The Monty Hall problem is a well known brain teaser. Here is a variant.
You're on a game show, and you're given the choice of three boxes. Two boxes each contain $1000; the third contains $4000.
You pick one box and the host picks another. The host removes this box, which contains $1000, and adds $1000 to your box. He then offers you the choice to switch to the remaining box.
Do you switch, or stick with your original box?