Probability: Three-flush to Flush

[Warik]

I know that if I have 1 card to make my flush by the turn, then the probability of hitting it on the river would be 37/9 ~ 4.11:1 (right?)

But if I flop 4 cards to a flush and need to make my flush by the river... how would that calculation work? Like this?

P(getting it on the turn) + P(getting it on the river assuming I didn't get it on the turn) + P(next two cards being of my suit)

P(turn) = 1 / (9/38 + 9/37 + 9/37 + 8/38) = 1.07083:1 (right? that seems ridiculously good to me)

If I do 1 - P(not getting any more of my suit) instead, I come up with 1.537:1 which seems right, but then I wonder how the heck I got 1.07083 before.

I'm curious about the previous calculation, but my main question is this: what if I flop only THREE cards to the flush and I need to hit the next two cards have to help my flush, how would I do that calculation?

help? [img]/images/graemlins/smile.gif[/img]