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.

Theres an easy solution  to this one as well.  If the board shows a king high straight flush, then, unless a player is holding the suited ace, all players are "playing the board", which is quite allowed, and not prohibited by the questions wording (saying there is "one hand" is in fact different from saying there is "exactly one 2-hole-card combination").  They each correctly claim that only one "hand" can beat them.

This aside, I think that the previous post (unless Ive deliberated so long that another post comes inbetween), is the intention of the author.

Posted by Cory Taylor on 2005-04-11 21:21:06