Can someone explain me how to determine the % on a straight draw?

[Shandrax]

Let us assume hole-cards + flop give me 5-6-7. What are my chances to complete the straight on the river?

This is what I have tried so far:
4/47 = 8,5%

now I can hit the upper or the lower end of my straight:

8,5% x 2 = 17%

then I have to hit the remaining card:

4/46 = 8,7%

then I multiply 17% x 8,7% = 1,48%

in the end I double that because I have two ways to hit my cards. Like 9-8 and 8-9 for example.

1,48% x 2 = 2,96%

The correct number should be 4%, so where is the mistake?

[LetYouDown]

I don't like the approach...so I stopped looking at the math almost immediately. Are you remembering 3-4, 4-8 and 8-9 count for you?

47 C 2 combinations remain for turn/river.

There are 16 combinations each of 3-4, 4-8 and 8-9...for a total of 48. 48/1081 = 4.4%.

[BruceZ]

[ QUOTE ]
Let us assume hole-cards + flop give me 5-6-7. What are my chances to complete the straight on the river?

This is what I have tried so far:
4/47 = 8,5%

now I can hit the upper or the lower end of my straight:

8,5% x 2 = 17%

[/ QUOTE ]

You can hit both the upper and lower end by the river, and this possibility is getting double counted when you multiply by 2 here, and then multiply by 2 again at the end of the calculation.


[ QUOTE ]
then I have to hit the remaining card:

4/46 = 8,7%

[/ QUOTE ]

8/46 = 17.4%.


[ QUOTE ]
then I multiply 17% x 8,7% = 1,48%

[/ QUOTE ]

17% x 17.4% = 2.96%


[ QUOTE ]
in the end I double that because I have two ways to hit my cards. Like 9-8 and 8-9 for example.

1.48% x 2 = 2.96%


[/ QUOTE ]

2.96% x 2 = 5.92%

Now we must subtract off the probability of 48 or 84 that got double counted.

5.92% - (8/47)x(4/46) = 4.4%.


[ QUOTE ]
The correct number should be 4%, so where is the mistake?

[/ QUOTE ]

Here is how I'd do it. The possible 2 card combinations that make a straight are 34, 48, or 89. Each of these has the same probability, and they are mutually exclusive, so the total probability is 3 times the probabilty of any one of these, or:

3*(8/47)*(4/46) = 4.4%.

[Cobra]

Here is another way at looking at the problem.

Case one you get a 4 or 8 on the turn, there is 8 outs and 47 cards. = 8/47 = 17.02%

Case two you get a 3 or 9 on the turn, there is 8 outs and 47 cards. = 8/47 = 17.02%

Now in case one you now have an open ended straight you can get a straight by hitting either a 3 or 9, so the chances of getting a straight are 8/46 = 17.39%

Now in case two you have a gut shot straight draw, you can get a straight by hitting only one specific card, the chances of getting a straight are 4/46 = 8.7%

With this information we will find the chance of getting a straight is

= 17.02% * 17.39% + 17.02% * 8.7% = 4.44% same answer as the combination technique.

Cobra

[Shandrax]

Cool, thanks.

Btw, I have really forgotten about 4-8....silly /images/graemlins/smile.gif