6-Max 4-Way All-In Everyone Flops FH - Odds?

[FakeKramer]

I was involved in what has to be a one in 10 million spot today - perhaps even much more rare. Alas, I'm really bad with probability math on stuff like this, so I have no idea what the true odds are. Here is the hand history:

PokertipsOzone: PokerStars Game #11930032917: Tournament #59838021, $20+$2 Hold'em No Limit - Level V (75/150) - 2007/09/07 - 20:37:02 (ET)
Table '59838021 17' 6-max Seat #3 is the button
Seat 1: pooey (5985 in chips)
Seat 2: Ozone23 (8443 in chips)
Seat 3: bradm8 (8010 in chips)
Seat 4: Coupe15 (11395 in chips)
Seat 5: ditsch24 (4365 in chips)
Seat 6: bodinarn (9330 in chips)
Coupe15: posts small blind 75
ditsch24: posts big blind 150
*** HOLE CARDS ***
Dealt to Ozone23 [Qd Qh]
bodinarn: raises 300 to 450
pooey: raises 750 to 1200
Ozone23: raises 7243 to 8443 and is all-in
bradm8: folds
Coupe15: raises 2952 to 11395 and is all-in
ditsch24: calls 4215 and is all-in
bodinarn: folds
pooey: calls 4785 and is all-in
bradm8 said, "wow"
*** FLOP *** [4c 4s 4d]
*** TURN *** [4c 4s 4d] [9s]
bradm8 said, "hahahaha"
*** RIVER *** [4c 4s 4d 9s] [Ad]
*** SHOW DOWN ***
Coupe15: shows [Ah Ac] (a full house, Aces full of Fours)
Ozone23: shows [Qd Qh] (a full house, Fours full of Queens)
bodinarn said, "loool"
Coupe15 collected 4916 from side pot-2
pooey: shows [Kh Kc] (a full house, Fours full of Kings)
Coupe15 collected 4860 from side pot-1
ditsch24: shows [Qs Qc] (a full house, Fours full of Queens)
Coupe15 collected 17910 from main pot

So the question is: What are the odds of four players getting all-in preflop at a 6-max table, all holding pocket pairs, and all flopping a full house?

Now, I realize this involves an estimation at some point. The odds do not involve four players merely being dealt pocket pairs, but rather four players being dealt pocket pairs and all four of them going all-in before the flop. Surely that's an extremely rare occurance. The flop containing three-of-a-kind just made it even crazier.

Anyway, I'd love to see some of the more mathematically gifted among you throw out some estimations of how often you're likely to see a hand like this.

[FakeKramer]

One thing I can calculate is that the odds of three random cards (the flop) all being of like-suit are 0.232%.

[DarkMagus]

Why do you care? There are probably thousands of "weird" situations like this that can happen. If you can think of 5,000 weird coolers or other situations, each of which occur with a frequency of once every 10,000,000 hands, you're still going to see one of these weird situations once every 2000 hands.

It wouldn't be too hard to calculate the probability of 4 players receiving pocket pairs and the flop being three of a kind, but it would be a meaningless number.

[RustyDagger]

This would be more interesting if some sucker would have called the 4 all-ins with an x-4 hand and taken the pot with that.
...and then it should happen in an MTT final table too. The sucker should be the big stack. With only 5 players left.
...and then the AA guy should be shortstacked and finish 5th! That would be something.

Odds? I'd tell you if I had a clue.

Anyway, when that happens don't forget to post!

I'm too tired to play poker, so I've elected to write this nonsense instead.