Odds of a pat straight flush

• Super Moderator
Super Moderator
Joined: 02.09.2010
According to this, http://poker.sportinglife.com/Strategies/story_55895.shtml it is 1 in 72,193

Can someone confirm that?
I figured it had to be a lot more rare than that.

Assume you have any card.
The odds that the next one is one of the other 4 that match is 4/51
The odds of the 3rd one being one of the remaining 3 is 3/50
and so on.

So it seems to me that the odds of being dealt a pat straight flush would be:
4/51 * 3/50 * 2/49 * 1/48
This is 0.0000040016
or 249,899 to 1.

Am I figuring this correctly?
If not, how do you do this properly?

The reason this came up is that I was dealt a pat straight flush tonight playing 5-Card draw.

What is even more amazing is that on two other occasions, I was dealt a 4-card straight flush -- and I think I've only ever seen a couple of those before.
• 6 replies
• Bronze
Joined: 24.09.2010
You are calculating for a specific straight flush, really.

Hopefully the following logic will make sense written out the way it does in my head:

If you have one card, there's 8 cards that can keep you drawing towards a straight flush.

If the next is connecting on either side, that leaves 6.

If the next again connects, keeping you on a OESFD every street, you have 4

Final card to be dealt you have 2.

This should open up significantly, if you somehow magically dodge at any point being gutshotting.

Your odds hold true for a steel wheel or a royal flush, where you are limited to an exact five cards of any suit locked to 4 possible cards once the first has been dealt determining suit.
• Super Moderator
Super Moderator
Joined: 02.09.2010
OK, I found the "real" answer, which makes total sense.
There are 2598960 possible 5-card hands.
You can do this in Excel -- the formula is =COMBIN(52,5) or the number of 5-card combinations taken from 52.

40 of those are straight flushes (including the royals): 4 suits whose lowest card is A through T.

So 40/2598960 (0.000015391) of the possible hands are straight flushes.
which works out to 64973:1 which is much closer to the first link, which still appears wrong. Formula is: (1-n)/n n in this case is 0.000015391
• Bronze
Joined: 29.08.2010
40 / C(52,5) is for straight flush
4 / C(52,5) is for Royal flush
36 / C(52,5) if for non-Royal straight flush

10 sequences of straights (A2345-AKQJT) in 4 colours (4x10=40)

It's so simple plz don't complicate this
• Super Moderator
Super Moderator
Joined: 02.09.2010
Originally posted by Huricano
It's so simple plz don't complicate this
Well, it is only simple once you understand the principles.
Until now, I had never done much with probability in any math course I ever took.
• Bronze
Joined: 29.08.2010
Originally posted by VorpalF2F
Originally posted by Huricano
It's so simple plz don't complicate this
Well, it is only simple once you understand the principles.
Until now, I had never done much with probability in any math course I ever took.
I was also sucking at math until I started playing 5CD which is all about mathematic.
AFAIR even some math professor (can't remember his nickname hmmm... ) have problems with 5cd math.

I'm just saying that you're complicating by trying to solve it this way:
4/51 * 3/50 * 2/49 * 1/48

when it's better to count this on fingers lol

//sorry for english

Post more about 5cd (if you still playing/enjoy it) so maybe we get more players in disscusion/play.
• Super Moderator
Super Moderator
Joined: 02.09.2010
Originally posted by Huricano
when it's better to count this on fingers lol

//sorry for english

Post more about 5cd (if you still playing/enjoy it) so maybe we get more players in disscusion/play.
I didn't know about the combin(n,m) function in Excel at all, but after I read about combinations/permutations, it just makes sense.