[MortalWombatDotCom]

[ QUOTE ]
[ QUOTE ]
((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


[/ QUOTE ]

Your calculation is the following:

(chance to make on turn) + (chance to make on river, assuming that you missed the turn) - (chance that you made both).

This isn't right -- for one thing, your calculation of the chance that you made both doesn't make sense. If you did, in fact, hit your flush on the turn, then another spade coming would actually be 8/46 instead of 9/46. That's why I don't do these calculations that way.. you'd need some sort of conditional branching to account for the different possibilities for the river.

To truly calculate flop odds, you must do the following:

(38/47) = chance of missing on the turn
(37/46) = chance of missing on river, given that you missed on the turn

(38/47) * (37/46) = 65.0%

This is your chance of missing the flush. Nothing is double-counted; this accurately describes your chances of NOT having a flush at the end of the hand.

Obviously, 1.00 - 0.650 = 0.35, and this (35%) is your chance of making the flush by the river.

Yours actually gave a result of 34.96%, where the correct math gives 35.0% - a trivial difference in this case, but I suspect larger numbers will give a more pronounced discrepancy.

How much was the bet?

-DB

[/ QUOTE ]

this is just plain wrong. simple algebra can demonstrate the two methods are the same. the difference was due to rounding error.