odds of two players flopping the same trips, 6 players

[FredJones888]

What are the odds of two players in a 6 player game flopping the same trips ? Both players have card X and the flop comes XXY.

[LetYouDown]

Well, the way you phrased it...I'm not sure that the number of people dealt in matters. If I hold A-J and you hold J-4...the odds that the flop comes J-J-X where X is not A or 4 is:

[C(2,2) * C(40,1)]/C(48,3) = 0.2312673% or about ~431 to 1

[Cobra]

When I read this I looked at it a little differently than LetYouDown. I am going to answer this question that at a six person table what are the odds that on the next deal you get a flop of XXY and any two people have an XY or XZ.

Without consideration of hold cards the flop will come XXY:
=13*(4c2)*48/(52c3) = 3744/22100 = 16.94%.

Now that the flop has come XXY we will determine the odds that two people were dealt XY or XZ. In order to do this you use inclusion exclusion. In this case there can be no more than two people who are dealt an XY or XZ therefore there are only two terms in the inclusion exculusion exercise. We are interested in the second term which gives the probability that two people are dealt that above hands.

= 4412*(6c2)/(49c2)/(47c2) = 5.21%

So the probability of this event occuring on the next deal is.

5.2%*16.9% = .882% or 1 in 113.3 hands.

Assuming you are a bystander and you see a flop of AAK the probability that two people were dealt an ace is 5.21%.

Cobra

[FredJones888]

thanks to both of you

[gol4pro]

Cobra is pretty much right. It's about the same odds as flopping quads.

The way that the OP phrased the question actually brings in conditional probability, but since you guys figured out what he meant, we won't go there.

6 or 10 handed doesn't actually make a difference here.

1/430 is slightly off, but about right. Your chance of flopping quads is 1/426 or so, so this has to be less, because we know 2 more cards in the deck preflop, eliminating many combinations.

Chance of flopping trips but NOT full house
(2c2)38c1/48c3
= 38/48c3
= .21%.... which is 1/450ish

Chance of one flopping trips, and one full house
2c2(6c1)/48c3
6/17296
= 1/3000ish