Optimal strategy for "continuous" Price Is Right

   n t_opt       p_n(t_opt)
=============================
   0 0.000000000 1.000000000
   1 0.570556528 0.424985743
   2 0.687915542 0.285915671
   3 0.748670992 0.217605794
   4 0.787111373 0.176352811
   5 0.814059234 0.148554963
   6 0.834190512 0.128482558
   7 0.849900286 0.113276325
   8 0.862557620 0.101341865
   9 0.873008133 0.091716843
  10 0.881805286 0.083784726