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.

I think that the solution may lie in the wording of the question. I think that there was a fourth player, beacause of the use of 'remaining players', that by folding his hand  allowed the remaining players to see that along with the community cards and the cards in their hands that there was only one possible combination that could beat them.   

Posted by noel thompson on 2005-04-23 16:22:49