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

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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

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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!

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  • I think you have not backwards. – paparazzo Apr 24 '18 at 13:41
  • Let me take a look – David C Apr 24 '18 at 13:41
  • You're correct @paparazo, thanks for pointing this out. The post has been edited correspondingly – David C Apr 24 '18 at 13:43
  • Did you down vote my answer? – paparazzo Apr 24 '18 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. – David C Apr 24 '18 at 13:49

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