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Provide WDL statistics
A number of engines, GUIs and tournaments start to report WDL estimates along or instead of scores. This patch enables reporting of those stats in a more or less standard way (http://www.talkchess.com/forum3/viewtopic.php?t=72140) The model this reporting uses is based on data derived from a few million fishtest LTC games, given a score and a game ply, a win rate is provided that matches rather closely, especially in the intermediate range [0.05, 0.95] that data. Some data is shown at https://github.com/glinscott/fishtest/wiki/UsefulData#win-loss-draw-statistics-of-ltc-games-on-fishtest Making the conversion game ply dependent is important for a good fit, and is in line with experience that a +1 score in the early midgame is more likely a win than in the late endgame. Even when enabled, the printing of the info causes no significant overhead. Passed STC: LLR: 2.94 (-2.94,2.94) {-1.50,0.50} Total: 197112 W: 37226 L: 37347 D: 122539 Ptnml(0-2): 2591, 21025, 51464, 20866, 2610 https://tests.stockfishchess.org/tests/view/5ef79ef4f993893290cc146b closes https://github.com/official-stockfish/Stockfish/pull/2778 No functional change
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@ -66,6 +66,11 @@ Currently, Stockfish has the following UCI options:
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If enabled by UCI_LimitStrength, aim for an engine strength of the given Elo.
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This Elo rating has been calibrated at a time control of 60s+0.6s and anchored to CCRL 40/4.
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* #### UCI_ShowWDL
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If enabled, show approximate WDL statistics as part of the engine output.
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These WDL numbers model expected game outcomes for a given evaluation and
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game ply for engine self-play at fishtest LTC conditions (60+0.6s per game).
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* #### Move Overhead
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Assume a time delay of x ms due to network and GUI overheads. This is useful to
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avoid losses on time in those cases.
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@ -1835,6 +1835,9 @@ string UCI::pv(const Position& pos, Depth depth, Value alpha, Value beta) {
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<< " multipv " << i + 1
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<< " score " << UCI::value(v);
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if (Options["UCI_ShowWDL"])
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ss << UCI::wdl(v, pos.game_ply());
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if (!tb && i == pvIdx)
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ss << (v >= beta ? " lowerbound" : v <= alpha ? " upperbound" : "");
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39
src/uci.cpp
39
src/uci.cpp
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@ -19,6 +19,7 @@
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*/
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#include <cassert>
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#include <cmath>
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#include <iostream>
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#include <sstream>
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#include <string>
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@ -182,6 +183,28 @@ namespace {
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<< "\nNodes/second : " << 1000 * nodes / elapsed << endl;
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}
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// The win rate model returns the probability (per mille) of winning given an eval
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// and a game-ply. The model fits rather accurately the LTC fishtest statistics.
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int win_rate_model(Value v, int ply) {
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// The model captures only up to 240 plies, so limit input (and rescale)
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double m = std::min(240, ply) / 64.0;
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// Coefficients of a 3rd order polynomial fit based on fishtest data
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// for two parameters needed to transform eval to the argument of a
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// logistic function.
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double as[] = {-8.24404295, 64.23892342, -95.73056462, 153.86478679};
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double bs[] = {-3.37154371, 28.44489198, -56.67657741, 72.05858751};
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double a = (((as[0] * m + as[1]) * m + as[2]) * m) + as[3];
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double b = (((bs[0] * m + bs[1]) * m + bs[2]) * m) + bs[3];
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// Transform eval to centipawns with limited range
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double x = Utility::clamp(double(100 * v) / PawnValueEg, -1000.0, 1000.0);
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// Return win rate in per mille (rounded to nearest)
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return int(0.5 + 1000 / (1 + std::exp((a - x) / b)));
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}
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} // namespace
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@ -269,6 +292,22 @@ string UCI::value(Value v) {
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}
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/// UCI::wdl() report WDL statistics given an evaluation and a game ply, based on
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/// data gathered for fishtest LTC games.
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string UCI::wdl(Value v, int ply) {
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stringstream ss;
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int wdl_w = win_rate_model( v, ply);
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int wdl_l = win_rate_model(-v, ply);
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int wdl_d = 1000 - wdl_w - wdl_l;
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ss << " wdl " << wdl_w << " " << wdl_d << " " << wdl_l;
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return ss.str();
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}
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/// UCI::square() converts a Square to a string in algebraic notation (g1, a7, etc.)
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std::string UCI::square(Square s) {
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@ -73,6 +73,7 @@ std::string value(Value v);
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std::string square(Square s);
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std::string move(Move m, bool chess960);
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std::string pv(const Position& pos, Depth depth, Value alpha, Value beta);
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std::string wdl(Value v, int ply);
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Move to_move(const Position& pos, std::string& str);
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} // namespace UCI
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@ -74,6 +74,7 @@ void init(OptionsMap& o) {
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o["UCI_AnalyseMode"] << Option(false);
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o["UCI_LimitStrength"] << Option(false);
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o["UCI_Elo"] << Option(1350, 1350, 2850);
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o["UCI_ShowWDL"] << Option(true);
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o["SyzygyPath"] << Option("<empty>", on_tb_path);
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o["SyzygyProbeDepth"] << Option(1, 1, 100);
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o["Syzygy50MoveRule"] << Option(true);
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