You double your chances of winning the $100 by choosing to swap the box you originally picked for the box remaining after an empty box has been removed. My reasoning is:
If your policy is not to swap boxes, then your probability of winning is 1 in 3, since you are choosing randomly from three boxes and only one box has the $100.
If, on the other hand, your policy is to swap boxes, then you will end up winning whenever your original pick is an empty box and the probability of that happening is 2 in 3.
