Getting out-tripped

[Malificent]

What are the odds that you're holding a pocket pair and someone else at the table is also holding a pocket pair and both of you hit your trips on the flop? I've had this happen twice in the past 24 hours, so I was just curious what the odds are on it happening.

[irchans]

Here is a rough estimate.

If you have n opponents and you hold a pair, then the expected number of opponents with pocket pairs is

n*( (1+12*6)/C[50,2]) ~= n*0.06.

If you and one opponent both have pairs, then the probability that both of you will hit trips is

2*2*44/C[48,3] ~= 0.01.

So the probabilty that someone else hit trips when you hit trips with your pair is about

n*.059*0.01 = n*0.0006

or about

n/1650.

[Ed Miller]

So the probabilty that someone else hit trips when you hit trips with your pair is about

n*.059*0.01 = n*0.0006

or about

n/1650.

While that is strictly speaking what he asked for, that is not such a relevant number. The more important number would be how often an opponent will have a set GIVEN that you have already flopped a set.