[andvanwyk]

I've been wanting to learn how to determine how often a player with a particular range flops a particular pair on a particular flop. For example: How often would a player with a 10% range(according to pokerstove) flop exactly one pair of queens on a Q84 rainbow board (so his hand can't be better or worse than a pair of queens).

My way of working this out was to work out the total combinations of cards that make up a a 10% range. In this case is 118 combinations of cards considering that board. The total number of queen combinations is 30. Therefor 30/118 = 25.4% of the time that person should have exactly a pair of queens on that flop. Is this method correct?

Total combinations of cards::
Pairs:
6 AA, 6 KK, 3 QQ, 6 JJ, 6 TT, 6 99, 3 88 = 36 pairs

Ax:
16 AK, 12 AQ, 16 AJ, 4 AJs, 4 ATs, 4 A9s = 56 Ax

Kx:
12 KQ, 4 KJs, 4 KTs = 20 Kx

Qx: 3 QJs, 3 QTs = 6 Qx


Total combinations of cards = 118

Combinations of cards containing queens:

AQ = 12
KQ = 12
QJs = 3
QTs = 3

Total combinations of cards containing Q's = 30

Another method has been suggested by bryce of stoxpoker using pokerstove. In this method you would input that board(Q84 rainbow) on pokerstove and fill out the turn and river with blank cards like 22 or 23. Then you give yourself the best hand that loses to a pair of Q's, which would be JJ, and give your opponent a 10% range and see what your winning percentage would be. In this case it would be 52%. After that you give yourself the worst hand that beats a pair of Q's, which in this case would be KK, and work out your winning percentage. In this case the answer is 86%. Then you subtract answer 2 from answer 1 and that should give you the amount of times your opponent has exactly a pair of Q's. In this case our answer is roughly 34%.

Clearly this answer is different to my answer and a 9% difference is pretty large. Can anyone tell me where my method or the pokerstove method is going wrong?