Odds of hitting 2 sets out of 30 flops

[Blackjack]

How do I compute this?
I've seen 30 flops with 30 pocket pairs and only hit sets twice.

Would that be (1/8.5)^2 x (7.5/8.5)^28?

[BruceZ]

[ QUOTE ]
How do I compute this?
I've seen 30 flops with 30 pocket pairs and only hit sets twice.

Would that be (1/8.5)^2 x (7.5/8.5)^28?

[/ QUOTE ]

For exactly twice:

C(30,2) x (1/8.5)^2 x (7.5/8.5)^28

where C(30,2) = 30*29/2

or use Excel function =BINOMDIST(2,30,1/8.5,false) = 18%.


For 0, 1 or 2 times:

(7.5/8.5)^30 + 30 x (1/8.5) x (7.5/8.5)^29 + C(30,2) x (1/8.5)^2 x (7.5/8.5)^28

or use Excel function =BINOMDIST(2,30,1/8.5,true) = 30%.

[slickpoppa]

First of all, you are probably looking for the probability of hitting two or fewer sets in 30 flops. That number is more important intuitively because 1 minus that number gives you the probability of hitting more than 2 sets in 30 flops. In that case the answer is:

[(1/8.5)^2]*[(7.5/8.5)^28]*[(30!)/(28!2!)] +
[(1/8.5)^1]*[(7.5/8.5)^29]*[(30!)/(29!1!)] +
[(1/8.5)^0]*[(7.5/8.5)^30]*[(30!)/(30!0!)] = Answer

If you really just want the probability of hitting 2 sets, then just compute the first term.

[slickpoppa]

beat me by a minute you bastard