Set over Set over Set

[TienXia]

Last night i lost a $700 pot live to a really sick set up. Basically i had 99, another guy had QQ and a lady had 44, flop was Qc9c4h and we all got it in. Can someone tell me the likelihood of set over set over set? Thanks in advance.

Tien

[Jouster777]

Depends how you frame the question. The simplest is if you assume that everyone has these starting hands say what is the probability the flop hits everyone like it did. In this case the probability is P(player1 hits)*P(player2hits given 1 hits)*P(player 3 hits given 1&2).

=[1-(48/50*47/49*46/48)]*[1-(47/49*46/48)]*[1-(46/48)]
=.04%

If you don't assume everyone starts with a PP then you can make a reasonable estimation by multiplying the above result by the likelihood that each gets a PP = .061*.061*.061*.0004
=9.02(E-8)
(this is a minimal overestimation as the likelihood of PP drops once you know someone else has one)

Obviously gets even more involved if you say that each only has to hit by the river.

[bigt2k4]

this happened to me once too, I had bottom set and should have folded, middle set ended up hitting quads on river. It was actually 4 to the flop and the guy who folded(after calling raise and reraise with AK hearts on QJ7 board with Q of hearts and 7 of hearts. River was J of hearts. I could not believe what I saw.

[TienXia]

Thanks man, the .04% is comforting =)