Re: what is the probability of any 3 cards on flop?
If you mean three specific cards, like K [img]/images/graemlins/diamond.gif[/img] 9 [img]/images/graemlins/spade.gif[/img] 3 [img]/images/graemlins/diamond.gif[/img], the answer is 1/22,100. This is also the probability of two flops in a row being identical except for order. If you are looking at one of the hands, then the odds go to zero for flops that contain one or more of the cards in that hand, and up to 1/19,600 for all other flops.
Normally you want to compute the probability of ranges of hand. Say you're holding two spades and want to know the probability of flopping a flush. You can pick 3 from the 11 remaining spades in 165 ways, so the chance is 165/19,600.
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