Odd of hitting a set by the river - Beginning Poker Questions

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Odd of hitting a set by the river

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12-23-2019 , 11:07 PM

Criminal Bizzy

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Join Date: Sep 2019 Posts: 81

I wasn't really sure which forum this question would go in but I started searching around to see if this statistic exists already and I can't find anything. The reason for this question is because I was thinking about a hand that I played earlier today where I rivered a set.

I know that you have about 7 to 1 chance of flopping a set but what are the odds that you will hit a set by the river?

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12-24-2019 , 01:07 AM

statmanhal

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Join Date: Jan 2009 Posts: 5,045

Given you have a pair, the probability of a third card of that rank falling (=set) by the river is

C(2,1)*C(48,4)/C(50,5) = 18.4%.

Therefore the odds are 0.816/0.184= 4.44 to 1 against.

For a set or quads, the probability increases to 19.2%

Last edited by statmanhal; 12-24-2019 at 01:13 AM.

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12-24-2019 , 11:06 AM

statmanhal

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Join Date: Jan 2009 Posts: 5,045

Quote:

Originally Posted by Criminal Bizzy

I know that you have about 7 to 1 chance of NOT flopping a set but what are the odds that you will hit a set by the river?

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12-24-2019 , 04:13 PM

Criminal Bizzy

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Join Date: Sep 2019 Posts: 81

Quote:

Originally Posted by statmanhal

Ah...thanks for correcting that.

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12-24-2019 , 04:16 PM

Criminal Bizzy

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Join Date: Sep 2019 Posts: 81

Quote:

Originally Posted by statmanhal

For a set or quads, the probability increases to 19.2%

I don't get this last sentence. Do you mean for a set to turn into quads?

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12-24-2019 , 06:01 PM

fozzy71

Carpal \'Tunnel

Join Date: Mar 2007 Posts: 38,226

I had a bookmark somewhere with a really good chart for this and other drawing outs but I can't find it now. I did find this similar page with a quick google search, hopefully it is accurate - https://www.tightpoker.com/poker_odds.html

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Your Texas Hold'em poker odds are given below for hitting a draw by the river with a given number of outs after the flop and turn, and examples of draws with specified numbers of poker outs given.

Example: if you hold [22] and the flop does not contain a [2], the odds of hitting a [2] on the turn is 22:1 (4%). If the turn is also not a [2], your poker odds of hitting it on the river are again 22:1 (4%). However, the combined hand odds of hitting a [2] on the turn or river is 12:1 (8%). For mathematical reasons, only use combined odds (two card odds) when you are in a possible all-in situation.

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12-24-2019 , 07:10 PM

statmanhal

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Join Date: Jan 2009 Posts: 5,045

Quote:

Originally Posted by Criminal Bizzy

I don't get this last sentence. Do you mean for a set to turn into quads?

No.

Given you have are dealt a pair, the chance of having a set or quads by the river is 19.2%.

Pr(exactly quads by river given dealt a pair) = C(2,2)*C(48,3)/C(50,5) = 0.082%

Quote:

Originally Posted by statmanhal

No.

Given you have are dealt a pair, the chance of having a set or quads by the river is 19.2%.

Pr(exactly quads by river given dealt a pair) = C(2,2)*C(48,3)/C(50,5) = 0.082%

Typo - answer is 0.82%

Last edited by Mike Haven; 12-26-2019 at 10:24 AM. Reason: 2 posts merged

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12-24-2019 , 07:45 PM

dilbag

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Join Date: Apr 2018 Posts: 70

Roughly 1 in 9.5 pairs will flop a set at 6 max
I think to river it is 1 in 5-6 roughly but that is without considering if someone has one of your cards in their hand at 6 max roughly 16% of the time someone will have one of your hole cards

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