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Old 12-16-2005, 03:10 PM
PseudoPserious PseudoPserious is offline
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Join Date: Oct 2002
Posts: 151
Default Re: how do you figure this out?

In general, you figure out the number of flops that fit the criteria you define, and divide it by the number of total possible flops. The easy way to do it is by using combinations.

Example. If you have 33, what are the odds of flopping trips, threes full, or quad 3s?

Number of flops that contain one '3': C(2,1)*C(48,2)
C(2,1) -> ways to choose 1 '3' from the pool of two '3's
C(48,2) -> ways to choose 2 'non-3's from the pool of 48 'non-3's
C(2,1)*C(48,2) -> multiply them together to get the number of flops that contain exactly one '3'

Number of flops that contain two '3's: C(2,2)*(48,1)
C(2,2) -> ways to choose 2 '3's from the pool of two '3's
C(48,1) -> ways to choose 1 'non-3' from the pool of 48 'non-3's
C(2,2)*C(48,1) -> multiply them together to get the number of flops that contain exactly two '3's

Total number of flops: C(50,3)
C(50,3) -> number of ways to choose 3 cards out of a pool of 50 cards

So, the probability of flopping one or two more threes is:
[C(2,1)*C(48,2) + C(2,2)*C(48,1)] / C(50,3) = ~11.8%, or roughly 7.5:1.

Example. If you have no hearts in your hand, what is the chance of three hearts flopping?

Number of flops that contain 3 hearts: C(13,3)
Total number of flops: C(50,3)
Probability of flopping 3 hearts: C(13,3)/C(50,3) = ~1.5%

Hope that helps,
PP
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