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[QUOTE="BelgoSuisse, post: 1108465, member: 30299"]
chances of flopping a set is 1 minus the chance of not flopping a set.

In order to not flop a set, you must miss the first card, miss the second card and miss the third one.

For the first card, you know 2 cards (your pocket pair) and out of the 50 unknown cards, 48 of them don't give you a set, so it's 48/50 .

For the second card, you know 3 cards (your pocket pair + first one on flop) and out of the 49 unknown cards, 47 of them don't give you a set, so it's 47/49 .

For the third card, you know 4 cards (your pocket pair + first two on flop) and out of the 48 unknown cards, 46 of them don't give you a set, so it's 46/48.

In order to not flop a set, you must miss the first one, then the second one, then the third one, so you multiply the probabilities of that and get (48*47*46)/(50*49*48) = 0.882. The rest of the time, you flop a set, so it's 1-0.882 = 0.118 = 11.8%

That was assuming you had a pocket pair. If you don't assume that, you first need the probability a having a pocket pair. That's easy to compute. The first card you get dealt can be any card, but the second one has to be one of the 3 remaining cards of the same value in the deck of 51 remaining cards, i.e. 3/51 = 0.059 = 5.9%

Now, in order to flop a set when you're dealt a random hand, you obviously first need to get dealt a pair, then to get a flop that hits your pair, and therefore you multiply both probabilities. that's 0.118 * 0.059 =  0.0069 = 0.69%

NOTE: " * " is the multiplication sign obviously
[/QUOTE]

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