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Calculate straights / flush

    • sc2zerker
      sc2zerker
      Gold
      Joined: 21.12.2012 Posts: 215
      How do we caculate the chances of hitting a flush / straight with suited connects...

      For example 45s

      4 :heart: 5 :heart:

      (x)(x)(x)4 :heart: 5 :heart:( x)(x)(x) so any of the x's can give us a straight

      (A)(2)(3)4 :heart: 5 :heart:( 6)(7)(8)
      (8%)(8%)(8%)4 :heart: 5 :heart:( 8%)(8%)(8%)


      What's the % of hitting a straight on the flop, then How is the math done? For the river and turn...

      Also how would the math be done for a gapping connector, for 57s

      (x)(x)5(x)7(x)(x)
      (8%)(8%)5(8%)7(8%)(8%)

      You can clearly see with a gap, you loose 1 X but what is that in %?

      Same question for flushes.

      45s
      4 :heart: 5 :heart:
      9hearts left, 8 hearts left, 7hearts, left...
      (18%)(16%)(14%)
  • 3 replies
    • TJtheTJ
      TJtheTJ
      Bronze
      Joined: 12.10.2011 Posts: 6,588
      Hey sc2zerker,

      Sorry for the late reply!

      Calculating the odds of hitting a straight or flush is relatively simple. It just requires some probability calculations and counting.

      Say you have 87s. There are now a few ways for you to flop a straight.

      1) 4,5,6
      2) 5,6,9
      3) 6,9,T
      4) 9,T,J

      The order in which these cards come on the flop is irrelevant. Therefore, for each different board there's 4^3=64 ways to make the straight. Since there are 4 different ways to flop a straight, there are 64*4 = 256 flop combinations on which you flop a straight. There are 19,600 different flop combinations available (calculation in spoiler for reference).

      50! / (3! * (50 - 3)!) = 19,600

      50 different cards, out of which we need 3.


      Therefore, the chance of flopping a straight is 256 / 19,600 = ~1.3%

      You can apply the same theory to flopping anything else. You have to figure out how many flop combinations will give you a specific hand, and then divide that by 19,600 to find out the probability of flopping that hand.

      Hopefully that makes sense :)

      Kind regards,
      Tino
    • sc2zerker
      sc2zerker
      Gold
      Joined: 21.12.2012 Posts: 215
      incredibly useful information man, thanks a lot!
    • TJtheTJ
      TJtheTJ
      Bronze
      Joined: 12.10.2011 Posts: 6,588
      You're welcome, glad I could help! :)