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Base WDL model on material count and normalize evals dynamically

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This PR proposes to change the parameter dependence of Stockfish's
internal WDL model from full move counter to material count. In addition
it ensures that an evaluation of 100 centipawns always corresponds to a
50% win probability at fishtest LTC, whereas for master this holds only
at move number 32. See also
https://github.com/official-stockfish/Stockfish/pull/4920 and the
discussion therein.

The new model was fitted based on about 340M positions extracted from
5.6M fishtest LTC games from the last three weeks, involving SF versions
from e67cc979fd (SF 16.1) to current
master.

The involved commands are for
[WDL_model](https://github.com/official-stockfish/WDL_model) are:
```
./updateWDL.sh --firstrev e67cc979fd
python scoreWDL.py updateWDL.json --plot save --pgnName update_material.png --momType "material" --momTarget 58 --materialMin 10 --modelFitting optimizeProbability
```

The anchor `58` for the material count value was chosen to be as close
as possible to the observed average material count of fishtest LTC games
at move 32 (`43`), while not changing the value of
`NormalizeToPawnValue` compared to the move-based WDL model by more than
1.

The patch only affects the displayed cp and wdl values.

closes https://github.com/official-stockfish/Stockfish/pull/5121

No functional change
This commit is contained in:
Robert Nurnberg
2024-03-17 15:39:01 +01:00
committed by Disservin
parent 117e08c264
commit 9b92ada935
5 changed files with 76 additions and 58 deletions
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99
src/uci.cpp
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@@ -28,6 +28,7 @@
#include <memory>
#include <optional>
#include <sstream>
#include <utility>
#include <vector>
#include "benchmark.h"
@@ -44,9 +45,8 @@
namespace Stockfish {
constexpr auto StartFEN = "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1";
constexpr int NormalizeToPawnValue = 356;
constexpr int MaxHashMB = Is64Bit ? 33554432 : 2048;
constexpr auto StartFEN = "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1";
constexpr int MaxHashMB = Is64Bit ? 33554432 : 2048;
namespace NN = Eval::NNUE;
@@ -338,15 +338,43 @@ void UCI::position(Position& pos, std::istringstream& is, StateListPtr& states)
}
}
int UCI::to_cp(Value v) { return 100 * v / NormalizeToPawnValue; }
namespace {
std::pair<double, double> win_rate_params(const Position& pos) {
std::string UCI::value(Value v) {
int material = pos.count<PAWN>() + 3 * pos.count<KNIGHT>() + 3 * pos.count<BISHOP>()
+ 5 * pos.count<ROOK>() + 9 * pos.count<QUEEN>();
// The fitted model only uses data for material counts in [10, 78], and is anchored at count 58.
double m = std::clamp(material, 10, 78) / 58.0;
// Return a = p_a(material) and b = p_b(material), see github.com/official-stockfish/WDL_model
constexpr double as[] = {-185.71965483, 504.85014385, -438.58295743, 474.04604627};
constexpr double bs[] = {89.23542728, -137.02141296, 73.28669021, 47.53376190};
double a = (((as[0] * m + as[1]) * m + as[2]) * m) + as[3];
double b = (((bs[0] * m + bs[1]) * m + bs[2]) * m) + bs[3];
return {a, b};
}
// The win rate model is 1 / (1 + exp((a - eval) / b)), where a = p_a(material) and b = p_b(material).
// It fits the LTC fishtest statistics rather accurately.
int win_rate_model(Value v, const Position& pos) {
auto [a, b] = win_rate_params(pos);
// Return the win rate in per mille units, rounded to the nearest integer.
return int(0.5 + 1000 / (1 + std::exp((a - double(v)) / b)));
}
}
std::string UCI::to_score(Value v, const Position& pos) {
assert(-VALUE_INFINITE < v && v < VALUE_INFINITE);
std::stringstream ss;
if (std::abs(v) < VALUE_TB_WIN_IN_MAX_PLY)
ss << "cp " << to_cp(v);
ss << "cp " << to_cp(v, pos);
else if (std::abs(v) <= VALUE_TB)
{
const int ply = VALUE_TB - std::abs(v); // recompute ss->ply
@@ -358,6 +386,30 @@ std::string UCI::value(Value v) {
return ss.str();
}
// Turns a Value to an integer centipawn number,
// without treatment of mate and similar special scores.
int UCI::to_cp(Value v, const Position& pos) {
// In general, the score can be defined via the the WDL as
// (log(1/L - 1) - log(1/W - 1)) / ((log(1/L - 1) + log(1/W - 1))
// Based on our win_rate_model, this simply yields v / a.
auto [a, b] = win_rate_params(pos);
return std::round(100 * int(v) / a);
}
std::string UCI::wdl(Value v, const Position& pos) {
std::stringstream ss;
int wdl_w = win_rate_model(v, pos);
int wdl_l = win_rate_model(-v, pos);
int wdl_d = 1000 - wdl_w - wdl_l;
ss << " wdl " << wdl_w << " " << wdl_d << " " << wdl_l;
return ss.str();
}
std::string UCI::square(Square s) {
return std::string{char('a' + file_of(s)), char('1' + rank_of(s))};
}
@@ -383,41 +435,6 @@ std::string UCI::move(Move m, bool chess960) {
return move;
}
namespace {
// The win rate model returns the probability of winning (in per mille units) given an
// eval and a game ply. It fits the LTC fishtest statistics rather accurately.
int win_rate_model(Value v, int ply) {
// The fitted model only uses data for moves in [8, 120], and is anchored at move 32.
double m = std::clamp(ply / 2 + 1, 8, 120) / 32.0;
// The coefficients of a third-order polynomial fit is based on the fishtest data
// for two parameters that need to transform eval to the argument of a logistic
// function.
constexpr double as[] = {-1.06249702, 7.42016937, 0.89425629, 348.60356174};
constexpr double bs[] = {-5.33122190, 39.57831533, -90.84473771, 123.40620748};
// Enforce that NormalizeToPawnValue corresponds to a 50% win rate at move 32.
static_assert(NormalizeToPawnValue == int(0.5 + as[0] + as[1] + as[2] + as[3]));
double a = (((as[0] * m + as[1]) * m + as[2]) * m) + as[3];
double b = (((bs[0] * m + bs[1]) * m + bs[2]) * m) + bs[3];
// Return the win rate in per mille units, rounded to the nearest integer.
return int(0.5 + 1000 / (1 + std::exp((a - double(v)) / b)));
}
}
std::string UCI::wdl(Value v, int ply) {
std::stringstream ss;
int wdl_w = win_rate_model(v, ply);
int wdl_l = win_rate_model(-v, ply);
int wdl_d = 1000 - wdl_w - wdl_l;
ss << " wdl " << wdl_w << " " << wdl_d << " " << wdl_l;
return ss.str();
}
Move UCI::to_move(const Position& pos, std::string& str) {
if (str.length() == 5)