[ccwhoelse?]

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I realize that it doesn't work to figure your chances of a flush draw by (9/47) + (9/46) after the flop. you have to do 1 - (38/47) - (37/46). I just don't get it why the first doesn't work. I am sure it is fairly obvious but I just feel dumb for not getting it because I have always been very strong in math and logic. Someone help me.

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i had the same question a few days ago, then i realized why you can't.

first, it's not (38/47) - (37/46) or (9/47) + (9/46)

you have to multiply (38/47)*(37/46). ok so, you can't figure your chances to make the flush by doing (9/47)*(9/46) because the first number (9/47) is the chance your flush card will come on the turn. meaning, when you flop a four flush, your outs are 9. (9/47) implies you hit one of your outs on the turn, giving you the flush. so (9/47)*(9/46) really doesn't mean much. also, if you wanted to know the chance that two cards of your suit would come out on the turn and river after you flopped a four flush it would be (9/47)*(8/46), the chances that the turn and river give a cards of the same suit.