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 Only One Hand (Posted on 2005-04-11)
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.

 See The Solution Submitted by David Shin Rating: 4.2857 (7 votes)

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 Better idea--solution? | Comment 3 of 31 |
(In reply to probably not quite it. by Charlie)

If the community cards contain 10,  Jack and Queen of a given suit (and two not so useful cards), and the player has a 8 and 9 of that suit, he has a Queen high straight flush.  Ordinarily a King high straight flush would beat it as would a royal flush, but in this instance no other player could have a King high straight flush as the announcing player has the 9 that's needed to be included in that. That leaves only the King and Ace of the common suit, forming a royal flush, to beat the hand the announcing player has.
 Posted by Charlie on 2005-04-11 15:27:10

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