The correct answer is that you should switch; you have a 2/3 chance of winning if you switch, and only a 1/3 chance of winning if you don't.
There is a 1/3 chance that your initial choice is the box with the money inside, so in this case, you 100% lose if you switch. However, you have a 2/3 chance of picking an empty box on your first choice, in which case the host would open the other empty box, and you would win if you switch.
