diff --git a/src/search.cpp b/src/search.cpp
index f398074065d..89879374c1a 100644
--- a/src/search.cpp
+++ b/src/search.cpp
@@ -678,9 +678,11 @@ Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, boo
 
                 int drawScore = TB::UseRule50 ? 1 : 0;
 
-                // use the range VALUE_MATE_IN_MAX_PLY to VALUE_TB_WIN_IN_MAX_PLY to score
-                value = wdl < -drawScore ? VALUE_MATED_IN_MAX_PLY + ss->ply + 1
-                      : wdl > drawScore  ? VALUE_MATE_IN_MAX_PLY - ss->ply - 1
+                Value tbValue = VALUE_TB - ss->ply;
+
+                // use the range VALUE_TB to VALUE_TB_WIN_IN_MAX_PLY to score
+                value = wdl < -drawScore ? -tbValue
+                      : wdl > drawScore  ? tbValue
                                          : VALUE_DRAW + 2 * wdl * drawScore;
 
                 Bound b = wdl < -drawScore ? BOUND_UPPER
@@ -1631,25 +1633,38 @@ Value value_to_tt(Value v, int ply) {
 // Inverse of value_to_tt(): it adjusts a mate or TB score
 // from the transposition table (which refers to the plies to mate/be mated from
 // current position) to "plies to mate/be mated (TB win/loss) from the root".
-// However, to avoid potentially false mate scores related to the 50 moves rule
-// and the graph history interaction problem, we return an optimal TB score instead.
+// However, to avoid potentially false mate or TB scores related to the 50 moves rule
+// and the graph history interaction, we return highest non-TB score instead.
+
 Value value_from_tt(Value v, int ply, int r50c) {
 
     if (v == VALUE_NONE)
         return VALUE_NONE;
 
-    if (v >= VALUE_TB_WIN_IN_MAX_PLY)  // TB win or better
+    // handle TB win or better
+    if (v >= VALUE_TB_WIN_IN_MAX_PLY)
     {
-        if (v >= VALUE_MATE_IN_MAX_PLY && VALUE_MATE - v > 99 - r50c)
-            return VALUE_MATE_IN_MAX_PLY - 1;  // do not return a potentially false mate score
+        // Downgrade a potentially false mate score
+        if (v >= VALUE_MATE_IN_MAX_PLY && VALUE_MATE - v > 100 - r50c)
+            return VALUE_TB_WIN_IN_MAX_PLY - 1;
+
+        // Downgrade a potentially false TB score.
+        if (VALUE_TB - v > 100 - r50c)
+            return VALUE_TB_WIN_IN_MAX_PLY - 1;
 
         return v - ply;
     }
 
-    if (v <= VALUE_TB_LOSS_IN_MAX_PLY)  // TB loss or worse
+    // handle TB loss or worse
+    if (v <= VALUE_TB_LOSS_IN_MAX_PLY)
     {
-        if (v <= VALUE_MATED_IN_MAX_PLY && VALUE_MATE + v > 99 - r50c)
-            return VALUE_MATED_IN_MAX_PLY + 1;  // do not return a potentially false mate score
+        // Downgrade a potentially false mate score.
+        if (v <= VALUE_MATED_IN_MAX_PLY && VALUE_MATE + v > 100 - r50c)
+            return VALUE_TB_LOSS_IN_MAX_PLY + 1;
+
+        // Downgrade a potentially false TB score.
+        if (VALUE_TB + v > 100 - r50c)
+            return VALUE_TB_LOSS_IN_MAX_PLY + 1;
 
         return v + ply;
     }
@@ -1866,7 +1881,7 @@ string UCI::pv(const Position& pos, Depth depth) {
         if (v == -VALUE_INFINITE)
             v = VALUE_ZERO;
 
-        bool tb = TB::RootInTB && abs(v) < VALUE_MATE_IN_MAX_PLY;
+        bool tb = TB::RootInTB && abs(v) <= VALUE_TB;
         v       = tb ? rootMoves[i].tbScore : v;
 
         if (ss.rdbuf()->in_avail())  // Not at first line
diff --git a/src/types.h b/src/types.h
index 0575f1d453c..3e00d68d19d 100644
--- a/src/types.h
+++ b/src/types.h
@@ -164,14 +164,16 @@ enum Bound {
 enum Value : int {
     VALUE_ZERO     = 0,
     VALUE_DRAW     = 0,
-    VALUE_MATE     = 32000,
-    VALUE_INFINITE = 32001,
     VALUE_NONE     = 32002,
+    VALUE_INFINITE = 32001,
+
+    VALUE_MATE             = 32000,
+    VALUE_MATE_IN_MAX_PLY  = VALUE_MATE - MAX_PLY,
+    VALUE_MATED_IN_MAX_PLY = -VALUE_MATE_IN_MAX_PLY,
 
-    VALUE_TB_WIN_IN_MAX_PLY  = VALUE_MATE - 2 * MAX_PLY,
+    VALUE_TB                 = VALUE_MATE_IN_MAX_PLY - 1,
+    VALUE_TB_WIN_IN_MAX_PLY  = VALUE_TB - MAX_PLY,
     VALUE_TB_LOSS_IN_MAX_PLY = -VALUE_TB_WIN_IN_MAX_PLY,
-    VALUE_MATE_IN_MAX_PLY    = VALUE_MATE - MAX_PLY,
-    VALUE_MATED_IN_MAX_PLY   = -VALUE_MATE_IN_MAX_PLY,
 
     // In the code, we make the assumption that these values
     // are such that non_pawn_material() can be used to uniquely
diff --git a/src/uci.cpp b/src/uci.cpp
index 95f6f349dd3..d0341bd7168 100644
--- a/src/uci.cpp
+++ b/src/uci.cpp
@@ -356,9 +356,9 @@ std::string UCI::value(Value v) {
 
     if (abs(v) < VALUE_TB_WIN_IN_MAX_PLY)
         ss << "cp " << UCI::to_cp(v);
-    else if (abs(v) < VALUE_MATE_IN_MAX_PLY)
+    else if (abs(v) <= VALUE_TB)
     {
-        const int ply = VALUE_MATE_IN_MAX_PLY - 1 - std::abs(v);  // recompute ss->ply
+        const int ply = VALUE_TB - std::abs(v);  // recompute ss->ply
         ss << "cp " << (v > 0 ? 20000 - ply : -20000 + ply);
     }
     else