Originally Posted by Bucko

capt_blunder:

Your calculation agrees with them.

They broke their calculation out by probability of getting a set, quads, and a FH. Adding all of theirs together gets the same probability that you got.

Here's an easy way to calculate this -- open an Excel spreadsheet and use the COMBIN function:

The total number of combinations of flops is COMBIN(50,3) (read 50 choose 3) or 19600. For your calculation there are 2 cards that create a set. You are interested in the number of combinations that will give a set. That is given by multiplying the number of cards of interest, COMBIN(2,1), by the number of cards that aren't interesting, COMBIN(48,2). That gives a total of 1128 combinations that gives you exactly a set. Dividing by the total number of possible hands gives a probability of .1152 or 11.52% chance of getting exactly a set.

Quads are done the same way:

Combin(2,2)*Combin(48,1)/Combin(50,3) = .002449 or .2449% chance of quads when holding a PP.

Adding the 2 numbers gives 0.11755, which is your answer when rounded.

What the web page where you got your answers did is break out the set, quad, and FH probabilities (FH probabilities are a little different, in that it can be made 2 ways -- 1 of your pair + another pair or trips on the flop. I can break things down further if you're interested). Your answer has any of the above in one number.

[Edit: Last line should read: Your answer has the set, quad, and the version of FH where 1 of your PP + another pair on the flop in it. The FH where you get a different trip on the flop is not in your calculations.]