Odds of straight flush w/ T9s?

[SlyAK]

A little embarrassed to post this as I should be smart enough to figure it out myself. The other night I had T /images/graemlins/spade.gif 9 /images/graemlins/spade.gif and flopped a straight flush, what are the odds of this???


Obviously there are 6/50 unknown cards that can keep the hope of the flopped str8 flush alive on the first card of the flop, (6,7,8,J,Q,K of spades).... so odds should be 6/50 x ?/49 x ?/48..... unfortunately I cant figure it out, it seems to vary based on which card gets dealt first on the flop.

Example if Jack spades is dealt... odds of 2nd flopped card helping are 4/49... (K,Q,8,7 of spades)... However if King is dealt first, odds of 2nd floopped card helping are 2/49... (Qs or Js). This is where I am getting confused there must be some sort of summation of all these possibilities but my remedial brain cannot figure it out.

Thanks for answer/explanation.

Sly

[SumZero]

It is a counting question.

How many possible flops are there when you hold T9s? 50 choose 3 = 50!/(47!*3!) = 50*49*48/3*2 = 19,600

How many of these flops give T9s the straight flush? KQJ, QJ8, J87, 876 of the suit in question = 4

So the probability is 4/19600 which is 1/4900 or around 0.02%

[SlyAK]

Thanks, that makes sense to me now. And I was lucky enough to nearly double up off of a maniac on that hand too!!!

Sly