That title may be a bit confusing.

Anyway, here is the scenario I ran into last night in a tourney that knocked me out. Not looking to gripe about the hand, but to learn about the probabilities and identify this.

I had AQ and made a 3xbb bet preflop. I think there were 3 callers. Flop comes xQx. Guy before me makes a small bet, I go pot sized raise, he re-raises. I call. A on turn. I make a 2/3 size bet, he goes all in. I call. He shows QQ to beat my two pair and I am done.

The question is not really how to play it as much as this:

When you have paired any card on the board with a card in your hand, what are the odds that someone else is holding that same card as a pocket pair in their hand?