You have three doors to choose from. One to freedom, two to certain death. You must choose. However, after you have chosen, your tormentor opens one of the remaining doors unto certain death and asks, 'Do you want to keep your initial choice or change?' You now have two choices left, the one you picked, or the other door.
Common intuition says that originally you had a one in three chance of choosing the right door. Then, after the tormentor's intercession, you have a one in two chance - the door you picked, or the other door. In other words, 50/50.
It turns out that this is not the case. You are much better off switching your choice to the other door. That has kept me awake tonight. What is going on?
The first assumption is correct. You have a one in three chance of choosing the correct door when the 'game' begins. However, by making your choice, you force your tormentor into a tricky position.
There is a 1/3 chance that you chose the right door to start with. If that is the case, your tormentor can open either of the other doors and if you choose to switch, to your death you go. That is, there is a 1 in 3 chance that you chose correctly, and changing your choice will send you to the pits of hell.
However, there is a 2/3 chance that you chose the wrong door to start with. If that is the case, your tormentor has given you the path out by eliminating the only remaining path to death. That is, if you switch, the only choice is life.
Therefore, given the choice, you should change doors. You have a 2/3 versus 1/3 chance of survival by doing so.
History is important. The rules of the game are important. By only looking at the choices in front of you now, you can be gamed. By looking at how you got here, you can make a wise choice. (Somewhere in the back of my mind, this seems to relate to Greece at the moment.) Perhaps I can sleep now?
I'm sure when I awake in the morning this will confuse me again. But now, I'm high on Limoncello and it all makes sense. Except the bit as to why it doesn't make sense without thinking and drinking about it to excess.
Such is life. Good night. And Greece - tell em' to fuck off. They are bad playmates. You'll get over it before they do.