Question for the whizes.
 

When you count your outs you count single card outs. The relevent percentages can easily be calculated mentally within a fraction of a percent. But commonly other outs may also exist, multiple card outs, when two card values are needed as for a straight. Not that you would bet on runner-runner but it must increase your overall probability. Could it be calculated as a fraction of an out (eg 6 1/2 outs)? How could this be incorporated in calculating the probability of improving yor hand?

Re: Question for the whizes.
 

IIRC, SSHE says a backdoor flush and a backdoor straight with no gaps are worth about 1.5 outs on the flop. I think a 1-gap BD straight is worth 1 out, and a 2 gapper is .5 outs.

Re: Question for the whizes.
 

I don't know what IIRC, SSHE is. A one-gap straight is 4 outs assuming the filling card is live (generally unless dealer mishandles). An open ender is 8 outs. So the qustion resolves to the outs for a straight needing two cards, either a 2-gap or 1-gap with needing either end and completing a 3-flush. Thank you for responding so I must keep podering.

Re: Question for the whizes.
 

For a real example, say you have Q [img]/images/graemlins/heart.gif[/img]J [img]/images/graemlins/heart.gif[/img], and the flop comes 10 [img]/images/graemlins/spade.gif[/img]6 [img]/images/graemlins/club.gif[/img]2 [img]/images/graemlins/heart.gif[/img]. When calculating your outs, you would give yourself 6 outs for the overcards, 1.5 outs for the backdoor flush and another 1.5 out for the backdoor straight, for a total of nine outs. Of course pairing one of your overs won't always win, so you should partially discount those outs.

Re: Question for the whizes.
 

IIRC= If I recall correctly
SSHE= Small Stakes Hold 'em (by Ed Miller, et al)

Re: Question for the whizes.
 

I think I'll do some math on your example and see how well it correlates as soon as I have time. I'll post my results if you are interested.

Re: Question for the whizes.
 

I want to see if I can calculate these fractional outs and correlate the percentages with known probabilities of outs and/or see if they are significant enough to even consider.

First I will start when a 3-flush flops. You will need runner-runner suited. Is this the correct math?

(10 C 1) * (9 C 1) / (52 C 5)

Re: Question for the whizes.
 

No, it's simply (10/47)*(9/46). On the turn there are 47 unknown cards, 10 of which help your flush draw. If you hit one, there are 9 out of 46 cards on the river which complete your flush.

Re: Question for the whizes.
 

Tom, if that math is correct your chances of getting a back door flush is ~ .4% This sounds about right but I don't know. Improving a hand with 2 outs by the river from the flop is ~8.4%. so that infers a back door flush is only about .2 outs. Does that sound correct to you?

Re: Question for the whizes.
 

You're off by a decimal place, it's 4%, not .4%