[asdf1234]

It's somewhat brutal, but you essentially have to calculate the number of possible boards that give you the hand out of the total number of possible boards.

For example, if you hold K [img]/forums/images/icons/spade.gif[/img] K [img]/forums/images/icons/diamond.gif[/img] and want to calculate the probability of hitting quads by the river, you need to find out exactly how many boards give you quads.

Obviously, to have quads, the other two kings out need to show up, so these are "locked in", and there are 48 remaining cards to show up on the board. Now just figure out how many ways out of 48 3 cards can show up C(48, 3) = 17296.

So there are 17296 boards that give you quads. Now just calculate the total possible boards C(50,5) = 2118760.

Dividing 17296/2118760 = .00816
So you get quads about .8% of the time with a pocket pair. (This is 121.5:1 against when you hold a pocket pair).

You can calculate C(n, r) with the formula

C(n,r) = (n!)/(r! * (n-r)!)
Most calculators that have factorial will probably have the combination function as well (usually called nCr).

Going back to the flush stuff, the numbers that you should apply to an actual game situation are probably a few points less than what I calculated. These are theoretical and assume that nobody ever folds (well, this isn't a far cry if you play on party). Most reasonable players will fold 82s from early position while you might be able to limp in from late position with 76s. It depends on the number of opponents you have and their caliber.