you have a set on the flop..

[morgant]

what are the numbers on filling up by the river? we had a discussion about this at a foxwoods table, one party said 1 in 7, the other said 50%. i felt it was somewhere around 30% of the time? can someone maybe give me the steps to figuring this out? thanks -morg.

[Henke]

Assuming:
1) You have no information about your opponents hands.
2) You haven't got a full house already (ie the flop is not paired)
3) You don't mind having quads by the river
4) You don't mind having set over set yourself by the river (ie fill up on both the turn and the river)
Then I think the probability is:
P(fill-up)=1-40/47*36/46=33.40%.

To figure this out, you know that you have XX in your hand. The flop comes XYZ, where X, Y and Z are all of different value. There are 3 other Y and Z in the deck, and one X. That leaves 47-3-3-1=40 cards that doesn't help your hand. If one of those 40 cards fall on the turn, then your hand gets 3 additional outs, meaning there are only 36 cards left that doesn't help your hand. So the probability of not filling up on the turn or river is then 40/47*36/46. Then the probability that you will fill up (to either a full house or quads) have to be 1-40/47*36/46. So your estimate of 30% was quite close!

[N4CER1]

Your very close...it is 33.40 % chance..........