[Pokerlogist]

Here's another way to look at this. I have never seen it explained this way:

By chance alone, you will initally choose an empty door 2 of every 3 times. At every one of those "empty door" times, Monty is being forced to choose the only remaining empty door. He must indicate the prize door by default with 100% certainity every one of those times. He has got to indicate the correct prize door 2/3 of the time. So by always switching you will have to be right 2/3 of the time.