You have answered all the questions on a quiz show and now the MC shows you 3 doors. He says, "Behind one of those doors, is 10 million dollars. Choose the correct one and it's yours. Please write down your selection and give it to me."
You hand him your selection and he says, "Because you seem like such a nice person, I'm going to open one of the doors and give you a chance to change your mind."
He opens a door and reveals the empty space behind it. There are two unopened doors remaining, one of which is your original choice. The 10 million dollars is behind one of the two doors. He then asks if you want to change your mind for a hundred dollars.
What do you say? Do you pay the hundred dollars and choose the other door, or do you stick with your original door?
Here is a hint that will test your understanding of empiricism. You can solve this problem empirically.