else if ( pos.non_pawn_material(BLACK) == Value(0)
- && pos.piece_count(BLACK, PAWN) == 0
- && pos.non_pawn_material(WHITE) >= RookValueMidgame)
+ if (is_KXK<WHITE>(pos))
{
- mi->evaluationFunction = &EvaluateKXK;
+ mi->evaluationFunction = &EvaluateKXK[WHITE];
return mi;
}
- else if ( pos.non_pawn_material(WHITE) == Value(0)
- && pos.piece_count(WHITE, PAWN) == 0
- && pos.non_pawn_material(BLACK) >= RookValueMidgame)
+
+ if (is_KXK<BLACK>(pos))
{
- mi->evaluationFunction = &EvaluateKKX;
+ mi->evaluationFunction = &EvaluateKXK[BLACK];
return mi;
}
- else if ( pos.pieces(PAWN) == EmptyBoardBB
- && pos.pieces(ROOK) == EmptyBoardBB
- && pos.pieces(QUEEN) == EmptyBoardBB)
+
+ if (!pos.pieces(PAWN) && !pos.pieces(ROOK) && !pos.pieces(QUEEN))
{
// Minor piece endgame with at least one minor piece per side and
// no pawns. Note that the case KmmK is already handled by KXK.
if ( pos.piece_count(WHITE, BISHOP) + pos.piece_count(WHITE, KNIGHT) <= 2
&& pos.piece_count(BLACK, BISHOP) + pos.piece_count(BLACK, KNIGHT) <= 2)
{
- mi->evaluationFunction = &EvaluateKmmKm;
+ mi->evaluationFunction = &EvaluateKmmKm[WHITE];
return mi;
}
}
// OK, we didn't find any special evaluation function for the current
// material configuration. Is there a suitable scaling function?
//
- // The code below is rather messy, and it could easily get worse later,
- // if we decide to add more special cases. We face problems when there
- // are several conflicting applicable scaling functions and we need to
- // decide which one to use.
- SF* sf;
+ // We face problems when there are several conflicting applicable
+ // scaling functions and we need to decide which one to use.
+ EndgameBase<ScaleFactor>* sf;
- if ((sf = funcs->get<SF>(key)) != NULL)
+ if ((sf = funcs->get<EndgameBase<ScaleFactor> >(key)) != NULL)
{
mi->scalingFunction[sf->color()] = sf;
return mi;
// Generic scaling functions that refer to more then one material
// distribution. Should be probed after the specialized ones.
// Note that these ones don't return after setting the function.
- if ( pos.non_pawn_material(WHITE) == BishopValueMidgame
- && pos.piece_count(WHITE, BISHOP) == 1
- && pos.piece_count(WHITE, PAWN) >= 1)
- mi->scalingFunction[WHITE] = &ScaleKBPsK;
-
- if ( pos.non_pawn_material(BLACK) == BishopValueMidgame
- && pos.piece_count(BLACK, BISHOP) == 1
- && pos.piece_count(BLACK, PAWN) >= 1)
- mi->scalingFunction[BLACK] = &ScaleKKBPs;
-
- if ( pos.piece_count(WHITE, PAWN) == 0
- && pos.non_pawn_material(WHITE) == QueenValueMidgame
- && pos.piece_count(WHITE, QUEEN) == 1
- && pos.piece_count(BLACK, ROOK) == 1
- && pos.piece_count(BLACK, PAWN) >= 1)
- mi->scalingFunction[WHITE] = &ScaleKQKRPs;
-
- else if ( pos.piece_count(BLACK, PAWN) == 0
- && pos.non_pawn_material(BLACK) == QueenValueMidgame
- && pos.piece_count(BLACK, QUEEN) == 1
- && pos.piece_count(WHITE, ROOK) == 1
- && pos.piece_count(WHITE, PAWN) >= 1)
- mi->scalingFunction[BLACK] = &ScaleKRPsKQ;
-
- if (pos.non_pawn_material(WHITE) + pos.non_pawn_material(BLACK) == Value(0))
+ if (is_KBPsKs<WHITE>(pos))
+ mi->scalingFunction[WHITE] = &ScaleKBPsK[WHITE];
+
+ if (is_KBPsKs<BLACK>(pos))
+ mi->scalingFunction[BLACK] = &ScaleKBPsK[BLACK];
+
+ if (is_KQKRPs<WHITE>(pos))
+ mi->scalingFunction[WHITE] = &ScaleKQKRPs[WHITE];
+
+ else if (is_KQKRPs<BLACK>(pos))
+ mi->scalingFunction[BLACK] = &ScaleKQKRPs[BLACK];
+
+ Value npm_w = pos.non_pawn_material(WHITE);
+ Value npm_b = pos.non_pawn_material(BLACK);
+
+ if (npm_w + npm_b == VALUE_ZERO)
{
if (pos.piece_count(BLACK, PAWN) == 0)
{
assert(pos.piece_count(WHITE, PAWN) >= 2);
- mi->scalingFunction[WHITE] = &ScaleKPsK;
+ mi->scalingFunction[WHITE] = &ScaleKPsK[WHITE];
}
else if (pos.piece_count(WHITE, PAWN) == 0)
{
assert(pos.piece_count(BLACK, PAWN) >= 2);
- mi->scalingFunction[BLACK] = &ScaleKKPs;
+ mi->scalingFunction[BLACK] = &ScaleKPsK[BLACK];
}
else if (pos.piece_count(WHITE, PAWN) == 1 && pos.piece_count(BLACK, PAWN) == 1)
{
// This is a special case because we set scaling functions
// for both colors instead of only one.
- mi->scalingFunction[WHITE] = &ScaleKPKPw;
- mi->scalingFunction[BLACK] = &ScaleKPKPb;
+ mi->scalingFunction[WHITE] = &ScaleKPKP[WHITE];
+ mi->scalingFunction[BLACK] = &ScaleKPKP[BLACK];
}
}
- // Compute the space weight
- if (pos.non_pawn_material(WHITE) + pos.non_pawn_material(BLACK) >=
- 2*QueenValueMidgame + 4*RookValueMidgame + 2*KnightValueMidgame)
+ // No pawns makes it difficult to win, even with a material advantage
+ if (pos.piece_count(WHITE, PAWN) == 0 && npm_w - npm_b <= BishopValueMidgame)
{
- int minorPieceCount = pos.piece_count(WHITE, KNIGHT)
- + pos.piece_count(BLACK, KNIGHT)
- + pos.piece_count(WHITE, BISHOP)
- + pos.piece_count(BLACK, BISHOP);
-
- mi->spaceWeight = minorPieceCount * minorPieceCount;
+ mi->factor[WHITE] = uint8_t
+ (npm_w == npm_b || npm_w < RookValueMidgame ? 0 : NoPawnsSF[Min(pos.piece_count(WHITE, BISHOP), 2)]);
}
- // Evaluate the material balance
- const int pieceCount[2][6] = { { pos.piece_count(WHITE, BISHOP) > 1, pos.piece_count(WHITE, PAWN), pos.piece_count(WHITE, KNIGHT),
- pos.piece_count(WHITE, BISHOP), pos.piece_count(WHITE, ROOK), pos.piece_count(WHITE, QUEEN) },
- { pos.piece_count(BLACK, BISHOP) > 1, pos.piece_count(BLACK, PAWN), pos.piece_count(BLACK, KNIGHT),
- pos.piece_count(BLACK, BISHOP), pos.piece_count(BLACK, ROOK), pos.piece_count(BLACK, QUEEN) } };
- Color c, them;
- int sign;
- int matValue = 0;
-
- for (c = WHITE, sign = 1; c <= BLACK; c++, sign = -sign)
+ if (pos.piece_count(BLACK, PAWN) == 0 && npm_b - npm_w <= BishopValueMidgame)
{
- // No pawns makes it difficult to win, even with a material advantage
- if ( pos.piece_count(c, PAWN) == 0
- && pos.non_pawn_material(c) - pos.non_pawn_material(opposite_color(c)) <= BishopValueMidgame)
- {
- if ( pos.non_pawn_material(c) == pos.non_pawn_material(opposite_color(c))
- || pos.non_pawn_material(c) < RookValueMidgame)
- mi->factor[c] = 0;
- else
- {
- switch (pos.piece_count(c, BISHOP)) {
- case 2:
- mi->factor[c] = 32;
- break;
- case 1:
- mi->factor[c] = 12;
- break;
- case 0:
- mi->factor[c] = 6;
- break;
- }
- }
- }
-
- // Redundancy of major pieces, formula based on Kaufman's paper
- // "The Evaluation of Material Imbalances in Chess"
- // http://mywebpages.comcast.net/danheisman/Articles/evaluation_of_material_imbalance.htm
- if (pieceCount[c][ROOK] >= 1)
- matValue -= sign * ((pieceCount[c][ROOK] - 1) * RedundantRookPenalty + pieceCount[c][QUEEN] * RedundantQueenPenalty);
-
- them = opposite_color(c);
-
- // Second-degree polynomial material imbalance by Tord Romstad
- //
- // We use NO_PIECE_TYPE as a place holder for the bishop pair "extended piece",
- // this allow us to be more flexible in defining bishop pair bonuses.
