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Old 06-18-2003, 10:13 AM
BruceZ BruceZ is offline
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Default Re: Odds to flop a draw?

Right, 4.2-1. It is complicated mainly because the exact answer requires that we compute the probability of flopping just a flush draw by itself without a straight draw, so that we can add that to the probability of flopping a straight draw which may include a flush draw, 9.5% + (11.1%-1.3%) = 19.3%. It is relatively easy to compute the probabilities of a straight draw which may include a flush draw, or a flush draw which may include a straight draw similar to what I did in the 2nd to the last paragraph. We can't just add these two together or we would be double counting the times we flop both draws. If we did add these numbers our answer would be off by 1.4%, so we would get 3.8-1 instead of 4.2-1. That's still a reasonable approximation, and a whole lot easier to compute than the exact answer as is often the case. For the exact answer, we had to compute the probability of making at least one of these draws without making the other draw, and then we can get the other one by subtracting as I did. I chose to compute the probability of a flush draw by itself rather than a straight draw by itself as this looked easier. I did a little more arithmetic at the end than was necessary to just answer your question because I was also interested in getting the probability of flopping just a straight draw by itself without the flush draw, since we get this almost for free once we've come this far.
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