First, for those who don't believe (yet), test it yourself. It won't take too many trials to convince you that switching is the correct strategy.

Jeri, however, has pointed to the correct detail. It matters if the one who opens the first cup, knows (and cares in opening) whether this cup contains the prize or not. This detail was not completely clear in Marion's first post. If just any cup is opened by chance and either you have lost at once (for this cup contains the prize) or you have the choice between the two remaining cups (in the other two third of the cases) then it does not matter at all whether you change your first choice or not.

Like in a variant of that problem, when a father of two comes up to you and says: 'I've two children, one of them is a boy' and you are asked what is the probability that the other child is a boy too. Depending upon conditions I have deliberately not mentioned the correct response is either 1/2 or 1/3.

Yes, there are experiments done on the Monty Hall dilemma. I've done one, for instance. In the classical situation Marion has described, only about 8 % of our subjects switched (made the experiment cheaper, for there was a real prize under there to take home). If we had 30 cups, however (28 with no prize opened after the first choice), about 2/3 of our subjects switched which shows that they were somehow sensible to the odds (in this case about 97 % probability for winning, if you switch).

The best recent article on these problems is by R. S. Nickerson in the Psychological Bulletin (circa 1997/98). Sorry, I don't find the exact reference right now.

If you've understood the problem so far, you're ready for the Russian Roulette variant (only one miss, all other options are prizes): 3 cups with two prizes and one miss. After your first choice an other cup that is known to contain a prize is opened, leaving you with two cups, one containing a prize. Should you switch??? Or does it not matter?

Of course it matters, you should not switch under these conditions, for you have a 2/3 probability of winning if you stay.

It is an open question for science (yes, we do have open questions, lots of), why in this situation when switching is bad many more subjects switch than in the standard version in which switching is good.

Well, people do have many difficulties with conditioned probabilities (even math profs and PhD's are on the record for defending a wrong solution for Monty Hall's dilemma with very strong words) and if you give me a new problem of that kind and ask me for my spontaneous solution (without using paper, pencil and Bayes' theorem) I'd not be surprised to be wrong.

Wolfgang