odds of specific hands coming on board.

[jojobinks]

what are the odds of:

exactly one flush and exactly one full house being on the board in 30 hands?

just wondering how the math works with this.

to simplify, (and i hope this is right), we can assume that a flush comes on board 1/509 times, and a FH 1/694 times.

then what?

[BruceZ]

[ QUOTE ]
what are the odds of:

exactly one flush and exactly one full house being on the board in 30 hands?

just wondering how the math works with this.

to simplify, (and i hope this is right), we can assume that a flush comes on board 1/509 times, and a FH 1/694 times.

then what?

[/ QUOTE ]

Actually the flush is 13*C(13,5)/C(52,5) = 1/505. The FH is 1/694 as you said. The odds of exactly one of each in 30 hands is:

C(30,2)*2*(1/505)*(1/694)*(1 - 1/505 - 1/694)^28 = 442-to-1