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.

The situation would be like this:

- Community cards --> A A A K 2

- Player 1 --> K 2
- Player 2 --> K J
- Player 3 --> K 6

All three players have Full House (A A A K K). It's impossible that any of them could have a Royal Flush or a Straight Flush... so there's only one hand that could beat them: Poker of A's (A A A A K).

Posted by Gus on 2005-04-11 16:49:54