Quote:
Originally Posted by BruceZ
The probability of set over set over set at a 9-handed table, with all pairs seeing the flop, is exactly
C(13,3)*43 / C(52,3) *
C(9,3) * 9/C(49,2) * 6/C(47,2) * 3/C(45,2)
=~ 1 in 111,666
The top line is the probability of 3 different ranks on the flop. The second line is the number of ways to choose the 3 players C(9,3), times the probability that each player has a different one of these 3 ranks. This is exact since only 3 players can have these 3 sets at one time.
The trick here is to consider the flop first. If you consider the players first, then the more pocket pairs that are out, the more likely it is that 3 players flop sets, so this becomes complicated. The above calculation avoids that.
Take a look here for more:
http://forumserver.twoplustwo.com/25...er-set-380320/
