Noob math question

I don't have a math degree.. actually, i kinda got bored with it and bailed at age 14. Either way I'm missing a piece of info for calculating some odds and would appreciate it if someone could fill the gap in my brain.

say i have a flush draw on the flop. I hit on the turn 19.14% of the time right?
ie. (9 / 47) x 100 = 19.14

if i miss the turn, i hit the river 19.56% of the time
ie. (9/46) x 100 = 19.56

so now, my uneducated brain says that i should be able to run something like this.

((9/47)x100)+((9/46)x100) = 38.71

but I know that I dont hit my flush on the turn or river 38.7% of the time, a quick gander at an outs chart says its 34.97

why is this so? is it because it allows for a runner runner hit? how would the correct equation look for calculating turn+river chances?

It's easier if you try to figure out how often you *won't* hit your flush. On the turn, 38 cards can fall that are not your flush cards. The river has 37 of those cards (since we're assuming one already fell on the turn).

Chance(miss) = (38/47) * (37/46) * 100 = 65.03%
Chance(hit) = 100 - 65.03 = 34.97%

or the 2/4 rule. count up the outs you have and multiply by 4 if there are 2 more comunity cards to be dealt or multiply by 2 if there is just one more comunity card to be dealt. this is an easy and aproximate way to do % to hit. the diff between exact math and this rule is about 1-2%.

but be aware, cause when you pay flop bet,ex: a FD, you dont have a 36% chance to hit, cause you may face another turn bet, you only pay for the turn card and you have 18% to hit on turn.

you do your % to hit by river only when you are AI on flop, otherwise you estimate your chance to hit for every card, turn and river. when you think you gonna face another turn bet, best calculate implied odds also and see if paying 2 bets when hit is +EV.

Rule of 2 and 4 works decently well, but you can refine the rule of 4 a bit when you have more than 8 outs: multiply by 4 and subtract the number of outs in excess of 8.

Do NOT apply the same correction for the rule of 2 though.

So if you have 13 outs (5 outs in excess of 8), you have about 13*4 - 5 = 47% to hit over the next two cards. The exact number is 1-(34/47)*(33/46) = 48.1%. The "raw" rule of 4 would give you 13*4 = 52%. Rule of 2 says 26% to hit on the turn. Exact number is 13/47=27.6%.

2/4 seems pretty good, good spot with the minus number of outs over 8 daviddem. Seems like outs*2+1 works well for turn calculations

I don't find its that often that i have to be super accurate though, I usually face really good odds or obviously bad odds..

thanks for the exact calc nigthgizmo