What are my odds of hitting a set with any pre-flop pair?

[Spuddy]

^^^^^


I've been wondering. If I play a pocket pair, what are the odds of me flopping a set?

[Zybomb]

roughly 8:1 on the flop roughly 5:1 by the river

[JTown15]

Pretty sure its like 7.5-1 to hit a set.

[Spuddy]

Thanks guys!

I appreciate it!

[Talking Poker]

[MathBabe]

Here's the math, for anyone interested in figuring it out from scratch:

You have a pair; there are 50 more cards. Two of them match your pair.

So, there's a 2/50 (or 1/25, or 24:1) probability of getting one of those two on the first flop card, 2/49 (or 23.5:1) on the second, and 2/48 (or 1/24, or 23:1) on the third.

We've double-counted a bit - if the first two cards on the flop are your card, for instance, we've counted it as both the 2/50 and 2/49. So we have to subtract (2/50*2/49)+(2/50*2/48)+(2/49*2/48) - a measly 2/1225 + 1/600 + 1/588 = .005 or .5%, but still statistically significant.

I don't know of any way of adding odds; I can only add probabilities, as fractions. (1*49*24)+(2*25*24)+(1*25*49)/25*49*24 = 3601/29400 = 12.24%. Subtract the .5% doublecounted, and get 11.74%. That's about 7.51 to 1.

If you still don't have it after the flop, it's a simple 2/47 on the turn (22.5:1) and 2/46 on the river (23:1).

In other news, I've been accepted to teacher's college in the fall! It's only a 9 month program, so sometime in the 2007/2008 school year you can expect to hear some kind of scandal about a Toronto teacher playing poker with her students, claiming to be teaching them probability.

MathBabe

[Talking Poker]

Damn, that was one sexy post.

7.51:1.... just like it says here:


Excellent.

[Robbr25]

Hey no picking on the MathBabe
Us math majors have to have our good posts.

[eejit101]

as TP says, thats one "sexy" post.

And damn, i wish you were my math teacher.

"lets go and play online poker on pokerstars for todays lesson kids, ill walk around helping and watching while you work out the odds"

why wasnt my school like that.

[MathBabe]

Can't you just tell I was one of the kids who said "but why?" whenever they were presented with some simple piece of information they were supposed to just accept and memorize???

But yes, I did check your page to make sure I was getting the right answer.

[Robbr25]

In math you always have to check your answers in the back of the book, lol

[Reel Deal]