[BruceZ]

[ QUOTE ]
[ QUOTE ]
Your expression gives the right anwer (1.860-to-1) by a self-cancelling error.

[/ QUOTE ]

that's classic. also, the Odyssey was not written by Homer, but by another author of the same name.

hey! you editted your post after i quoted it. equally silly, but less quotable.

[/ QUOTE ]

You're wrong and need to think about this a lot more. You in no way can justify the factor of (9/47)*(9/46) which appears in the poster's derivation. This is supposed to be the proability of getting a flush card on both the turn and the river which is (9/47)*(8/46). You also cannot justify the 9/47 + 8/46. This corresponds to nothing. You cannot add these probabilities because the 8/46 is on a different sample space than the 9/47, namely, it applies only after the flush card is dealt. You must add both probabilities before either card is dealt, which is 9/47 + 9/47, or else add 9/47 + (38/47)*(9/46) as I have shown above. Both of these are very common errors, BTW.

The fact that you can derive the poster's equation from my equation by alegebra in no way means that the original derivation makes any sense. He explained what his terms were supposed to represent, and that explanation was wrong. He made two errors which happen to cancel to give the correct numerical answer, just as I said. I also don't post things that are "silly", and you should have considered that before you made a huge ass of yourself. If you say "his basic method is sound" as you have done below, then you also do not know how to properly derive this formula.