base WDL model on material count and normalize evals dynamically

src/evaluate.cpp

@@ -92,11 +92,11 @@ std::string Eval::trace(Position& pos, const Eval::NNUE::Networks& networks) {
 
     Value v = networks.big.evaluate(pos, false);
     v       = pos.side_to_move() == WHITE ? v : -v;
-    ss << "NNUE evaluation        " << 0.01 * UCI::to_cp(v) << " (white side)\n";
+    ss << "NNUE evaluation        " << 0.01 * UCI::to_cp(v, pos) << " (white side)\n";
 
     v = evaluate(networks, pos, VALUE_ZERO);
     v = pos.side_to_move() == WHITE ? v : -v;
-    ss << "Final evaluation       " << 0.01 * UCI::to_cp(v) << " (white side)";
+    ss << "Final evaluation       " << 0.01 * UCI::to_cp(v, pos) << " (white side)";
     ss << " [with scaled NNUE, ...]";
     ss << "\n";
 

src/nnue/nnue_misc.cpp

@@ -54,11 +54,11 @@ void hint_common_parent_position(const Position& pos, const Networks& networks)
 
 // Converts a Value into (centi)pawns and writes it in a buffer.
 // The buffer must have capacity for at least 5 chars.
-static void format_cp_compact(Value v, char* buffer) {
+static void format_cp_compact(Value v, char* buffer, const Position& pos) {
 
     buffer[0] = (v < 0 ? '-' : v > 0 ? '+' : ' ');
 
-    int cp = std::abs(UCI::to_cp(v));
+    int cp = std::abs(UCI::to_cp(v, pos));
     if (cp >= 10000)
     {
         buffer[1] = '0' + cp / 10000;
@@ -90,9 +90,9 @@ static void format_cp_compact(Value v, char* buffer) {
 
 
 // Converts a Value into pawns, always keeping two decimals
-static void format_cp_aligned_dot(Value v, std::stringstream& stream) {
+static void format_cp_aligned_dot(Value v, std::stringstream& stream, const Position& pos) {
 
-    const double pawns = std::abs(0.01 * UCI::to_cp(v));
+    const double pawns = std::abs(0.01 * UCI::to_cp(v, pos));
 
     stream << (v < 0   ? '-'
                : v > 0 ? '+'
@@ -113,7 +113,7 @@ std::string trace(Position& pos, const Eval::NNUE::Networks& networks) {
         board[row][8 * 8 + 1] = '\0';
 
     // A lambda to output one box of the board
-    auto writeSquare = [&board](File file, Rank rank, Piece pc, Value value) {
+    auto writeSquare = [&board, &pos](File file, Rank rank, Piece pc, Value value) {
         const int x = int(file) * 8;
         const int y = (7 - int(rank)) * 3;
         for (int i = 1; i < 8; ++i)
@@ -124,7 +124,7 @@ std::string trace(Position& pos, const Eval::NNUE::Networks& networks) {
         if (pc != NO_PIECE)
             board[y + 1][x + 4] = PieceToChar[pc];
         if (value != VALUE_NONE)
-            format_cp_compact(value, &board[y + 2][x + 2]);
+            format_cp_compact(value, &board[y + 2][x + 2], pos);
     };
 
     // We estimate the value of each piece by doing a differential evaluation from
@@ -179,13 +179,13 @@ std::string trace(Position& pos, const Eval::NNUE::Networks& networks) {
     {
         ss << "|  " << bucket << "        ";
         ss << " |  ";
-        format_cp_aligned_dot(t.psqt[bucket], ss);
+        format_cp_aligned_dot(t.psqt[bucket], ss, pos);
         ss << "  "
            << " |  ";
-        format_cp_aligned_dot(t.positional[bucket], ss);
+        format_cp_aligned_dot(t.positional[bucket], ss, pos);
         ss << "  "
            << " |  ";
-        format_cp_aligned_dot(t.psqt[bucket] + t.positional[bucket], ss);
+        format_cp_aligned_dot(t.psqt[bucket] + t.positional[bucket], ss, pos);
         ss << "  "
            << " |";
         if (bucket == t.correctBucket)

src/search.cpp

@@ -155,7 +155,8 @@ void Search::Worker::start_searching() {
     {
         rootMoves.emplace_back(Move::none());
         sync_cout << "info depth 0 score "
-                  << UCI::value(rootPos.checkers() ? -VALUE_MATE : VALUE_DRAW) << sync_endl;
+                  << UCI::to_score(rootPos.checkers() ? -VALUE_MATE : VALUE_DRAW, rootPos)
+                  << sync_endl;
     }
     else
     {
@@ -1898,10 +1899,10 @@ std::string SearchManager::pv(const Search::Worker&     worker,
 
         ss << "info"
            << " depth " << d << " seldepth " << rootMoves[i].selDepth << " multipv " << i + 1
-           << " score " << UCI::value(v);
+           << " score " << UCI::to_score(v, pos);
 
         if (worker.options["UCI_ShowWDL"])
-            ss << UCI::wdl(v, pos.game_ply());
+            ss << UCI::wdl(v, pos);
 
         if (i == pvIdx && !tb && updated)  // tablebase- and previous-scores are exact
             ss << (rootMoves[i].scoreLowerbound

src/uci.cpp

@@ -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) {
+
+    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 62.
+    double m = std::clamp(material, 10, 78) / 62.0;
+
+    // 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];
 
-std::string UCI::value(Value v) {
+    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)

src/uci.h

@@ -42,11 +42,11 @@ class UCI {
 
     void loop();
 
-    static int         to_cp(Value v);
-    static std::string value(Value v);
+    static int         to_cp(Value v, const Position& pos);
+    static std::string to_score(Value v, const Position& pos);
     static std::string square(Square s);
     static std::string move(Move m, bool chess960);
-    static std::string wdl(Value v, int ply);
+    static std::string wdl(Value v, const Position& pos);
     static Move        to_move(const Position& pos, std::string& str);
 
     static Search::LimitsType parse_limits(const Position& pos, std::istream& is);