Calculating outs for Turn+River

[Colombo]

Say on the flop you are drawing to a flush, which gives you 9 outs. If someone goes all in, thus disallowing betting on the turn, how can you calculate the odds of catching on the turn and river combined?

[OrianasDaad]

Outs on turn/unseen cards + outs on river/unseen cards. You add them since it's an "or" question. You can make your flush on either either the turn "or" the river. If it were a runner runner draw, you'd multiply your outs for each street, since it's an "and" question (you need an out to hit on the turn "and" the river.)

9/47 + 9/46 = .38714 = 38.7%

I'm not a NL player, but it would seem that calling all-in bets would be a bad idea with a draw unless your stack were much larger than your opponents. I'd also prefer more ways of winning the pot, like the possibility of making a higher pair, etc.

[BruceZ]

[ QUOTE ]
Outs on turn/unseen cards + outs on river/unseen cards. You add them since it's an "or" question. You can make your flush on either either the turn "or" the river. If it were a runner runner draw, you'd multiply your outs for each street, since it's an "and" question (you need an out to hit on the turn "and" the river.)

9/47 + 9/46 = .38714 = 38.7%

[/ QUOTE ]

Incorrect, as you only want the 9/46 on the river after you miss on the turn. It should be 9/47 + (1 - 9/47)*9/46 = .34968 = 35.0%. That is, hit on the turn OR miss on the turn AND hit on the river. You can also compute the probability of missing on both the turn AND the river, and subtract from 1. That is, 1 - (38/47)*(37/46) = .34968.

[CrazyN8]

[ QUOTE ]
It should be 9/47 + (1 - 9/47)*9/46 = .34968 = 35.0%.

[/ QUOTE ]

man....that's where I was missing it. I was looking at a table and couldn't figure out how Warren was doing the 2 cards to come line. Thanks!

one card to come was easy...I was missing the (1-9/47).