Tweak time management

Using a SPSA tuning session to optimize the time management
parameters.

With SPSA tuning it is not always possible to say where improvements
came from. Maybe some variables changed randomly or because result
was not sensitive enough to them. So my explanation of changes will
not be necessarily correct, but here it is.

• When decrease of thinking time was added by Joost a few months ago
if best move has not changed for several plies, one more competing
indicator  was introduced for the same purpose along with increase
in score and absence of fail low at root. It seems that tuning put
relatively more importance on that new indicator what allowed to save
time.
• Some of this saved time is distributed proportionally between all
moves and some more time were given to moves when score dropped a lot
or best move changed.
• It looks also that SPSA redistributed more time from the beginning to
later stages of game via other changes in variables - maybe because
contempt made game to last longer or for whatever reason.

All of this is just small tweaks here and there (a few percentages changes).

STC (10+0.1):
LLR: 2.96 (-2.94,2.94) [0.00,4.00]
Total: 18970 W: 4268 L: 4029 D: 10673
http://tests.stockfishchess.org/tests/view/5a9291a40ebc590297cc8881

LTC (60+0.6):
LLR: 2.95 (-2.94,2.94) [0.00,4.00]
Total: 72027 W: 12263 L: 11878 D: 47886
http://tests.stockfishchess.org/tests/view/5a92d7510ebc590297cc88ef

Additional non-regression tests at other time controls

Sudden death 60s:
LLR: 2.95 (-2.94,2.94) [-4.00,0.00]
Total: 14444 W: 2715 L: 2608 D: 9121
http://tests.stockfishchess.org/tests/view/5a9445850ebc590297cc8a65

40 moves repeating at LTC:
LLR: 2.95 (-2.94,2.94) [-4.00,0.00]
Total: 10309 W: 1880 L: 1759 D: 6670
http://tests.stockfishchess.org/tests/view/5a9566ec0ebc590297cc8be1

This is a functional patch only for time management, but the bench
does not reflect this because it uses fixed depth search, so the number
of nodes does not change during bench.

No functional change.

src/search.cpp

@@ -325,7 +325,7 @@ void Thread::search() {
 
       // Age out PV variability metric
       if (mainThread)
-          mainThread->bestMoveChanges *= 0.505, mainThread->failedLow = false;
+          mainThread->bestMoveChanges *= 0.517, mainThread->failedLow = false;
 
       // Save the last iteration's scores before first PV line is searched and
       // all the move scores except the (new) PV are set to -VALUE_INFINITE.
@@ -444,21 +444,21 @@ void Thread::search() {
               const int F[] = { mainThread->failedLow,
                                 bestValue - mainThread->previousScore };
 
-              int improvingFactor = std::max(229, std::min(715, 357 + 119 * F[0] - 6 * F[1]));
+              int improvingFactor = std::max(246, std::min(832, 306 + 119 * F[0] - 6 * F[1]));
 
               // If the bestMove is stable over several iterations, reduce time accordingly
               timeReduction = 1.0;
               for (int i : {3, 4, 5})
                   if (lastBestMoveDepth * i < completedDepth)
-                     timeReduction *= 1.3;
+                     timeReduction *= 1.25;
 
               // Use part of the gained time from a previous stable move for the current move
               double unstablePvFactor = 1.0 + mainThread->bestMoveChanges;
-              unstablePvFactor *= std::pow(mainThread->previousTimeReduction, 0.51) / timeReduction;
+              unstablePvFactor *= std::pow(mainThread->previousTimeReduction, 0.528) / timeReduction;
 
               // Stop the search if we have only one legal move, or if available time elapsed
               if (   rootMoves.size() == 1
-                  || Time.elapsed() > Time.optimum() * unstablePvFactor * improvingFactor / 605)
+                  || Time.elapsed() > Time.optimum() * unstablePvFactor * improvingFactor / 581)
               {
                   // If we are allowed to ponder do not stop the search now but
                   // keep pondering until the GUI sends "ponderhit" or "stop".

src/timeman.cpp

@@ -33,8 +33,8 @@ namespace {
   enum TimeType { OptimumTime, MaxTime };
 
   const int MoveHorizon   = 50;   // Plan time management at most this many moves ahead
-  const double MaxRatio   = 7.09; // When in trouble, we can step over reserved time with this ratio
-  const double StealRatio = 0.35; // However we must not steal time from remaining moves over this ratio
+  const double MaxRatio   = 7.3; // When in trouble, we can step over reserved time with this ratio
+  const double StealRatio = 0.34; // However we must not steal time from remaining moves over this ratio
 
 
   // move_importance() is a skew-logistic function based on naive statistical
@@ -44,9 +44,9 @@ namespace {
 
   double move_importance(int ply) {
 
-    const double XScale = 7.64;
-    const double XShift = 58.4;
-    const double Skew   = 0.183;
+    const double XScale = 6.85;
+    const double XShift = 64.5;
+    const double Skew   = 0.171;
 
     return pow((1 + exp((ply - XShift) / XScale)), -Skew) + DBL_MIN; // Ensure non-zero
   }

src/ucioption.cpp

@@ -68,7 +68,7 @@ void init(OptionsMap& o) {
   o["Skill Level"]           << Option(20, 0, 20);
   o["Move Overhead"]         << Option(30, 0, 5000);
   o["Minimum Thinking Time"] << Option(20, 0, 5000);
-  o["Slow Mover"]            << Option(89, 10, 1000);
+  o["Slow Mover"]            << Option(84, 10, 1000);
   o["nodestime"]             << Option(0, 0, 10000);
   o["UCI_Chess960"]          << Option(false);
   o["SyzygyPath"]            << Option("<empty>", on_tb_path);