calculate odds

  • 1 reply
    • VorpalF2F
      VorpalF2F
      Super Moderator
      Super Moderator
      Joined: 02.09.2010 Posts: 8,904
      Disclaimer:

      I am not a mathematician, but I pretend well.

      You are already part way there.

      From flop to turn, you have n outs, and there are 47 cards you don't know.
      So the chance of hitting one of them is n/47.

      The chance of missing all of them is 1 - (n/47)


      From the turn to the river (assuming you missed going from flop to turn):
      You still have n outs, but now there are only 46 unknown cards, so the chance of hitting one of them is n/46.

      The chance of missing all of them is 1- (n/46)

      The chance of missing all of them both times is:
      (1-n/47) * (1-n/46)

      And the chance of hitting any out from flop to river is:
      1 - ((1-n/47) * (1-n/46))

      This is beginning to look ugly.
      Let's use a standard 9-out flush draw.

      9/47 = 0.191
      9/46 = 0.196

      Chance of missing on the flop: 1 - 0.191 = 0.809
      Chance of missing on the turn: 1- 0.196 = 0.804
      Chance of missing both times: = 0.809 * 0.804 = 0.650
      Chance of hitting on one of the streets: 1 - 0.650 or 0.35

      Notice I said "chance of" each time.
      "Odds" is the ratio of chance of missing of to chance of hitting

      so the odds of hitting at least one of your outs on two streets is:
      0.65/0.35 : 1 or 1.85:1 against.

      I hope that helped.

      If not, have a look at:
      http://www.pokerstrategy.com/strategy/bss/1563/1/


      Best of luck,
      --VS