What am I missing here?

As David Sklansky demonstrated earlier, determining the odds of flopping two pair is fairly simple. My question is: how do you determine the odds of flopping two pair or better?


Example: 83o. There is no possible straight or flush on the flop, for simplicity's sake. You need two cards to improve to two pair or better, and you really don't care whether the third card makes you a boat or quads.


I can see three possible ways to calculate this, but I am not sure which is correct.


1) 6/50 * 5/49 * 3 ~= 3.67%

2) 6/49 * 5/48 * 3 ~= 3.83%

3) (6/50 * 5/49) + (6/50 * 5/48) + (6/49 * 5/48) = 3.75%


Granted, .16% isn't the end of the world, especially when you're dealing with probabilities this small (25.1/1 vs. 26.25/1), but I'm a perfectionist, I guess.


Thanx in advance,

Big John