# The probability of flopping a set in holdem

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• December 19th 2006, 07:07 AM
fobster
The probability of flopping a set in holdem
Hi

I was just trying to work out the probability of flopping a set on the flop in texas holdem but don't know if its exactly. I'm assuming only a set and not four of a kind.

My workings:

P(Flopping a Set)=[(2/50)*(48/49)*(47/48)]+[(48/50)*(2/49)*(47/48)]+[(48/50)*(47/49)*(2/48)]

= 0.11510204 or about odds of 8.688:1

Does that seem correct?
• December 19th 2006, 07:33 AM
ThePerfectHacker
Quote:

Originally Posted by fobster
Hi

I was just trying to work out the probability of flopping a set on the flop in texas holdem but don't know if its exactly. I'm assuming only a set and not four of a kind.

My workings:

P(Flopping a Set)=[(2/50)*(48/49)*(47/48)]+[(48/50)*(2/49)*(47/48)]+[(48/50)*(47/49)*(2/48)]

= 0.11510204 or about odds of 8.688:1

Does that seem correct?

You mean 3 cards in consecutive order?

I do not think there is a numerical answer to your question. I might depend on how many players are in the game.

However, I can compute it for you assuming you deal those first.
• December 19th 2006, 10:13 AM
JakeD
Quote:

Originally Posted by fobster
Hi

I was just trying to work out the probability of flopping a set on the flop in texas holdem but don't know if its exactly. I'm assuming only a set and not four of a kind.

My workings:

P(Flopping a Set)=[(2/50)*(48/49)*(47/48)]+[(48/50)*(2/49)*(47/48)]+[(48/50)*(47/49)*(2/48)]

= 0.11510204 or about odds of 8.688:1

Does that seem correct?

Looks good to me. You assumed you have a pair and calculated the probability of catching exactly one of the two remaining cards of the pair in the 3 cards of the flop.
• December 19th 2006, 10:33 AM
MathGuru
Do you mean everyone playing flops a set?

Wouldnt it be more interesting to see the probability of flopping a set given a pocket pair?

*Ooops I get it thats exactly what you did*
• December 19th 2006, 01:22 PM
Shmuel
what about after the river?
What about hiting a set after the final fifth card?

In other words if I go all in preflop with a pocket pair . . . what are my chances of hitting my set after all cards are on the table?
• December 19th 2006, 01:25 PM
Quick
Quote:

Originally Posted by Shmuel
What about flopping a set after the final fifth card?

In other words if I go all in preflop with a pocket pair . . . what are my chances of hitting my set?

is a set three-of-a-kind or three in a row?
• December 19th 2006, 01:33 PM
MathGuru
A set is 3 of the same card (different suits)

In texas hold'em each player is dealt 2 cards and then 5 community cards (first 3 (called flop) then 1 (called turn) then 1 (called river)). The best 5 card hand (each player makes a 5 card hand from 7 available cards) wins.
• December 19th 2006, 05:29 PM
ThePerfectHacker
The probability of a Royal Flush is 1 in 50,000.
But for some reason when I deal the cards it is much much much more common, hmm, did I do something wrong in my calculation :rolleyes: .
• December 19th 2006, 05:48 PM
Quick
Quote:

Originally Posted by Shmuel
What about hiting a set after the final fifth card?

In other words if I go all in preflop with a pocket pair . . . what are my chances of hitting my set after all cards are on the table?

First, I assume no one else is playing.

You have a pair, the odds that the third card isn't in the first four flips is: $\frac{48}{50}\times\frac{47}{49}\times\frac{46}{48 }\times\frac{45}{47}=\frac{207}{245}$
(that number is according to excel)

Then the odds of a match in the last flip is: $\frac{2}{46}=\frac{1}{23}$

So you multiply that together to get: $\frac{1}{23}\times\frac{207}{245}=\frac{9}{245}\ap prox3.67\%$

So it's very low.

But what if you're playing with $n$ amount of people (including yourself, also this assumes they don't have your needed card). Then the equation would be:
$\frac{50-2n}{52-2n}\times\frac{49-2n}{51-2n}\times\frac{48-2n}{50-2n}\times\frac{47-2n}{49-2n}\times\frac{2}{48-2n}$
• December 20th 2006, 10:33 AM
MathGuru
I think Shmuel was asking what are the chances that any of the 5 community cards are the same as his 2 cards.

• December 20th 2006, 12:26 PM
Quick
Quote:

Originally Posted by MathGuru
I think Shmuel was asking what are the chances that any of the 5 community cards are the same as his 2 cards.

It's the same odds (remember the commutative property)
• December 21st 2006, 08:58 AM
MathGuru
I dont think so.

If the odds of hitting 3 of a kind with 3 community cards is 0.11510204
then how could it be lower with 5 community cards?
• December 21st 2006, 05:59 PM
Quick
Quote:

Originally Posted by MathGuru
I dont think so.

If the odds of hitting 3 of a kind with 3 community cards is 0.11510204
then how could it be lower with 5 community cards?

Maybe excel is doing something wrong...
• December 21st 2006, 07:31 PM
JakeD
Quote:

Originally Posted by fobster
Hi

I was just trying to work out the probability of flopping a set on the flop in texas holdem but don't know if its exactly. I'm assuming only a set and not four of a kind.

My workings:

P(Flopping a Set)=[(2/50)*(48/49)*(47/48)]+[(48/50)*(2/49)*(47/48)]+[(48/50)*(47/49)*(2/48)]

= 0.11510204 or about odds of 8.688:1

Does that seem correct?

Quote:

Originally Posted by Shmuel
What about hiting a set after the final fifth card?

In other words if I go all in preflop with a pocket pair . . . what are my chances of hitting my set after all cards are on the table?

Extending (and simplifying) fobster's calculation to 5 cards:

$P = 5 *\frac{2*48*47*46*45}{50*49*48*47*46} = .1837.$
• April 11th 2007, 03:21 AM
Jameson
How does other people playing lower your odds? You hold a pocket pair and are seeking one of two cards left in the starting deck to appear on the flop.
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