From 93ed4b53c4f602c4cc41dbdb67961a2a4712c60b Mon Sep 17 00:00:00 2001
From: tony <35334345+TonyCongqianWang@users.noreply.github.com>
Date: Fri, 10 Jul 2026 20:17:55 +0200
Subject: [PATCH] Dynamic root score ema2

Improves calculation of root move score averages by dynamically calculating weight based on effort

Passed STC
https://tests.stockfishchess.org/tests/view/6a4ada97f97ff95f78795d5a
```
LLR: 2.93 (-2.94,2.94) <0.00,2.00>
Total: 157248 W: 41003 L: 40515 D: 75730
Ptnml(0-2): 419, 18320, 40644, 18836, 405
```

Passed LTC
```
LLR: 3.03 (-2.94,2.94) <0.50,2.50>
Total: 197460 W: 51626 L: 50982 D: 94852
Ptnml(0-2): 85, 20849, 56237, 21455, 104
```

closes https://github.com/official-stockfish/Stockfish/pull/6960

Bench: 2388656
---
 src/search.cpp | 31 ++++++++++++++++++++++++++-----
 1 file changed, 26 insertions(+), 5 deletions(-)

diff --git a/src/search.cpp b/src/search.cpp
index bc922119c..28367605e 100644
--- a/src/search.cpp
+++ b/src/search.cpp
@@ -24,6 +24,7 @@
 #include <cassert>
 #include <chrono>
 #include <cmath>
+#include <cstdint>
 #include <cstdlib>
 #include <initializer_list>
 #include <iostream>
@@ -1408,12 +1409,32 @@ moves_loop:  // When in check, search starts here
 
             rm.effort += nodes - nodeCount;
 
-            rm.averageScore =
-              rm.averageScore != -VALUE_INFINITE ? (value + rm.averageScore) / 2 : value;
+            u64 N      = nodes - nodeCount;
+            u64 E_prev = std::max(u64(1), rm.effort - N);
 
-            rm.meanSquaredScore = rm.meanSquaredScore != -VALUE_INFINITE * VALUE_INFINITE
-                                  ? (value * std::abs(value) + rm.meanSquaredScore) / 2
-                                  : value * std::abs(value);
+            // Dynamic EMA parameters for root move
+            constexpr u64 Scale          = 32;
+            constexpr u64 ChiNumerator   = 3;
+            constexpr u64 ChiDenominator = 2;   // Chi = 3/2 = 1.5
+            constexpr u64 MinWeight      = 12;  // 37.5% minimum weight
+            constexpr u64 MaxWeight      = 24;  // 75% maximum weight
+
+            u64 w     = std::clamp((Scale * N * ChiDenominator)
+                                     / (N * ChiDenominator + ChiNumerator * E_prev),
+                                   MinWeight, MaxWeight);
+            u64 w_mss = std::min(w, u64(16));
+            i64 v2    = i64(value) * std::abs(value);
+
+            if (rm.averageScore == -VALUE_INFINITE)
+                rm.averageScore = value;
+            else
+                rm.averageScore = Value((value * w + rm.averageScore * (Scale - w)) / Scale);
+
+            if (rm.meanSquaredScore == -VALUE_INFINITE * VALUE_INFINITE)
+                rm.meanSquaredScore = value * std::abs(value);
+            else
+                rm.meanSquaredScore =
+                  Value((v2 * w_mss + int64_t(rm.meanSquaredScore) * (Scale - w_mss)) / Scale);
 
             // PV move or new best move?
             if (moveCount == 1 || value > alpha)