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 (Second Try!) by ajosin)

Both players with the aces can be beat by an A and 5 - King as well as the 4 of a kind Kings. I had an idea after reading your solution and I think this works.

If the community cards are:

A(Hearts) A(Diamonds) Q(Spades) Q(Diamonds) K(Clubs)

No Royal flush possible.

And the player cards:

Ace(Spades) King(Hearts)

Ace(Clubs) King(Diamonds)

Queen(Hearts) Queen(Clubs)

In this situation, both players with the Aces know that nobody can have 2 aces, so an Ace - King would be the next best. Since they have the king, the 4 of a Kind Queens is the only other possibility.

The player with the Queens knows that only a player with 2 aces in their hand can beat them.

Posted by Kardo on 2005-04-12 12:16:18