what am i missing here? (flush flop question)

[tpir90036]

what is wrong with calculating the odds of flopping a four-flush *or better* like this:

(11 Choose 2) X 48 (Other cards in the deck)
-------------------------------------
19600 (# of possible flops)

seems to make sense. however, if you calculate the odds of flopping *only* 2 of your suit and the odds of flopping all 3 of your suit and add them up....it doesn't add up to the same thing.

what am i missing?

[BruceZ]

what is wrong with calculating the odds of flopping a four-flush *or better* like this:

(11 Choose 2) X 48 (Other cards in the deck)
-------------------------------------
19600 (# of possible flops)

seems to make sense. however, if you calculate the odds of flopping *only* 2 of your suit and the odds of flopping all 3 of your suit and add them up....it doesn't add up to the same thing.


You have to separate the cases of flopping 2 and flopping 3, otherwise you will be counting the cases where you flop a flush 3 times since the 48 and the C(11,2) can pick the same flush cards 3 different ways. This is a common error. Always make sure the numbers you multiply represent distinct sets of cards. Otherwise, if you do it the other way, you would actually have to subtract off twice the number of cases where you flop a flush:

[ C(11,2)*48 - 2*C(11,3) ] / C(52,3) = 11.8%

same as the normal way:

[ C(11,2)*39 + C(11,3) ] / C(52,3) = 11.8%

[tpir90036]

thanks dude. i figured out my error on the way home work after posting this with the help of a math friend of mine. thanks for the response though.....