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 06-29-2012, 05:09 PM #2 Carpal \'Tunnel     Join Date: Jun 2005 Location: Psychology Department Posts: 7,419 Re: Two cards vs. one card - pointless pre-flop equity puzzler I'm assuming that any two card hand has more equity than any one card hand, so the goal is simply to find the matchup where a one card hand does as best as possible. Intuitively it seems like the solo hand would definitely be an A. I am thinking the two card hand would either be 22 or 23 (sharing a suit with the A of course). This seems too easy to be correct, but I will leave it here as a starter.
06-29-2012, 05:34 PM   #3

Join Date: Nov 2005
Posts: 843
Re: Two cards vs. one card - pointless pre-flop equity puzzler

Quote:
 Originally Posted by Sherman I'm assuming that any two card hand has more equity than any one card hand, so the goal is simply to find the matchup where a one card hand does as best as possible.
That's not true - for example, 6d2d has less than 50% equity vs. an ace, same suit or not.

Quote:
 Intuitively it seems like the solo hand would definitely be an A. I am thinking the two card hand would either be 22 or 23 (sharing a suit with the A of course). This seems too easy to be correct, but I will leave it here as a starter.

2s2d vs. As: 391555/544824 (0.7186816292968005)

 06-29-2012, 06:14 PM #4 veteran   Join Date: Jan 2009 Posts: 2,326 Re: Two cards vs. one card - pointless pre-flop equity puzzler Since the pair of twos greatly reduce the chances for a wheel draw for the ace, 6s6d vs As seems like an obvious candidate to get closer to 50% - but not a lot closer I would think.
 06-29-2012, 06:18 PM #5 adept   Join Date: Nov 2005 Location: Colorado Posts: 843 Re: Two cards vs. one card - pointless pre-flop equity puzzler Sorry if I wasn't clear - the 71.87% figure is the equity for the _deuces_. Making it sixes makes things worse - in the 74% range.
 06-29-2012, 07:06 PM #6 veteran   Join Date: Jan 2009 Posts: 2,326 Re: Two cards vs. one card - pointless pre-flop equity puzzler No, you were clear; it's my quick thinking that was muddled!
06-29-2012, 07:07 PM   #7
Carpal \'Tunnel

Join Date: Jun 2005
Location: Psychology Department
Posts: 7,419
Re: Two cards vs. one card - pointless pre-flop equity puzzler

Quote:
 Originally Posted by statmanhal Since the pair of twos greatly reduce the chances for a wheel draw for the ace, 6s6d vs As seems like an obvious candidate to get closer to 50% - but not a lot closer I would think.
I agree with your thinking but, I went with the deuces though because the A would win on boards like JJ99x where the deuces get counterfeited.

06-29-2012, 07:08 PM   #8
Carpal \'Tunnel

Join Date: Jun 2005
Location: Psychology Department
Posts: 7,419
Re: Two cards vs. one card - pointless pre-flop equity puzzler

Quote:
 Originally Posted by bachfan That's not true - for example, 6d2d has less than 50% equity vs. an ace, same suit or not.
I did not know this.

 06-29-2012, 07:55 PM #9 grinder     Join Date: Jul 2008 Location: Istanbul Posts: 529 Re: Two cards vs. one card - pointless pre-flop equity puzzler I am thinking 4d5h v 7h. Those suits only though.
06-29-2012, 07:56 PM   #10
veteran

Join Date: Jan 2009
Posts: 2,326
Re: Two cards vs. one card - pointless pre-flop equity puzzler

Quote:
 Originally Posted by Sherman I agree with your thinking but, I went with the deuces though because the A would win on boards like JJ99x where the deuces get counterfeited.
Right. There are more chances for a 2345x board for a wheel than JJ99x, but there are many other two pair combos that will counterfeit the deuces so the counterfeiting possibility is more likely than the straight.

 06-29-2012, 08:34 PM #11 newbie     Join Date: Sep 2009 Location: Eire?!?! Posts: 23 Re: Two cards vs. one card - pointless pre-flop equity puzzler I'm the guy in the prop bet who has the one card - I have the 9 of hearts vs 23o with no suits covered. I like my side of the bet intuitively, since 23o has to improve and I still have 3 outs when it makes a pair! 3 outs is a lot of outs!
06-29-2012, 08:35 PM   #12

Join Date: Nov 2005
Posts: 843
Re: Two cards vs. one card - pointless pre-flop equity puzzler

Quote:
 Originally Posted by GarethChantler I am thinking 4d5h v 7h. Those suits only though.
Excellent - this is very close to the best answer with 49.67% equity for 4d5h.

5h4d vs. 7h: 315731/635628 (0.4967229259881566)

The optimal answer gets us to 49.978 - anybody want to take a shot?

 06-30-2012, 04:24 AM #13 journeyman   Join Date: Sep 2004 Posts: 360 Re: Two cards vs. one card - pointless pre-flop equity puzzler I would guess 4d5h vs 8h gives 4d5h the extra 0.3%?
06-30-2012, 11:11 AM   #14

Join Date: Nov 2005
Posts: 843
Re: Two cards vs. one card - pointless pre-flop equity puzzler

Quote:
 Originally Posted by cyberfish I would guess 4d5h vs 8h gives 4d5h the extra 0.3%?
No, that takes us slightly in the wrong direction.

 06-30-2012, 11:33 AM #15 Carpal \'Tunnel     Join Date: Sep 2002 Posts: 8,885 Re: Two cards vs. one card - pointless pre-flop equity puzzler Which are the closest if we exclude ties?

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