Increase optimumTime by 10%

STC 10+0.1 :
LLR: 2.94 (-2.94,2.94) <-0.50,2.50>
Total: 47032 W: 12078 L: 11841 D: 23113
Ptnml(0-2): 159, 5098, 12746, 5373, 140
https://tests.stockfishchess.org/tests/view/613f9df1f29dda16fcca8731

LTC 60+0.6 :
LLR: 2.95 (-2.94,2.94) <0.50,3.50>
Total: 66248 W: 16631 L: 16301 D: 33316
Ptnml(0-2): 44, 6560, 19578, 6906, 36
https://tests.stockfishchess.org/tests/view/6140603d7315e7c73204a4c1

Non-regression tests with other time control styles:

Moves/Time 40/10+0 :
LLR: 2.93 (-2.94,2.94) <-2.50,0.50>
Total: 51640 W: 13350 L: 13254 D: 25036
Ptnml(0-2): 183, 5770, 13797, 5908, 162
https://tests.stockfishchess.org/tests/view/6141592b7315e7c73204a599

TCEC Style 10+0.01 :
LLR: 2.94 (-2.94,2.94) <-2.50,0.50>
Total: 20592 W: 5300 L: 5157 D: 10135
Ptnml(0-2): 81, 2240, 5544, 2317, 114
https://tests.stockfishchess.org/tests/view/61425bb27315e7c73204a6a2

Sudden death 15+0 :
LLR: 2.94 (-2.94,2.94) <-2.50,0.50>
Total: 127104 W: 32728 L: 32741 D: 61635
Ptnml(0-2): 735, 13973, 34149, 13960, 735
https://tests.stockfishchess.org/tests/view/614256a77315e7c73204a699

The first 3 tests were run with an initial version of the code, which was then modified to make the amount of extra time dependent on the size of increment. No increment gives no extra time, and the extra time given increases until an increment of 1% or more of remaining time gives 10% extra thinking time.

closes #3702

Bench 6658747

src/timeman.cpp

@@ -68,6 +68,9 @@ void TimeManagement::init(Search::LimitsType& limits, Color us, int ply) {
   TimePoint timeLeft =  std::max(TimePoint(1),
       limits.time[us] + limits.inc[us] * (mtg - 1) - moveOverhead * (2 + mtg));
 
+  // Use extra time with larger increments
+  double optExtra = std::clamp(1.0 + 10.0 * limits.inc[us] / limits.time[us], 1.0, 1.1);
+
   // A user may scale time usage by setting UCI option "Slow Mover"
   // Default is 100 and changing this value will probably lose elo.
   timeLeft = slowMover * timeLeft / 100;
@@ -78,15 +81,16 @@ void TimeManagement::init(Search::LimitsType& limits, Color us, int ply) {
   if (limits.movestogo == 0)
   {
       optScale = std::min(0.0084 + std::pow(ply + 3.0, 0.5) * 0.0042,
-                           0.2 * limits.time[us] / double(timeLeft));
+                           0.2 * limits.time[us] / double(timeLeft))
+                 * optExtra;
       maxScale = std::min(7.0, 4.0 + ply / 12.0);
   }
 
   // x moves in y seconds (+ z increment)
   else
   {
-      optScale = std::min((0.8 + ply / 128.0) / mtg,
-                            0.8 * limits.time[us] / double(timeLeft));
+      optScale = std::min((0.88 + ply / 116.4) / mtg,
+                            0.88 * limits.time[us] / double(timeLeft));
       maxScale = std::min(6.3, 1.5 + 0.11 * mtg);
   }