How often do you flop mid pair with A9?

[SteveY]

Hey guys, I was wondering about the ? I asked in the topic /images/graemlins/tongue.gif

I thought I knew this, but unfortunately have run into trouble. I thought it would go something like this:

Possible Flop Combinations:
9OU
9UO
O9U
OU9
UO9
U9O

And you just go well I'll find the probabilites for all of these scenarios and add them up. But I'm deathly confused to say the least /images/graemlins/frown.gif

[BruceZ]

[ QUOTE ]
Hey guys, I was wondering about the ? I asked in the topic /images/graemlins/tongue.gif

I thought I knew this, but unfortunately have run into trouble. I thought it would go something like this:

Possible Flop Combinations:
9OU
9UO
O9U
OU9
UO9
U9O

And you just go well I'll find the probabilites for all of these scenarios and add them up. But I'm deathly confused to say the least /images/graemlins/frown.gif

[/ QUOTE ]

That's fine. There are 3 nines, 16 Os (4 each of T,J,Q,K), and 28 Us (4 each of 2,3,4,5,6,7,8). So the total number of ways to make 9OU in that order is 3*16*28. Now, the probabilities for each of these 6 arrangements are the same, so multiply this by 6 to get 3*16*28*6. Then divide this by the total ways the 3 flop cards can come, which is 50*49*48. This gives a probability of 3*16*28*6/(50*49*48) = 6.9% or 1 in 14.6.

[SteveY]

awesome! thanks /images/graemlins/smile.gif