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12-28-2005 04:46 AM

Odds of 3 people with pocket pairs all flopping a set in holdem
I have no clue how to calculate this and someone asked me. I assume the odds are different if you count the odds of 3 people having pocket pairs dealt and then all 3 flopping sets, compared to WHEN 3 people have pocket pairs how often do they flop the set. Or maybe not...its 2:45am [img]/images/graemlins/laugh.gif[/img]

Pog0 12-28-2005 07:12 AM

Re: Odds of 3 people with pocket pairs all flopping a set in holdem
If three players see a flop, all holding a different pocket pair, then we've got (6/46)*(4/45)*(2/44)=0.0527% or 1 in 1897.5.

12-28-2005 01:08 PM

Re: Odds of 3 people with pocket pairs all flopping a set in holdem
I understand how you got the 46,45,44. Start with 52 cards, they each have 2 hole cards, so the next 3 draws are 46,45,44. I also understand that there are 6 cards that will help our 3 players get their sets. There are 3 groups of 4 cards, or 12 cards total, and our players already have 6 cards they were dealt.

What I don't understand is why we use 6, then 4, then 2 as the numerator in the (6/46)*(4/45)*(2*44) in the equation.

6+4+2=12 which is the total of the 3 sets of cards perhaps. But I don't see why the 6,4.2.

Can you help me understand that part?

Thank you.


12-28-2005 01:18 PM

Re: Odds of 3 people with pocket pairs all flopping a set in holdem
I think I got it [img]/images/graemlins/smile.gif[/img].
All 3 players need to get a set. So after the first player gets his set, with the first flop card. that takes 2 cards, not one, out of the pool. The card he drew to get his set, and the other, 4th card of that value, that will not help the other 2 players get their set.


ohnonotthat 12-28-2005 08:37 PM

Re: Odds of 3 people with pocket pairs all flopping a set in holdem
PogO gave the correct answer to the question, "what are the odds that three players all holding PPs all flop sets ?".

As to how often will a full table see set-over-set . . .

In a million+ hands online I have seen it happen four times, though I'm certain it has escaped my notice a few times. (I used to automatically oreder a HH for all huge pots and a set-set-set flop will almost always generste a huge pot).

In what I'd guestimate to be a half million live hands I've seen it only once but 90% of my live play has been at limits higher than I play online and higher limits are unforgiving of people who automatically play any pair - ergo it would rate to happen less.

Set over set is something I've seen plenty of and this is one of those situations that seperates the men from the boys.

Mucking a set is hard - period - but it sometimes comes to pass that your little set just cannot win. Example -

I was in a game of 4-8 spread-limit out west some years ago with THE tightest player I'd ever seen. (They used to be very popular in the smaller rooms and were referred to as "four double eights"). He raised UTG, got 5 callers (all of whom were clearly paying close attention to his play:)) and I called with 9-9 on the button.

The flop came A-9-4/rainbow and he bet out; 3 or 4 called and I raised. He called.

The turn was a 2. He checked, next to his right bet, I raised, he re-raised and the original raisor capped. I mucked without a moment's hesitation; this guy could not have anything other than A-A.

When the hands were rolled I got was doubly pleased; the rock did indeed have A-A, and (hehehe) he didn't get the pot - 5/3 did. (Yeah, there were a few in that game who would cold-call raises with 5-3).

Let's start from square one.

Calling all mathmaniacs - calling all mathmaniacs . . .

What are the chances that 3 players at a 10-handed game will be dealt a pair ?

4 players ? . . . 5 players ?

ohnonotthat 12-28-2005 08:47 PM

The above reply is incomplete
I hit "send" accidentally.

I was about to suggest that someone who's cabable of it tell us how often a full table would even have 3, 4 or 5 players all dealt a pocket pair. (6 or more would seem to be extremely unlikely though it would be nice to know the odds for this, as well as 7,8,9 and 10).

From there we mortals could see how often S/S/S would figure to occur. (The proviso that all pairs see the flop would not be at all far fetched for PARTY games up to 3-6).

It seems this is something that a 40-hour/week low-limit multi-tabler ought to see from time to time; I'm not suggesting it would be commonplace but it should happen with some regularity.

As it stands, it seems to be an extremely rare event. Even allowing for the fact that we are not always privy to it's occurence it still seems to happen far less than one might expect.

Well, more often than "I" would expect.


Any volunteers ?

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