How to Calculate Your Odds of Winning in Percentages

    • Optroot
      Optroot
      Bronze
      Joined: 11.05.2008 Posts: 250
      I've been looking around and this, and it seems that not many people know about this, but anyway:

      If you want your percent chance of winning from the FLOP to the RIVER (2 cards) you just multiply your outs by 4. This will give you a good approximation that's easy to do in your head.

      If you want your percent chance of winning from the TURN to the RIVER (1 card) you can just multiply by 2. Again easy to do in your head.

      Here are the formulae:

      (1 card to come)

      %Win=2*Outs
      If you want it exactly it's:
      %Win = Outs/46*100 = 100*Outs/46

      (2 cards to come)

      %Win=4*Outs
      If you want it exactly it's:
      %Win = 46*Outs/C(47,2)*100% = 2*Outs/47*100 = 200*Outs/47

      Good luck to you all :)
  • 2 replies
    • Nunki
      Nunki
      Bronze
      Joined: 25.10.2006 Posts: 865
      Originally posted by Optroot
      If you want it exactly it's:
      %Win = 46*Outs/C(47,2)*100% = 2*Outs/47*100 = 200*Outs/47


      %win =1- [(47-no. of outs)/47]*[(46- no. of outs)/46]

      eg. 15 outs ->54% (The "rule of 4" tends to slightly overestimate your win% if you got a lotta outs.
    • Optroot
      Optroot
      Bronze
      Joined: 11.05.2008 Posts: 250
      %win =1- [(47-no. of outs)/47]*[(46- no. of outs)/46]

      eg. 15 outs ->54% (The "rule of 4" tends to slightly overestimate your win% if you got a lotta outs.


      Your right but multiplying by four is easier ;) .

      If you want the exact formula you can use your equation that simplifies to:

      %win=Outs*(93-Outs)/21.62

      (too complecated to do quickly)

      In order to make the numbers easier you need to ignore the Outs^2 (too hard to do in your head) and round the numbers to 100 and 25, but then you'll wind up with the same formula. So, if you stilll want to keep it easy you can do:

      4*Outs - Outs^2/20
      which is about 3.75*Outs

      But you're absolutely right as your outs get larger the Outs^2 gets larger and larger so we can't ignore them...

      So unfortunately it works up until about 9 outs,

      here is the table of values:

      Outs | Multiply to get %
      1 | 4.26
      2 | 4.21
      3 | 4.16
      4 | 4.12
      5 | 4.07
      6 | 4.02
      7 | 3.98
      8 | 3.93
      9 | 3.89
      10 | 3.84
      11 | 3.80
      12 | 3.75
      13 | 3.70
      14 | 3.65
      15 | 3.61

      etc.

      So, unfortunately if you have more than 10 outs the easiest thing I can think of now is to multiply by 3.75, or just use the original formula.