#1
|
|||
|
|||
Which is correct regarding a flush draw?
Two different sites and I quote:
[ QUOTE ] N.B. If you take two sutied cards to the river, you have a 15/1 (6.4%) chance of making a flush in your suit by then. [/ QUOTE ] [ QUOTE ] Finally for all the possibilities if you start suited and stay to see all seven cards (your two and the five board cards) the probability that you will make a flush is 5.77%. The odds against you are 16.3:1 [/ QUOTE ] Which of the above is correct, please? Also, I thought I read (and I searched for this a long time) that there was something like a 60% probability that the board could be exactly 2 suited. Can that be?? Thank you! |
#2
|
|||
|
|||
Re: Which is correct regarding a flush draw?
Question 1)
If you start with 2 suited cards then you will make a flush (or straight flush): C(11,3)*C(47,2)/C(50,5) = 8.42% = 10.9:1 against However, that includes the times that the board contains 4 or 5 of your suit which you generally would not prefer. The probability of making exactly a 5 card flush (or straight flush) is: C(11,3)*C(39,2)/C(50,5) = 5.77% = 16.3:1 against Question 2) Not sure what you mean by "exactly 2 suited". Can you give an example? Lost Wages |
#3
|
|||
|
|||
Re: Which is correct regarding a flush draw?
I'm pretty sure the second one is correct. I just remember hearing that you make the flush slightly less than 6% of the time.
|
#4
|
|||
|
|||
Re: Which is correct regarding a flush draw?
5.77% is the chance of having a board with EXACTLY 3 of your suit.
6.4% is the chance of EXACTLY 3 OR EXACTLY 4. Lost wages gives the correct calculation for having a flush made any way at all (including a str8 flush). gm EDIT: Actually, LostWages calculation is not quite right for making a flush any way at all. It counts certain hands multiple times. The correct answer is 6.4%, because having a board of 5 suited cards does not even affect the calculation by as much as 1 digit. |
#5
|
|||
|
|||
Re: Which is correct regarding a flush draw?
Dave,
In case you want to see the math, here it is: ncr(11,3)*ncr(39,2)/ncr(50,5)=.0577 (EXACTLY 3) ncr(11,4)*ncr(39,1)/ncr(50,5)=.0060 (EXACTLY 4) ncr(11,5)/ncr(50,5)=.0002 (EXACTLY 5) Add them all together for the final answer, which is about 6.4% gm |
#6
|
|||
|
|||
Re: Which is correct regarding a flush draw?
Good catch, I fudged it.
Lost Wages |
#7
|
|||
|
|||
Re: Which is correct regarding a flush draw?
Thanx for your help!
By 2 suited, I meant two and ONLY two suits on the board, i.e. 2 diamonds and 3 spades, 4 hearts and 1 club, etc. |
#8
|
|||
|
|||
Re: Which is correct regarding a flush draw?
Yes, I absolutely wanted to see the math. Thank you very much!
|
#9
|
|||
|
|||
Re: Which is correct regarding a flush draw?
[ QUOTE ]
By 2 suited, I meant two and ONLY two suits on the board, i.e. 2 diamonds and 3 spades, 4 hearts and 1 club, etc. [/ QUOTE ] ncr(4,2)* (ncr(13,1)*ncr(13,4)*2 + ncr(13,2)*ncr(13,3)*2)/ncr(52,5) This works out to 14.5%. So yes, the 60% is way off. gm |
|
|