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.

Assuming that a player can use 4 of the community cards and one of his own to form a hand, the community cards might have the 10, Jack, Queen and King from a certain suit (and some other card from some other suit, say a three).  The player making the statement holds a 9 of the common suit in the community cards, so he has a King-high straight flush.  The one hand that would beat this would be one containing the ace in the common suit, making a royal flush.

But on second thought, the way hands are defined here, there are many hands (of two cards) that include the ace of the needed suit, rather than just one.

Posted by Charlie on 2005-04-11 15:19:24