I came up with a little variation on the Monty Hall problem.

Let there be n doors. One is the "good" door, the others are "bad" doors. You pick one and one of the doors opens which was bad. Then you randomly select one of the remaining doors. Then one of the bad doors is open again. Now you select one of the remaining doors. If you continue this process until you pick between two remaining doors what is the probability that you win?

And we can even make this problem more challenging by creating different strategies to the player. Such as he picks and stays until the end.