Splitting AA

[ChromePony]

This one may have been answered before, but its happened to me twice in about 50-60 AA hands and I was curious. If you're holding AA (or any pocket pair). What are the odds that someone else is too?

[pzhon]

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If you're holding AA (or any pocket pair). What are the odds that someone else is too?

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The probability that any particular opponent has AA given that you have AA is 1/(50 choose 2)=1/1225. The events are disjoint, so the total probability is the sum of the probability for each opponent, 9/1225 at a full table, or about 135.1:1.

The probability that some pair of players is dealt all 4 aces is (10 choose 2)/(52 choose 4) = 45/270725.