Did I win this bet?

[Billy Baroo]

Hopefully the good folks at the 2+2 forums can help settle a bet between me and an acquaintance.

Here's the bet. An acquaintance bet me that I don't know how to calculate how flop outs correspond to odds. For instance, most of us know that a flush draw in hold 'em has 9 outs, and is about 1.9: 1 on the flop. His bet was that I couldn't do the math that proves it, and he doesn't believe my answer. We are using 2+2 to officially settle our bet.

Here was my answer (for the uninitiated, I have included how to do this with a 9 out flush draw as it is IMO a little easier to follow it that way):

((Outs/unseen cards on turn)+(Outs/unseen cards on river))
-((Outs/unseen cards on turn)* (Outs/unseen cards on river))
=% hand will be made

100-% hand will be made= x

x/% hand will be made= odds: 1

So did I win the bet? Below is an example of how the math works out for a 9 out flush draw.

((9/47)+(9/46))-((9/47)* (9/46))=35%

100-35= 65
65/35= 1.857
The odds of making a flush are 1.857:1 when you have 4 of the suit on the flop.