- for (int pt1 = NO_PIECE_TYPE; pt1 <= QUEEN; pt1++)
- {
- int c1 = sign * pieceCount[c][pt1];
- if (!c1)
- continue;
-
- matValue += c1 * LinearCoefficients[pt1];
-
- for (int pt2 = NO_PIECE_TYPE; pt2 <= pt1; pt2++)
- {
- matValue += c1 * pieceCount[c][pt2] * QuadraticCoefficientsSameColor[pt1][pt2];
- matValue += c1 * pieceCount[them][pt2] * QuadraticCoefficientsOppositeColor[pt1][pt2];
- }
- }
+ mi->factor[BLACK] = uint8_t
+ (npm_w == npm_b || npm_b < RookValueMidgame ? 0 : NoPawnsSF[Min(pos.piece_count(BLACK, BISHOP), 2)]);
}
- mi->value = int16_t(matValue / 16);
- return mi;
-}
-
-/// EndgameFunctions member definitions.
+ // Compute the space weight
+ if (npm_w + npm_b >= 2 * QueenValueMidgame + 4 * RookValueMidgame + 2 * KnightValueMidgame)
+ {
+ int minorPieceCount = pos.piece_count(WHITE, KNIGHT) + pos.piece_count(WHITE, BISHOP)
+ + pos.piece_count(BLACK, KNIGHT) + pos.piece_count(BLACK, BISHOP);
-EndgameFunctions::EndgameFunctions() {
+ mi->spaceWeight = minorPieceCount * minorPieceCount;
+ }
- add<EvaluationFunction<KNNK> >("KNNK");
- add<EvaluationFunction<KPK> >("KPK");
- add<EvaluationFunction<KBNK> >("KBNK");
- add<EvaluationFunction<KRKP> >("KRKP");
- add<EvaluationFunction<KRKB> >("KRKB");
- add<EvaluationFunction<KRKN> >("KRKN");
- add<EvaluationFunction<KQKR> >("KQKR");
- add<EvaluationFunction<KBBKN> >("KBBKN");
+ // Evaluate the material imbalance. We use PIECE_TYPE_NONE as a place holder
+ // for the bishop pair "extended piece", this allow us to be more flexible
+ // in defining bishop pair bonuses.
+ const int pieceCount[2][8] = {
+ { pos.piece_count(WHITE, BISHOP) > 1, pos.piece_count(WHITE, PAWN), pos.piece_count(WHITE, KNIGHT),
+ pos.piece_count(WHITE, BISHOP) , pos.piece_count(WHITE, ROOK), pos.piece_count(WHITE, QUEEN) },
+ { pos.piece_count(BLACK, BISHOP) > 1, pos.piece_count(BLACK, PAWN), pos.piece_count(BLACK, KNIGHT),
+ pos.piece_count(BLACK, BISHOP) , pos.piece_count(BLACK, ROOK), pos.piece_count(BLACK, QUEEN) } };
- add<ScalingFunction<KNPK> >("KNPK");
- add<ScalingFunction<KRPKR> >("KRPKR");
- add<ScalingFunction<KBPKB> >("KBPKB");
- add<ScalingFunction<KBPPKB> >("KBPPKB");
- add<ScalingFunction<KBPKN> >("KBPKN");
- add<ScalingFunction<KRPPKRP> >("KRPPKRP");
- add<ScalingFunction<KRPPKRP> >("KRPPKRP");
+ mi->value = int16_t((imbalance<WHITE>(pieceCount) - imbalance<BLACK>(pieceCount)) / 16);
+ return mi;
}
-EndgameFunctions::~EndgameFunctions() {
- for (map<Key, EF*>::iterator it = maps.first.begin(); it != maps.first.end(); ++it)
- delete (*it).second;
+/// MaterialInfoTable::imbalance() calculates imbalance comparing piece count of each
+/// piece type for both colors.
