Wow, I'll have to come back here when I have more time and study the new responses to the cups problem, but let me just say this for now:

Mary, you're not suppsed to think while you're at work? What do you do exactly? :)

Andres, you were right in the beginning that the house does know where the prize is, and will always uncover an empty cup.

And I've thought about the red/white problem, which I'll copy here since it's way up there:

"This problem seems to be related to one which was first aired in Scientific American in the 60's, and which stirred a fair amount of debate. There are three cards, one is red on both sides, one is white on both sides, and one is red on one side and white on the other. The dealer places them in a bag, shakes them then slides out one card onto the table so that only one face is visible. The face is red. What is the probability that the other face is red? "

Here's my answer: the probability is 2/3 that the side you can't see is red. A little counterintuitive, but simpler (I hope!) to explain than the cups problem.

I think the key is to look not at the number of cards but at the number of sides. There are three red sides. Of those three, two have red on their opposites, and one has white on its opposite.

Are you still around, Murray? Is this what the Scientific American said?

Marion