Super newbie probability/odds question (I'm so ashamed)

[rgrouch]

I have a question about probability/odds that is probably quite simple:

Lets say the game is hold em, and after the flop I am sitting on the nut flush draw. I know how to calculate my odds against making my hand based on the number of outs in my hand (9 out of 47 possible cards), and then to do so again for the river card should I not hit on the turn.

What is the combined probability/odds against for my flush draw then with 2 cards to come (the turn and the river)? And what is the formula used to make these calculations?

Note: I am not using the terms "probability" & "odds" interchangeably.

Thanks.

[gaming_mouse]

Prob of hitting first card: 9/47
Prob of not hitting first card: 38/47
Prob of not hitting second card: 37/46

The chance that you don't make it, then, is: (38/47)*(37/46)

The chance that you do make it by the river:

1 - (38/47)*(37/46) = 35%

gm

[rgrouch]

so then how do i calculate the odds against?

[gaming_mouse]

(1-.35)/.35 = 1.8571 to 1 against.

In general, if the chance (probability) of something is x, then the odds against it are:

(1-x)/x

gm

[Ellis]

A simplier, but less accurate, way of figuring out the percentage of completing your hand is to multiply your outs by 4 to figure flop to river (2 cards to come), or multiply your outs by 2 to find flop to turn/turn to river (1 card to come).

For your nut flush example (you flop a 4-flush):
Flop to River: 9 * 4 = 36. so, about 36% shot to complete it
Flop to Turn (or Turn to River): 9 * 2 = 18. so, about 18% shot of hitting it
(obviously you're dividing by 100 to get the percentage)

These numbers aren't as exact (the actual prob. of hitting your flush w/ 2 to come is 35%. Also, your turn to river calculation will be slightly off on the low side). However, this is easier to do off the top of your head.

That being said, you probably can memorize the percentages (or better yet, odds) pretty easily.

Also, make sure to note that you may have more than 9 outs w/ the nut flush draw.

Hope this helps.

[rgrouch]

Thank you all for your help!