Odds: Two 4 of a kinds in the same hand

Hi.

My brother and I were talking shortly after he won a hand in which his 4 of a kind beat someones full house. The board read 4 4 k k 5. My brother had a pair of 4's in the hole, his opponent had KQ.

After the hand I hypothetically asked him "would if a king came on the river?". He then asked "what would be the odds of that?" We then went tried pathetically to guess the odds with little to no knowledge about the math.

Anyways. My question is simply this: What are the odds of two people getting four of a kind in the same hand in a game of Texas Holdem? I tried using the search function but no luck. If you know a link that explains this that's fine or if you could give me those odds yourself I would greatly appreciate it.

Thanks in advance.

Nobody?

[Archetype]

Im really curious about this too. Actually, I wouldnt mind knowing what the odds of two people getting four of a kind with both hole cards being used by both people. Ex;

Board: 8-8-K-K-5

Hero: 8-8
Villian: K-K

That is the minimum requirement for Party Poker's bad beat jackpot as far as I know, and I am VERY curious to see what the odds are of winning that jackpot.

I estimated:

p(pocket pair): 6%
p(hitting set): 18% (given you have a pocket pair)
p(getting quads) = p(pocket pair) * p(hitting set)^2 = 0.2%

10-person table: ~2% that someone will have a PP and get quads.

2 people doing that on same hand: 2% * 2% = 0.04%

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The math wizzes can give you an exact answer. But, it's very conditional too. I mean, my # includes the time that someone with pocket 2's stays in the hand no matter what the preflop bets, positions, or flop shows. So, in practice, it'll be much less common than even the 0.04% would indicate.

(It's very likely I messed this up big time, but I'm just estimating. We'll see the real answer when a math wiz tells us! /images/graemlins/laugh.gif )

[ QUOTE ]
My brother and I were talking shortly after he won a hand in which his 4 of a kind beat someones full house. The board read 4 4 k k 5. My brother had a pair of 4's in the hole, his opponent had KQ.

After the hand I hypothetically asked him "would if a king came on the river?". He then asked "what would be the odds of that?" We then went tried pathetically to guess the odds with little to no knowledge about the math.

[/ QUOTE ]

Actually, that question is easier. There is 1 King left in the deck. The probability that the 4th King would come on the River would be 1/44 (44 cards left unseen) or 2.27%.

[ QUOTE ]
I estimated:

p(pocket pair): 6%
p(hitting set): 18% (given you have a pocket pair)
p(getting quads) = p(pocket pair) * p(hitting set)^2 = 0.2%

10-person table: ~2% that someone will have a PP and get quads.

2 people doing that on same hand: 2% * 2% = 0.04%

------

The math wizzes can give you an exact answer. But, it's very conditional too. I mean, my # includes the time that someone with pocket 2's stays in the hand no matter what the preflop bets, positions, or flop shows. So, in practice, it'll be much less common than even the 0.04% would indicate.

(It's very likely I messed this up big time, but I'm just estimating. We'll see the real answer when a math wiz tells us! )

[/ QUOTE ]

Thanks KipBond! Right or wrong I appreciate the effort and the input. Better than I could ever do that's for sure.

let me guess it happened on party poker

[KJL]

Assuming that one player holds KQ and one player holds 44, the odds of the board reading: 44KKK is 1/C(48,5) or 1/1712304 or about .00006%.
Assuming one player holds 44 and one holds 88, the chance of the borad reading 4488x is 44/1712304 or about .003%