- for (map<Key, SF*>::iterator it = maps.second.begin(); it != maps.second.end(); ++it)
- delete (*it).second;
-}
+template<Color Us>
+int MaterialInfoTable::imbalance(const int pieceCount[][8]) {
-Key EndgameFunctions::buildKey(const string& keyCode) {
+ const Color Them = (Us == WHITE ? BLACK : WHITE);
- assert(keyCode.length() > 0 && keyCode[0] == 'K');
- assert(keyCode.length() < 8);
+ int pt1, pt2, pc, v;
+ int value = 0;
- stringstream s;
- bool upcase = false;
+ // Redundancy of major pieces, formula based on Kaufman's paper
+ // "The Evaluation of Material Imbalances in Chess"
+ if (pieceCount[Us][ROOK] > 0)
+ value -= RedundantRookPenalty * (pieceCount[Us][ROOK] - 1)
+ + RedundantQueenPenalty * pieceCount[Us][QUEEN];
- // Build up a fen string with the given pieces, note that
- // the fen string could be of an illegal position.
- for (size_t i = 0; i < keyCode.length(); i++)
- {
- if (keyCode[i] == 'K')
- upcase = !upcase;
+ // Second-degree polynomial material imbalance by Tord Romstad
+ for (pt1 = PIECE_TYPE_NONE; pt1 <= QUEEN; pt1++)
+ {
+ pc = pieceCount[Us][pt1];
+ if (!pc)
+ continue;
- s << char(upcase? toupper(keyCode[i]) : tolower(keyCode[i]));
- }
- s << 8 - keyCode.length() << "/8/8/8/8/8/8/8 w -";
- return Position(s.str()).get_material_key();
-}
+ v = LinearCoefficients[pt1];
-const string EndgameFunctions::swapColors(const string& keyCode) {
+ for (pt2 = PIECE_TYPE_NONE; pt2 <= pt1; pt2++)
+ v += QuadraticCoefficientsSameColor[pt1][pt2] * pieceCount[Us][pt2]
+ + QuadraticCoefficientsOppositeColor[pt1][pt2] * pieceCount[Them][pt2];
- // Build corresponding key for the opposite color: "KBPKN" -> "KNKBP"
- size_t idx = keyCode.find("K", 1);
- return keyCode.substr(idx) + keyCode.substr(0, idx);
+ value += pc * v;
+ }
+ return value;
}
-template<class T>
-void EndgameFunctions::add(const string& keyCode) {
- typedef typename T::Base F;
+/// MaterialInfoTable::game_phase() calculates the phase given the current
+/// position. Because the phase is strictly a function of the material, it
+/// is stored in MaterialInfo.
- get<F>().insert(pair<Key, F*>(buildKey(keyCode), new T(WHITE)));
- get<F>().insert(pair<Key, F*>(buildKey(swapColors(keyCode)), new T(BLACK)));
-}
+Phase MaterialInfoTable::game_phase(const Position& pos) {
-template<class T>
-T* EndgameFunctions::get(Key key) const {
+ Value npm = pos.non_pawn_material(WHITE) + pos.non_pawn_material(BLACK);
- typename map<Key, T*>::const_iterator it(get<T>().find(key));
- return (it != get<T>().end() ? it->second : NULL);
+ return npm >= MidgameLimit ? PHASE_MIDGAME
+ : npm <= EndgameLimit ? PHASE_ENDGAME
+ : Phase(((npm - EndgameLimit) * 128) / (MidgameLimit - EndgameLimit));
}