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Hi! Let's say that I have a flus draw on the flop and gets all-in, then I say that it is:
(9/47)+(9/46)=0,387141.......
That's quite right, right?
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Wrong. It is 9/47 + (1-9/47)*9/46. The 9/46 only applies to the times that you miss on the turn since the 9/47 already accounts for the times that you hit on the turn, so you must multiply 9/46 by the probability of missing on the turn (1-9/47). This gives P(hit on the turn) + P(miss on the turn AND hit on the river).
This post gives 3 correct methods for the flush draw problem. Method 3 is the
inclusion-exclusion principle.