If I am holding a pocket pair does that effect the probability my opponent has a pocket pair.
2 Answers
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!
-
-
-
You're correct @paparazo, thanks for pointing this out. The post has been edited correspondingly– David CApr 24, 2018 at 13:43
-
-
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.– David CApr 24, 2018 at 13:49