What are the odds of a pair flopping??

NM

[Bozeman]

About 4.6:1 against

(13*6*48 + 13*4)/C(52,3) = 17.2% or 4.8-1.

This is (pairs + sets)/total flops

So a pair should flop roughly 1 in 5 times?

[David Sklansky]

The easiest way to do this is to calculate the chances of no pair. That's 48/51 times 44/50 or 82.82%. A pair or trips is therefore 17.18%. That's about 4.82 to one. A pair precisely is 17.18% minus the probability of trips (3/51 times 2/50 or 1/425) which leaves you with 16.94% (4.9 to one). You could get this number directly by assuming the second card pairs the first and the third doesn't (3/51 times 48/50 = .05647) and multiplying by three since the odd card can be in any of three spots.

The odds are about 5-1 but the CHANCES are about one in six.

[BruceZ]

You might appreciate this. Check out my post "Neat Trick" in the probability forum under the "How Many Aces" thread. There you will recognize a couple of your simplifications combined with one of my own to make an otherwise complicated problem easy.