Quote:
Originally Posted by whosnext
At the risk of beating a dead horse, the number of hands that make a flush, excluding royal or straight flushes, in 7-card stud (or 1-player hold-em) is, I think, given by:
4*{C(13,7)+C(13,6)*C(39,1)+C(13,5)*C(39,2)-[C(5,5)*C(47,2)+9*C(5,5)*C(46,2)]}
which, if I evaluated this correctly, is 4,047,644, the number also given by the Wizard.
Of course there are C(52,7)=133,784,560 total deals possible.
So the true exact fraction is pretty well known at this point.
Thank you for taking your time and thank you for answering my question (and thanks to the OP also).
The reason why I posted my previous post was: After I read this thread for the first time, I went checking and googling, because I was curious why has royal flush higher accourance probability than other straight flushes –make sense now that I know… Then I find the table that has slightly different numbers that OP calculated and I was curious why is that… so posted table here and waited for explanation… now I know..
…
Now, I checked your calculations (also checked almost every possible site that I could find on the internet that has calculated flush probability and result is allways the same;like yours and OP; so correct)…..also makes sense that probability numbers at holdem are the same as 7 card stud…
I have some other question….I do not understand why are some things in the way they are.... I mean yes, I can calculate this, if I found method somewhere(for example here), but it is important for me that I understand exactly why results are in the way they are….so....
This is from wikipedia:
I Quote:
»The Ace-high straight flush or royal flush is slightly more frequent (4324) than the lower straight flushes (4140 each) because the remaining two cards can have any value; a King-high straight flush, for example, cannot have the Ace of its suit in the hand (as that would make it ace-high instead).«
All nine (not royal flush) straight flushes has 4140 each….? All together this is 37,260 as required…..
This is what I expected before reading mentioned quote from wikipedia: same number for 8 non-royal straight flushes… expect from A to 5 straight flush…
Why is A to 5 straight flush same frequent as the other 8 non-royal straight flushes (it is »blocked« down)? Simple and logical explanation? You people can probably explain this faster than I would figure it out (I do not want to lose one week to figure it out why some calculations ended in the way they do
)..
I hope you understand what I am asking... Since I am allready on this forum, I would like to learn the most I can (and the fastest). Thank you for answers in advance.
Last edited by blackspoker; 08-11-2017 at 06:12 AM.