Probability (Hold'em) of a flopped bottom boat being up against a better hand on a paired flop - Gambling and Probability

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Probability (Hold'em) of a flopped bottom boat being up against a better hand on a paired flop

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08-08-2015 , 04:48 AM

alvin_

centurion

Join Date: Sep 2013 Posts: 138

In Hold'em, if I flop the bottom boat on a paired flop (ex:55 on a flop:577), what are the chances of being behind to a better hand (57 or 77) per player in the pot?

My (possibly naive) calculation is 1 in 360 (0.2775%) per player, but I'm not sure I know what I'm doing here...

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08-08-2015 , 07:49 AM

RustyBrooks

Carpal \'Tunnel

Join Date: Feb 2006 Posts: 24,647

What is your opponent's range?

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08-08-2015 , 07:58 AM

alvin_

centurion

Join Date: Sep 2013 Posts: 138

Hand range? I'm not asking about a particular hand here, just strictly a mathematical question.

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08-08-2015 , 10:07 AM

heehaww

Pooh-Bah

Join Date: Aug 2011 Posts: 5,081

There are 2 combos of 75 and one combo of 77 for a total of 3 combos, and 47 unknown cards. So vs one villain the chance is 3/C(47,2) = 3/1081, or about 1/360 like you said.

In this case, it is accurate to say that's your chance "per villain" because more than one villain can't both have you beat. So if there are 3 villains then the chance is about 1/120.

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08-08-2015 , 01:25 PM

alvin_

centurion

Join Date: Sep 2013 Posts: 138

wow i got it right!!

i assume it would be safe to say that if you had the high full house (ex: 55 on: 3--3-5) you could divide those chances by 3, since you are only beat by one hand, right?

thanks for the help here, by the way!

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08-08-2015 , 01:53 PM

RustyBrooks

Carpal \'Tunnel

Join Date: Feb 2006 Posts: 24,647

Quote:

Originally Posted by alvin_

Hand range? I'm not asking about a particular hand here, just strictly a mathematical question.

It depends on what possible cards your opponent could have. For example, 57 might not be a hand he would/could even have. If his range is small and include the hands you're looking for, then it will happen more often than if his range is ATC.

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08-18-2015 , 02:01 AM

alvin_

centurion

Join Date: Sep 2013 Posts: 138

Quote:

Originally Posted by RustyBrooks

What does ATC mean?

My question is just an abstract math question, nothing more.

Are you saying there are players out there that won't limp in late position, or complete the SB, with suited connectors? I find that hard to believe, in fact. Plus, perhaps you have heard of a "big blind special"?

I personally would just limp in middle-late position with 55 after a few other limpers, and I think that is a reasonable choice. With 6 limpers, only a totally ignorant player wouldn't limp or complete with 57s! Come on!

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08-18-2015 , 02:47 AM

heehaww

Pooh-Bah

Join Date: Aug 2011 Posts: 5,081

He's saying people are more likely to play 77 and 75 than 72, 83 etc.

ATC means "any two cards". The math I did assumed they're playing ATC. If they're not, then the chance you're beat is higher than what I said. The percentage depends on their range.

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08-18-2015 , 10:37 AM

RustyBrooks

Carpal \'Tunnel

Join Date: Feb 2006 Posts: 24,647

The question has been answered from a pure math perspective, which is fine, I just wanted to point out that this answer won't match with what you see in actual game play, because he's LESS likely to have a lot of hands that don't hit (such as 72, 83 etc as noted above). So the percentage of times he'll have a hand you're afraid of is higher than if he had 2 random cards.

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