A pair on the board

[NoPepperJack]

I have done the math in my head but doubt my understanding of how to get there. Here is the problem..
Assuming that no one has a matching card, what are the chances the board will pair on the flop? Then what is the chance, if the flop has a pair.. that someone at the table has made a set... and does the number of players at the table make a difference?

This came up because yesterday I was plaqued with catching top pair... but facing the flop with a pair... making me lay down my top pair when someone bet hard at the pot.

Please explain how you came to your numbers?

Thanks,

Jack

[Cornell Fiji]

You might do better moving this post to the probability forum.

[slickterp]

for starters, assuming no ne has the matching card to any on the flop, then it's 9/(49-total # hole cards). so the chances do depend on how many people.

[TommyO]

Which is why it is crucial to raise pre-flop with big cards to minimize the chances that someone flopped trips.