In a game of Texas Hold'em, all 5 community cards are dealt, and the three remaining players simultaneously say, "Well, there's only one hand that can beat me."

How can this situation arise? Assume that the players do not lie.

Here, "one hand" means a unique combination of 2 cards, out of the (52 choose 2) = 1326 possible ones.

For those unfamiliar with the basic rules of Texas Hold'em: each player has two face down cards, and there are five face up cards on the table. Each player makes the best possible 5-card poker hand using any of the 5 community cards and his 2 private cards.

(In reply to re(2): Solution (Second Try!) w/ my solution by ajosin)

I agreed with you, and your idea is the first that came to my mind, but David Shin, in his post, restated the problem in other words to make it more clear.  He was saying how any of the players would say, "If you beat me, I can tell you what your two cards are."  While the players in your scenario have only one hand beating each of them, no one could guess each other's cards.

I now think Kardo's solution is the correct one.

Posted by Dustin on 2005-04-12 17:02:48