# Probability your opponent has a pocket pair when you are paired versus not

If I am holding a pocket pair does that effect the probability my opponent has a pocket pair.

I think if you have a pocket pair the probability your opponent has a pocket pair goes up slightly. You basically have less blockers.

you have pair the opponent = combin(4;2) * 12 + 1 = 73 = 5.959184%

you don't have a pair the opponent = combin(4:2) * 11 + 2 * combin(3;2) = 72 = 5.877551%

So the probability goes up 1/72 if you hold a pocket pair

When not holding a pocket pair:

``````((4 choose 2) * 11 + (3 choose 2) * 2) / (50 choose 2) = 5.87755%
``````

When holding a pocket pair

``````((4 choose 2) * 12 + (2 choose 2) * 1) / (50 choose 2) = 5.95918%
``````

So your opponent has a slightly better chance of getting a pocket pair when you hold one yourself, but the difference is indeed slight!

• I think you have not backwards. Commented Apr 24, 2018 at 13:41
• Let me take a look Commented Apr 24, 2018 at 13:41
• You're correct @paparazo, thanks for pointing this out. The post has been edited correspondingly Commented Apr 24, 2018 at 13:43
• Did you down vote my answer? Commented Apr 24, 2018 at 13:45
• I did, it does not seem clear to me how you derived your answer, nor does it seem to be correct. I will be happy to remove my down-vote if you make it more clear, and correct the mistakes. Commented Apr 24, 2018 at 13:49