Did I win this bet?

[Billy Baroo]

From Bruce Z's post:
[ QUOTE ]
Your expression gives the right anwer (1.860-to-1) because of 2 errors which cancel

[/ QUOTE ]

Did the two errors cancel out just in this case, or will they always cancel out. In response to dtbog's post, I worked out the answers using both my method and yours for calculating a 15 out straight-flush draw. The answers were the same.

[ QUOTE ]
the fact that the original poster used this formula without explaining how or why he derived it (and i suspect someone else derived it and he just saw the end product) doesn't make him wrong.

[/ QUOTE ]

As far as how I derived it, I am proud to say that I came up with that sloppy formula on my own. I can't really say why I thought it would work. It just intuitively made sense to me (whether it makes sense to others is another matter) and when I plugged in a 9 out flush draw it ended up with the answer I knew was correct beforehand. So I figured I had it right.

[MortalWombatDotCom]

[ QUOTE ]
[ QUOTE ]
the fact that the original poster used this formula without explaining how or why he derived it (and i suspect someone else derived it and he just saw the end product) doesn't make him wrong.

[/ QUOTE ]

As far as how I derived it, I am proud to say that I came up with that sloppy formula on my own. I can't really say why I thought it would work. It just intuitively made sense to me (whether it makes sense to others is another matter) and when I plugged in a 9 out flush draw it ended up with the answer I knew was correct beforehand. So I figured I had it right.

[/ QUOTE ]

well, if i were your probability instructor and you provided this as an answer on an exam, i would take off points, maybe all of them. personally, i think if you are going to memorize one of the aforementioned formulae, yours has the benefit of being the easiest to get close enough to correct in ones head at a poker table. it doesn't give any insight into how one would, for example, compute the odds of making a flush in a hold-em like game with an extra card on the end, whereas the other approaches mentioned in this thread extend more or less intuitively into variations of that nature. YMMV.

[BruceZ]

[ QUOTE ]
Did the two errors cancel out just in this case, or will they always cancel out.

[/ QUOTE ]

They will always cancel out, if by "always" you mean for any number of outs when computing the probability of completing a hand by the river.

[ QUOTE ]
As far as how I derived it, I am proud to say that I came up with that sloppy formula on my own. I can't really say why I thought it would work.

[/ QUOTE ]

In other words, you could not prove it would work.