Calculating Runner Runner Outs

[jpg7n16]

I know if you have a 4-flush there are 9 outs to complete that flush and you can use that for probability and stuff. Not hard.

But how do you calculate runner-runner outs? I've never been told how to do this for part of my calculations.

I mean... I have a K7 4-flush on the flop with an A on the board. There are 9 outs to complete my flush, and then there are X - outs to get trip kings if there were runner runner kings, and X - more for runner runner 7's. How many outs is each runner runner possibility? 1 or 1/2 or something totally different?

[OatmealJoe]

[ QUOTE ]
How many outs is each runner runner possibility? 1 or 1/2 or something totally different?

[/ QUOTE ]

If you are talking about a specfic rank (i.e. King), it is probably about 1/10 an out (not very likely). If you are talking about for a backdoor flush, it is probably closer to 1 3/4 to 2 outs.

[OrianasDaad]

You've seen five out of 52 cards, 47 unknown. Your chances of catching running kings are (3/47)(2/46) = 6/2162 = 1/360 = 1:359 against. Not really enough for adding any kind of outs. It's worth about .13 outs.

Runner runner flush draws are much more worthwhile. (9/47)(8/46) = 72/2162 = 1/5 = 1:30 against. About 1.5 outs.

Runner runner straight draws are trickier, depending on how many gaps you need to fill.
Zero Gap(7,8,9) = (8/47)(8/46) = 1:33, 1.4 outs
One Gap(7,8,T) = (4/47)(8/47) = 1:66.5, 0.7 outs
Two Gap(6,8,T) = (4/47)(4/47) = 1:134, 0.23 outs.

Still fairly new to the math. Mabye someone could check my logic here.

[OrianasDaad]

Whoops.

Runner-runner flush draws are: (10/47)(9/46) = 1:23, 2 outs.

[jpg7n16]

you;re using odds to calculate outs, and I thought it was the other way around... like for example

Open ended straight draw on the flop (6,7,8,9). You have 8 outs to complete the straight (4 - 5's and 4 - 10's). Odds are (8/47)(8/46)=32/1081= 1:33.78, but that has 8 outs.

You gave the same odds of completion for an open-ended straight draw as a runner-runner open-end straight draw, but not the same amount of outs. So what makes one have more outs than the other? Why if they have the same odds does one have 8 outs and the other only 1.4?

[OrianasDaad]

Odds are just like ratios, since you are looking at flop decisions, I just translate into an X:47 ratio.

Zero Gap(7,8,9) = (8/47)(8/46) = 1:33, 1.4 outs
1:33 = X:47... X = 1.4

The probabilities have to be multiplied together for runner-runner draws because each card is required for the straight to come in. An OESD has eight outs. Since you can get it on EITHER the turn or river, you add those probabilites together. (8/47)+(8/46).

As a general rule, the only backdoor draws I add outs for are backdoor flushes and backdoor zero-gap straights.

Thinking about it, I may have gotten some of these probabilities off a little. Zero-gap straight draws have two ways of making a straight. By improving to an open-ended straight draw, and by improving to a gutshot. The correct calculation would be:

(8/47)(8/46) + (8/47)(4/46) = 1:22.3 = 2.1 outs.

I think. Since there's two ways to make the straight, then you add the two ways together. More complicated backdoor draws are possible, I suppose.

I'd ask in the probability forum, mabye. Wait, do a search first. Then ask if you can't find anything.

Hope any of this helps!