? outs and %win at river

[glass_onion]

I've been reading a lot of books, but I still can't get something. If I have an ace high flush draw, 9 outs, thats approximately 20% to hit on the turn, 35% by the river (all the books tell me). I can see how to compute 20% (9/47), but not the 35% by teh river. Wouldn't it be (9/47)+(9/46). If so thats about 38.6%. I'm sure I'm missing something.

Can someone help me understand this. I'd like to be able to better gauge value bets in larger out games like omaha and 08 where 12 or 13 outs is common on the flop to st8's.

Thanks

[Jimbo]

You are counting an out twice. If you hit your flush on the turn the river becomes irrelevant.

[glass_onion]

So how specifically does the math change? 9/47 chance of hitting a flush on the turn. IF I hit, than I have a100% chance of hitting the flush by the river. My question really is how to accurately predict the % of time I will hit a hand by the river (on the flop) by counting outs.
In this case it is nine. I've been thinking and the best I can come up with again is (9/47)+(9/46) = 38.6%. The books ALL say 35% for the flush draw on the flop.

Thanks for any help.

[Jimbo]

Count the number of times you won't hit your outs, not the number of times you will. This prevents yor from double counting your outs.

[Kaeser]

The method I use is (# of outs)*(# of cards to come)*2

For example with a flush draw you have 9 cards that will make your hand and 2 cards to come so 9*2*2=36%. This isn't completely accurate but It's very easy to do the math in your head at the table.

[gobboboy]

I think the easiest way to do it is to calculate the percentage that you will NOT hit it and simply take the inverse. (38/47)*(38/46). It's much easier to do this in your head.

[nanoCRUSHER]

Building off what Jimbo and gobbo said...

Chance of hitting flush draw = chance of hitting on fourth + (chance of not hitting on fourth)*(chance of hitting on fifth)
So the math goes:
F = 9/47 + (1-[9/47])*9/46 = 34.97%

We need to include the (chance of not hitting on fourth) because we would be calculating the times you hit your flush card on fourth and fifth street as separate occurances, which inflates your chances by a little (apparently 3% or so).

As gobbo stated, you can also calculate your chances of hitting a flush draw by the chances of you not hitting, which makes the math substantially simpler in this case

Chance of hitting a flush draw = 1 - (chance of not hitting on fourth)*(chance of not hitting on fifth)
F = 1-(38/47)*(37/46) = 34.97%

i still don't get how to do the math...

(38/47)*(38/46) = 0.80*0.82 = doesn't equal 35%

[elmitchbo]

you have to take the inverse.

1-(.80*.82)=34.4%