How good are you at finding what's best? Test your intution and brains

Good decision makers often wind up with the best things available. But how do they do they do it? Finding the best thing involves searching, but it also involves knowing when to stop searching. How good a searcher are you? Do you search too much, or just the right amount?

Psychologists and economists have extensively studied problems of "sequential search" and “optimal stopping”. Fancy terms for a basic idea. Consider this simple game

You have been captured by an evil  dictator. He forces you to play a game. He brings you into a room with many brightly colored gift boxes. Each box has a different amount of money in it. You can open any number of boxes in any order. After opening each box, you can decide to open another box or you can stop. If you say “stop” after opening the box with the most money in it (of all the boxes) you get to live and keep the money. However, if you stop at any other time, you lose and the evil dictator will kill you.
If you were in this situation, what would your strategy be? How likely would you be to survive?
There’s much academic interest in this simple game because it is analogous to many real life situations in which once you pass something, there’s no going back. It’s even been compared to finding the love of your life: people date a number of others looking for that special someone, but if they pass somebody up, there’s no guarantee that he or she will still be single in the future.
So that you can test your brains and intuition  for searching and stopping search, I’ve created a little game: