So why does runner runner straight count as 1.5 outs?

[Yads]

I was thinking about this last night. Why are runner runner straights even counted as outs? They complete 1.5% of the time compared to backdoor flushes which complete 4% of the time. So why do we give them the same number of outs? I think I'm going to stop counting runner runner straights as outs unless the decision is really close to call and I do have a runner runner straight possiblity.

[davelin]

Funny, I was thinking the same thing a week or two ago.

[cold_cash]

[ QUOTE ]
I think I'm going to stop counting runner runner straights as outs unless the decision is really close to call and I do have a runner runner straight possiblity.


[/ QUOTE ]

When else have you been doing it?

[DrBob]

Your math is wrong. 3-to-a-straight comes in 4.4% as long as it's open on both sides for 2 cards, e.g. QJT but not KQJ. If the turn card is adjacent (8 cards) you have 8 outs for the river. If the first card gives you a gutshot (8 cards) you have 4 outs for the river. This is a total of 8*8+8*4 possibilities, out of 47*46 total possibilities.

[Yads]

Ahh interesting point. I guess you should only count 3 to straight as runner runner candidates. Thanks DrBob.

[DrBob]

You're very welcome. Yup, things like QJ9, etc., should get fewer outs.

[77rules]

[ QUOTE ]
You're very welcome. Yup, things like QJ9, etc., should get fewer outs.

[/ QUOTE ]
In SSH, not all runner runner str8s are counted as 1.5 outs, only the 3 in a row. If I'm not mistaken, a two gapper is only counted as 0.5 outs.

[DrBob]

That sounds right. A 2-gapper would have 8*4 ways, versus the 8*8+8*4 ways for the original case. This is 1/3 the chance, so going from 1.5 to 0.5 outs is logical.

[meep_42]

Someone did the algebra for this a couple days ago, here's my attempt at a recreation:



With 3 connected cards (567, TJQ, etc):
You have 8 cards that give you an OESD (4/8 or 9/K)(8 outs)
You have 8 cards that give you a gutshot (3/9 or 8/A) (4 outs)
Or, a 17% chance at having 8 outs = 1.36 outs plus a 17% chace at 4 outs = .68 = ~2, discounted to 1.5

With 1-gapped cards (467, 9JQ, etc)
You have 4 cards that make an OESD (a 5 or T) (8 outs)
You have 8 cards that give a gutshot (a 3/8 or 8/K)(4 outs)
8.5% * 8 outs + 17% * 4 outs = .68 + .68 = 1.36 outs, discounted to 1

With 2-gapped cards (367, 8JQ, etc) (or two single-gapped cards like 357 or 8TQ):
You have 8 cards that give you a gutshot (4 outs)
17% * 4 outs = .68, discounted to .5 outs

I could have sworn the math I saw was cleaner, but that's about the gist of it.

-d