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?

(In reply to similarities to problem number... by Cory Taylor)

But it's the fact that Kevin's Ace that was chosen at random, while Nick's was constrained by the pre-selection of Ace, that makes Kevin's probability higher of having another Ace.

The psychological factor is more akin to pid#7 than pid#5. Nick is in the position of having been asked "Is at least one an Ace?", and therefore has a lower probability than if, out of the blue, he had announced he had at least one Ace. (This is considering all cards equally deserving of mention; but then again, aces are special. But presumably Nick's announcement of an Ace was prompted by Kevin's cue, not by the prior special value of an Ace.)

 

Posted by Charlie on 2005-03-04 16:22:16