Playing five-card stud poker with two friends one night, one of them, Kevin, accidentaly drops one of his cards on the table, the ace of hearts. My other friend, Nick, laughs and says, "I also have at least one ace in my hand." I have no reason not to believe him. Now, I do not have any aces in my hand, but I do have a pair of kings. Which of my friends is more likely to have at least a pair of aces (that is to say, at least one more ace) in his hand?

Charlie, this is a first. And I've been around a long time.

I disagree with your analysis, though I immediately see why. My interpretation of the problem gives both players the identical probability of pairing the Ace. The difference in reasoning is basically the same as the trick behind pid#5. Had the first player dropped, say, a five instaed of an ace, the second player simply would have remained silent, thus producing no perplexus problem (or less likely, claimed to hold a five, but I digress), not then claimed to have at least an ace. It is the assumptions we build into the motivation of announcement that decide the answer (and since we dont know the two friends' natures, we cannot conclusively know the motivation...).

The real answer though, has not been hit yet. If you have no reason not to believe your friend's claims of (presumedly) hidden cards, you've never played poker before. The friend who showed the Ace needs one more in 4 cards, the claiming friend needs two aces in five cards - much less likely.

Posted by Cory Taylor on 2005-03-02 19:30:33