Probability of set over set over set?

[carpe2k]

In my ring game last night I had pocket 66, another 88, and another KK. The flop came 6 8 K. Anyone know the odds of set over set over set? [img]/images/graemlins/confused.gif[/img] A search turned up nothing on this. Thanks in advance.

[pokerponcho]

The odds of three people flopping sets given a non-paired board, from an outsiders point of view, which I think is what your asking would be if I'm not mistaken calculated as follows:

we'll have BS stand for bottom set, MS stand for MS and, and TS stand for top set. n will be the number of players.

P_BS() = (3 C 2) / (47 C 3) * 9 = 3 / 16215 * 9
P_MS() = (3 C 2) / (45 C 3) * 8 = 3 / 14190 * 8
P_TS() = (3 C 2) / (43 C 3) * 7 = 3 / 12341 * 7

P = P_BS()*P_MS()*P_TS() = approx 4.8 billion : 1

I must have gotten my numbers crossed somewhere. That seems far too far on the astronomical side, doesn't it? Someone help me!!

pokerponcho

[Dave H.]

Here is what you want I believe...

Set Over Set Odds

P.S. You can go directly to the very last line if you don't want to read the explanation. It states and I quote:

[ QUOTE ]
So if you are playing in a game where players holding pocket pairs stay to see the flop, you should be seeing flops with two or more players making sets on the flop about once every 167 hands.


[/ QUOTE ]

[Dave H.]

Oops...sorry, I thought you wanted set over set odds.

Apologies

[slickpoppa]

[ QUOTE ]
In my ring game last night I had pocket 66, another 88, and another KK. The flop came 6 8 K. Anyone know the odds of set over set over set? [img]/images/graemlins/confused.gif[/img] A search turned up nothing on this. Thanks in advance.

[/ QUOTE ]

You have to clarify your question. Do you mean, what is the probability of this happening on ANY deal, or given that three people have pocket pairs?

[carpe2k]

Three different players having pocket pairs, is not the question. [img]/images/graemlins/crazy.gif[/img]All three improving to a set on the flop is the question. [img]/images/graemlins/confused.gif[/img]Though you have to have the first obviously to improve to the second. [img]/images/graemlins/grin.gif[/img]
Thanks.

[Cobra]

Assuming three people go all in and they have three pocket pair, the probability of all three flopping sets is.

=2*2*2/(46c2) = 6/1035 = .005797 or 1 in 172.5 flops

Cobra

[carpe2k]

Thanks, Cobra.
Yes, we were all-in quickly. Two of us all out quickly too. [img]/images/graemlins/frown.gif[/img]
No one at the table could remember ever seeing this.

[MickeyHoldem]

I'd try 2*2*2/46c3 = 8/15180 = .000527009 or 1 in 1897.5 flops

I've had lots of days like this!!! [img]/images/graemlins/grin.gif[/img]

[carpe2k]

I must say this sounds closer to the truth.
Other info provided seems to be set over set, rather than three ways. If it were in the 1 in 176-206 range, more people would remember seeing it. Though memories are faulty. [img]/images/graemlins/grin.gif[/img]