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: solution maybe by Kardo)

The reason for the confusion here is the uncertain definition of "non-important card", especially for those unfamiliar with the game.  3A + 2K is the best possible full house (3A + 3K is not possible, as a player may only use 5 of the availbale cards). 

The only hands which beat the above full house are 4 of a kind, or a royal flush.  Therefore in Jason's scenario the 5th card cannot be a Q, J or 10 of the same suit as both an Ace and King on the board, otherwise a royal flush also becomes available to the other players, and no-one can declare that only one hand beats them.

 

Posted by Adam Champken on 2005-04-20 16:02:36