Refine probcut

Allow probcut for depth 3 and disable deeper verification search when it would simply repeat the qsearch.

Passed STC
LLR: 2.93 (-2.94,2.94) <0.00,2.00>
Total: 283232 W: 74450 L: 73760 D: 135022
Ptnml(0-2): 1052, 33780, 71349, 34296, 1139
https://tests.stockfishchess.org/tests/view/67843b58460e2910c51ddcc6

Passed LTC
LLR: 2.94 (-2.94,2.94) <0.50,2.50>
Total: 339654 W: 86845 L: 85893 D: 166916
Ptnml(0-2): 298, 37734, 92802, 38704, 289
https://tests.stockfishchess.org/tests/view/678aa722c00c743bc9e9face

closes https://github.com/official-stockfish/Stockfish/pull/5797

bench 1288648

src/search.cpp

@@ -860,7 +860,7 @@ Value Search::Worker::search(
     // If we have a good enough capture (or queen promotion) and a reduced search
     // returns a value much above beta, we can (almost) safely prune the previous move.
     probCutBeta = beta + 174 - 56 * improving;
-    if (depth > 3
+    if (depth >= 3
         && !is_decisive(beta)
         // If value from transposition table is lower than probCutBeta, don't attempt
         // probCut there and in further interactions with transposition table cutoff
@@ -871,6 +871,7 @@ Value Search::Worker::search(
         assert(probCutBeta < VALUE_INFINITE && probCutBeta > beta);
 
         MovePicker mp(pos, ttData.move, probCutBeta - ss->staticEval, &thisThread->captureHistory);
+        Depth      probCutDepth = std::max(depth - 4, 0);
 
         while ((move = mp.next_move()) != Move::none())
         {
@@ -899,9 +900,9 @@ Value Search::Worker::search(
             value = -qsearch<NonPV>(pos, ss + 1, -probCutBeta, -probCutBeta + 1);
 
             // If the qsearch held, perform the regular search
-            if (value >= probCutBeta)
-                value =
-                  -search<NonPV>(pos, ss + 1, -probCutBeta, -probCutBeta + 1, depth - 4, !cutNode);
+            if (value >= probCutBeta && probCutDepth > 0)
+                value = -search<NonPV>(pos, ss + 1, -probCutBeta, -probCutBeta + 1, probCutDepth,
+                                       !cutNode);
 
             pos.undo_move(move);
 
@@ -909,7 +910,7 @@ Value Search::Worker::search(
             {
                 // Save ProbCut data into transposition table
                 ttWriter.write(posKey, value_to_tt(value, ss->ply), ss->ttPv, BOUND_LOWER,
-                               depth - 3, move, unadjustedStaticEval, tt.generation());
+                               probCutDepth + 1, move, unadjustedStaticEval, tt.generation());
 
                 if (!is_decisive(value))
                     return value - (probCutBeta - beta);