Can someone explain me how to determine the % on a straight draw?
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? |
Re: Can someone explain me how to determine the % on a straight draw?
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%. |
Re: Can someone explain me how to determine the % on a straight draw?
[ 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%. |
Re: Can someone explain me how to determine the % on a straight draw?
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 |
Re: Can someone explain me how to determine the % on a straight draw?
Cool, thanks.
Btw, I have really forgotten about 4-8....silly [img]/images/graemlins/smile.gif[/img] |
All times are GMT -4. The time now is 04:16 AM. |
Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2024, vBulletin Solutions Inc.