+ // The win rate model returns the probability (per mille) of winning given an eval
+ // and a game-ply. The model fits rather accurately the LTC fishtest statistics.
+ int win_rate_model(Value v, int ply) {
+
+ // The model captures only up to 240 plies, so limit input (and rescale)
+ double m = std::min(240, ply) / 64.0;
+
+ // Coefficients of a 3rd order polynomial fit based on fishtest data
+ // for two parameters needed to transform eval to the argument of a
+ // logistic function.
+ double as[] = {-8.24404295, 64.23892342, -95.73056462, 153.86478679};
+ double bs[] = {-3.37154371, 28.44489198, -56.67657741, 72.05858751};
+ 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];
+
+ // Transform eval to centipawns with limited range
+ double x = std::clamp(double(100 * v) / PawnValueEg, -1000.0, 1000.0);
+
+ // Return win rate in per mille (rounded to nearest)
+ return int(0.5 + 1000 / (1 + std::exp((a - x) / b)));
+ }
+