Probability of your opponent hitting TOP pair

[That guy]

Say you have a pocket pair (say deuces for the purposes of this) and it has been folded to you in the Small Blind...

Say you raise and your opponent in the BB calls...

I know that any unpaired cards will pair the flop (or better) ~1/3 of the time...

My question is, what is the % chance your opponent hit TOP pair??? How can you estimate this?? Also, how often will he hit 2nd pair...

This is just to get a general idea of this...

[gaming_mouse]

Well, let's assume he'll call your steal raise with any 2 -- which isn't such a far-fetched assumption. In that case, assuming that the board does not pair, there are exactly 3 cards that match the top board card. If you do not hold any of them yourself, then there are 47 unseen cards left.

1 - (44 choose 2)/(47 choose 2) = 0.124884366

About 12%

[binions]

You are 29% to flop one pair with any unpaired starting hand. (You are ~3.5% to flop 2 pair or better, depending on if you are suited or connected).

Since there are 3 cards on the flop, on AVERAGE, one-third of that 29%, you will flop top pair.

Now, 32 can never flop top pair, and if AK flops one pair, it will always be top pair, so the answer is highly hand dependent.

[That guy]

ok, so call it a ~12% chance to hit top pair and another 12% chance to hit 2nd pair and a few percent to hit 2 pair (assuming starting hand is unpaired)... and a small percent (on average using a random hand) to have some kind of flopped straight or flush...

essentially, its 3-1 for all of that and 2.5-1 if you include bottom pair...

[Cobra]

Lets say the board comes JT5.

The probability your opponent holds:
A J or T, A J and T, or Two J's or T's is

=6*41+combin(6,2)/combin(47,2) = 24.1% or 1 in 4.1

The probability your opponent holds:
A J or T, any two pair, any set is:

=6*41+combin(9,2)/combin(47,2) = 26.1% or 1 in 3.8

The probability your opponent holds:
A J or T or 5, any two pair, any set

=9*38+combin(9,2)/combin(47,2) = 35.0% or 1 in 2.9

If the board comes three to a suit add the following

You have one of the suit = 3.3%
You don't have one of the suits = 4.2%

If the board allows a strt the chance your opponent holds those random cards is = 1.5 %

Cobra