Hi, Suboptimal88,

Can you provide a concrete example?

(please don't say "pavement"

)

I'll have a stab at what I THINK you mean:

Hole cards:

7:s5

Flop:

6:sQ:d2

So you want to know the odds of hitting EITHER the straight OR the flush by the river.

Is that correct?

There are 47 unknown cards.

10 will get us one step close to a flush, and 8 will get us one step closer to a straight.

10/47=21.3%

8/47=17.0%

So the odds of getting one step closer are 18/47 or 38.3% or 1.61:1

So we hit one, and there are now 46 unknown cards.

If we hit one of the flush outs OTT we have 9 outs to hit a flush OTR

If we hit one of the str8 outs, OTT we still have 8 outs to hit the straight OTR

So:

Odds of hitting the flush OTR (assuming we now have a four-flush):

9/46=19.6% to hit a flush if we already have one.

8/46=17.4% to hit a straight if we already have one.

So to hit a runner-runner flush the odds on the flop are:

21.3% x 19.6% = 3.7% (multiply the odds of one by the odds of the other)

Odds to hit a runner-runner straight:

17.0% x 17.4% = 3.0%

Add the two together to get the odds for both paths:

6.7%

If you really wanted something different, please let me know.

@All math whizzes:

If I totally farked that calculation, please correct me!

Cheers,

--VS