Flop Probability

[KungFuSandwich]

Does anyone know how to figure your odds of hitting an 8 out straight draw on the flop with 67? Please tell me your formulas and reasoning. Also do your calculations include Double gutted straight draws?

Thanks [img]/images/graemlins/club.gif[/img]

[gaming_mouse]

Not sure what you mean by double gutted, but...

For open-ended straight draws only, not flopped strights:

1. 6789
2. 4567
3. 5678

How many flops will give you 1? That is, how many contain an 8 and 9 but no five or ten?

4*4*(52-2-2-4-4) =
4*4*42=672

Simalarly for 2 and 3.

So

672*3 = 2016

flops give us the 8 out straight draw.

Total number of possible flops is:

ncr(50,3)=19600

2016/19600=.1028

making you a 9 to 1 dog for the draw.

gm

[Precision1C]

1. 98x x/= T,5,9,8 4*4*36 (50-3-3-4-4) =576
2. 988 4*4*3/2=24
3. 998 =24

totals 624 for each of the 3 combinations that make non- double gut straights, 98? 85? and 65?=1872.

4. T84 4*4*4=64
5. 953 =64

So the double gut possiblity adds 128 combinations for a total of 2000. Total number of flops is C(50,3)=19,600 so the odds of flopping a 8 draw straight is 10.2%.

[Lost Wages]

1. 98x x/= T,5,9,8 4*4*36 (50-3-3-4-4) =576

Should be 4*4*34 (50-4-4-4-4) = 544
Otherwise you are correct.

Lost Wages

[KungFuSandwich]

Thanks. Thats what I got (but my work was alot longer)I just want sure it was right since its supposed to be harder to get a flush than a straight. My work said it was about one percent easier to get the flush draw and once you got the draw youd have 9 outs instead of 8. I guess it must be significantly easier to get connecting starting cards than flush cards but it seems to me that if you get an 7 [img]/images/graemlins/spade.gif[/img] then you have 8 cards that would connect and 12 [img]/images/graemlins/spade.gif[/img]s.


I guess theres just more possible straights to make, and unplayable hands like 5 9 can make straights, just not good ones.

Thanks for ya'lls help