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(3): Solution (Second Try!) w/ my solution by Dustin)

In Kardo's scenario not all can guess eachothers "hands" either. The player with 2 queens does not know wich of the possible A-K combinations the other two players are holding.

I think that to satisfy the problem, each player has to know only of one unique hand that can beat them. That is why the condition of the problem starts by  "IF you beat me ...". The conclusions they draw AFTER they talk out loud are irrelevant.

Therefore, I still believe that the second solution I posted is correct.

Posted by ajosin on 2005-04-12 19:04:42