perplexus.info :: Games : Only One Hand

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.

Submitted by David Shin

Rating: 4.2857 (7 votes)

Solution: (Hide)

An example of this type of situation is when the table has AAK99, and the three players have AK, AK, and 99. The players with AK can only be beaten by 99, and the player with 99 can only be beaten by AA.

Another example is when the table has AKK62, and the three players have AK, AK, and AA. The players with AK can only be beaten by AA, and the player with AA can only be beaten by KK.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Quibble ...	JayDeeKay	2009-07-08 17:24:53
re: Another solution	tomarken	2006-03-15 14:23:03
Another solution	tomarken	2006-03-15 14:14:50
No Subject	hookedonphonics	2005-10-08 20:41:24
I joined this web-site to rank on this question	Vincent	2005-06-14 19:59:39
On the official solution	Tristan	2005-06-02 00:14:40
solution	lizperp	2005-05-13 20:06:08
No Subject	noel thompson	2005-04-23 16:22:49
re: solution maybe	Jason	2005-04-21 06:02:22
re(2): solution maybe	Adam Champken	2005-04-20 16:02:36
re: solution maybe	Kardo	2005-04-19 17:05:30
solution maybe	Jason	2005-04-19 09:55:32
re: Limits on possible solutions	Tristan	2005-04-14 21:53:45
Limits on possible solutions	Tristan	2005-04-13 00:04:20
re(4): Solution (Second Try!) w/ my solution	ajosin	2005-04-12 19:04:42
re(3): Solution (Second Try!) w/ my solution	Dustin	2005-04-12 17:02:48
re(2): Solution (Second Try!) w/ my solution	ajosin	2005-04-12 15:21:48
re: Solution (Second Try!) w/ my solution	Kardo	2005-04-12 12:16:18
re: No Subject	David Shin	2005-04-12 04:25:11
No Subject	Cory Taylor	2005-04-11 21:21:06
Solution (Second Try!)	ajosin	2005-04-11 19:45:06
re(2): Solution	ajosin	2005-04-11 19:25:26
Comments	David Shin	2005-04-11 18:31:22
re: Solution	Gus	2005-04-11 16:59:20
re: Solution	Dustin	2005-04-11 16:58:17
What about this?	Gus	2005-04-11 16:49:54
re: Better idea--solution?	ajosin	2005-04-11 15:42:53
Solution	ajosin	2005-04-11 15:38:41
Better idea--solution?	Charlie	2005-04-11 15:27:10
probably not quite it.	Charlie	2005-04-11 15:19:24
I forget	Bryan	2005-04-11 15:15:06

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