wrong thread maybe?
Anyway isn't that the famous Monty Hall problem? I remember I heard of the exact problem, the only difference being that there are three doors and behind one of them is a car and behind two of them is a sheep. If it is then I think it goes like this:
If you choose box 1 and behind it is the keys, then the host will open either box 2 or 3 (they both have the coal so it doesn't matter which one he opens) --> then you should stay.
If you choose box 1 and behind it is one of the coal pieces, then the host will open the only other box with the coal --> then you should switch.
If you choose box 1 and behind it is the other of the coal pieces, then the host will - similarly to the previous situtaion - open the other one with the coal hence you should switch.
So the answer to this probability problem is that there is a 2/3 chance for you to win the key if you switch after your first choice, and a 1/3 chance for you to win the key if you stay on your first choice