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 solution maybe by Jason)

Looks like it could be close, but that other "non-important" card is actually very important. No matter what that card is, a player could have 2 of them and make 3 of a kind, beating the pair of kings (unless I messed up and don't understand and the full house of 3 aces and 2 other cards loses to the full house with aces and kings)

Looking beyong that, there is also the fact that the players dont know the other kings are in eachothers hands. If someone has 2 kings (but this I suppose goes back to the previous problem I had, is Do 3 aces+ 3 kings beat 3 aces+ 2 kings?) they will also be ahead.

Other than that looks good to me

Edited on April 19, 2005, 5:07 pm

Posted by Kardo on 2005-04-19 17:05:30