A question that has probably been asked a million times .....

[BugSplatt]

Can someone tell me the math involved in this common everyday occurence. You have two suited cards, flop two suited cards - what is the formulation that stipulates that you have a 34.97% chance of hitting one of your flush cards on turn or river?

I know, for example, how to calculate the chance of flopping a flush: ((11/50)*(10/49)*(9/48)) = 0.84
but my statistical knowledge ends there.

Thanks in advance,

Bug

[Lost Wages]

Figure the probability of missing your flush draw and subtract that from one.

P(miss) = (38/47)*(37/46) = 0.6503
P(hit) = 1 - P(miss) = 1 - 0.6503 = 0.3497

Note that 34.97% represents the probability of catching one or two of your suit. (9/47)*(8/46) = 3.3% of the time you will catch running cards in your suit which is usually not a good thing.

Lost Wages

[aloiz]

You can either calculate the odds of hitting your flush on the turn/river, or calculate the odds of missing your flush on both the turn and river, and subtract that from 1.

P(making flush) = P(hitting on turn) + P(not hitting on turn) * P(hitting on river) = 9/47 + 38/47 * 9/46 = 34.97%

P(making flush) = 1 - P(not making flush) = 1 - 38/47 * 37/46 = 34.97%

aloiz

[CitricAcid13]

Out of the 47 cards left, 38 will miss for you, and if you miss on turn, then 37 out of 46 will miss.
(38/47)*(37/46)