Odds of a pat straight flush

    • VorpalF2F
      VorpalF2F
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      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
    • fruktpuff
      fruktpuff
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      Joined: 24.09.2010 Posts: 3,982
      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.
    • VorpalF2F
      VorpalF2F
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      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
    • Huricano
      Huricano
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      Joined: 29.08.2010 Posts: 2,228
      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 :)
    • VorpalF2F
      VorpalF2F
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      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.
    • Huricano
      Huricano
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      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... :D ) 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.
    • VorpalF2F
      VorpalF2F
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      Joined: 02.09.2010 Posts: 8,904
      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.

      Your English is fine.

      I've been crawling along w/ 5CD -- I'm playing about 200 hands or so a day to relax in the evening. This help recover my ego after getting my face kicked in each day playing NL2 X(