Re: Can someone explain me how to determine the % on a straight draw?
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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%
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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.
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then I have to hit the remaining card:
4/46 = 8,7%
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8/46 = 17.4%.
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then I multiply 17% x 8,7% = 1,48%
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17% x 17.4% = 2.96%
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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%
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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%.
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The correct number should be 4%, so where is the mistake?
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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%.
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