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What is a the probability of getting a straight flush with 54s? What is a the probability of getting a straight flush with 54s?

06-05-2018 , 06:02 AM
What is a the probability of getting a straight flush with 54s in Texas Holdem? both hold cards must be used

and also what is probability with hands like 68s (3way getting a straight flush), 69s (2way), 6Ts (1 way)?
What is a the probability of getting a straight flush with 54s? Quote
06-05-2018 , 01:44 PM
Given 45s to TJs, the probability of flopping a straight flush is

4*/Combin(50,3) = 0.02%.

For 45s, 4 is the number of successful combos, namely A23, 236, 367 and 678, all of the required suit.

For a straight flush by the river with middle suited connectors, the probabiliity is 0.19% using the same general thinking but being careful not to include duplicate entries and insuring the both hole cards form the SF.

For 6Ts, the SF flop probability is

1/C(50,3) = 0.005%

By the river, you have to exclude J of the suit so both hole cards are used.

Prob = 1*C(46,2)/C(50,5) = 0.05%,
What is a the probability of getting a straight flush with 54s? Quote
06-06-2018 , 02:49 AM
Do I understand correctly that formula for:
a) hands with 4 number of successfful combos (f.e. 54s, 98s) is 4*C(46,2)/C(50,5)
b) hands with 3 number of successfful combos (f.e. 64s, QTs) is 3*C(46,2)/C(50,5)
c) hands with 2 number of successfful combos (f.e. 52s, K9s) is 2*C(46,2)/C(50,5)
d) hands with 1 number of successfful combos (f.e. A2s, 73s) is 1*C(46,2)/C(50,5)?

I mean probability by the river
What is a the probability of getting a straight flush with 54s? Quote
06-06-2018 , 11:23 AM
You have to avoid double counting. For 54s, the successful outcomes are as follows: (x = excluding)

123 45 x6 Combos = 1*C(46,2)
x1 23 45 6 x7 Combos = 1*C(45,.2)
x2 3 45 67 x8 Combos = 1*C(45,.2)
x3 45 678 x9 Combos = 1*C(45,.2)
What is a the probability of getting a straight flush with 54s? Quote
06-17-2018 , 04:21 AM
Quote:
Originally Posted by mutanNZ
Do I understand correctly that formula for:
a) hands with 4 number of successfful combos (f.e. 54s, 98s) is 4*C(46,2)/C(50,5)
b) hands with 3 number of successfful combos (f.e. 64s, QTs) is 3*C(46,2)/C(50,5)
c) hands with 2 number of successfful combos (f.e. 52s, K9s) is 2*C(46,2)/C(50,5)
d) hands with 1 number of successfful combos (f.e. A2s, 73s) is 1*C(46,2)/C(50,5)?

I mean probability by the river
Yes, I think this is correct.

Quote:
Originally Posted by statmanhal
You have to avoid double counting. For 54s, the successful outcomes are as follows: (x = excluding)

123 45 x6 Combos = 1*C(46,2)
x1 23 45 6 x7 Combos = 1*C(45,.2)
x2 3 45 67 x8 Combos = 1*C(45,.2)
x3 45 678 x9 Combos = 1*C(45,.2)
I don't understand what this is saying.

It seems to me that the formulas given above by mutanNZ are correct. Am I totally misunderstanding something?

Sorry for such a late reply. This is the first time I have taken a look at this thread.
What is a the probability of getting a straight flush with 54s? Quote
06-17-2018 , 04:56 AM
I think it's 4*46C2/50C5 like mutanNZ wrote, at least for 45s. statmanhal made an error when he excludes cards for 6high, 7high and 8high straight. there is no need to exclude the bottom card, for example 6high straight flush is 23456 without 7, there is no reason why 1 should be excluded.

at least, that formula is good for cases where you need to use both of your hole cards to make a straight flush. there is an option for a 9high straight flush also.

Last edited by md46135; 06-17-2018 at 05:02 AM.
What is a the probability of getting a straight flush with 54s? Quote
06-17-2018 , 09:31 AM
Quote:
Originally Posted by md46135
I think it's 4*46C2/50C5 like mutanNZ wrote, at least for 45s. statmanhal made an error when he excludes cards for 6high, 7high and 8high straight. there is no need to exclude the bottom card, for example 6high straight flush is 23456 without 7, there is no reason why 1 should be excluded.
.
Right. Should have realized that the high card exclusions account for no duplicates.
What is a the probability of getting a straight flush with 54s? Quote

      
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