We were discussing this over lunch, and the best way we found was just to walk through it. You have 3 doors, A, B and C and the prize is behind C.

If you choose A, he reveals B, and the correct choice is to switch to C.
If you choose B, he reveals A, and the correct choice is to switch to C.
If you choose C, he reveals A or B, and the correct choice is not to switch from C.

So in two out of three original choices, it is better to switch.