What about that third flop card ???

[BasketballNYC]

This may be a ridiculously simple probability question but I am not very good at calculating these things yet. I have seen the result for the probability of flopping a flush draw in hold'em when I have suited cards is 11%. Yet I do not know how that number was computed. If the flop were only two cards it would be easy. But what about that third opportunity. It has to make the number much bigger, but how is that calculated? Thanks for any help.

Matt F.

[uuDevil]

A longwinded, but straightforward approach is:

Say you hold 2 clubs. Then 11 clubs remain in the 50 cards left in the deck. So the probability of a club coming on the first card is 11/50. If the first card is a club, the probability of the second card being a club is 10/49. Now 9 clubs and 39 nonclubs are left in the remaining 48 cards. So the probability of the 3rd card NOT being a club is 39/48. The total probability of the cards coming in this PRECISE order is (11/50)*(10/49)*(39/48).

However, the cards can come in any order. How many ways are there for three cards, 2 of which are clubs, to come? Three ways. (If C=club and X=nonclub, the possible orders are CCX, CXC, and XCC.)

So P(2 and only 2 clubs on the flop)=
3*(11/50)*(10/49)*(39/48)= 0.1094