Slowly, the clouds part, and a ray of light penetrates the dank, dark place that is my brain. Thinking about what Jim has said, I see that the the probabilites are affected by the "house-knows-something-you-don't" factor. I had a pretty slim chance of being right when I picked at random from 1,000 cups. The house selected the other cup to not turn over, and the house KNOWS which cup hides the prize. Since my chances of being right in the first place were not so good, I switch to the house's pick.

I don't know if this words as well with only three cups to start with - my chances of being right initially weren't so bad, but at least I've got the idea now.