Two players getting quads

[karlwig]

OK, I know this is a silly question that doesn't really help with anything.

But here goes:

Say player A and player B are playing holdem, seeing the flop with a pocket pair each.
Whats the odds of both players making quads by river?

I've seen this only a few times, but would think the odds are very, very small. So I'm excited to find out, if anybody care to actually do the math.

[img]/images/graemlins/smile.gif[/img]

[BritNewbie]

Assume those two players each have a pocket pair (say Aces and Kings).

There are 48 cards remaining and the hand is completed by picking 5 of those cards for the board.
There are 48C5 ways of choosing 5 from 48.
That's 1 712 304 ways.

For both players to get quads, we need 2 of the 5 cards to be the remaining Aces, and we need 2 of the 5 cards to be the remaining Kings. That leaves one more community card which can be any of the remaining 44 cards.
So there are 44 ways of filling the board to give the result we want.

The probability of both players getting quads, given that they're currently sitting there with pocket pairs,
is 44 out of 1 712 304.

I make that 0.0000257 correct to 3 significant figures.

I hope that's right.

[jesse8888]

I think this is correct, assuming the 48C5 number is correct.