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EV Calculations without calculator.

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  • EV Calculations without calculator.

    Say if someone offered you a deck of cards and it cost you $1 to draw if you hit an ace you get paid $5 and if you hit the ace of spades you get $20.

    So it would be:

    3/52 = (3x100)/52 = 6r12/100 = 0.06 - 0.012 = 0.057
    1/52 = (1x100)/52 = 2r4/100 = 0.02 - 0.004 = 0.016
    48/52 = (48x10)/52 = 9r12/10 = 0.90 - 0.012 = 0.88

    0.057 x 5 = (0.057x1000) x 5 = 285/1000 = 0.28
    0.016 x 20 = (0.016x1000) x 20 = 320/1000 = 0.32
    0.88 x -1 = (0.88x100) x -1 = -88/100 =-0.88

    -0.88 + 0.32 + 0.28 = -0.28

    So your EV is -0.28.

    The percentages only add up to about 95% so i'm doing something wrong also is there an easier way of doing this in your head maybe using ratios or fractions? I don't know any other methods of dividing small numbers by big numbers other than multiplying and dividing which takes me a while without a calculator.

    Any advice is appreciated.
    Last edited by Guyguyson; Wed Dec 19, 2012, 07:18 PM. Reason: Can't keep the equations in line for some reason, sorry if it's annoying to read.

  • #2
    Hi Guyguyson!

    3 of 52 times you will win $4 ($5-$1 entry fee)
    1 of 52 times you will win $19
    48 of 52 times I lose $1

    .231+.365-.923=-.327 so I expect to lose 32.7 cents each time

    John (JWK24)
    Super-Moderator



    6 Time Bracelet Winner


    Comment


    • #3
      How did you get those numbers? I get 0.285 + 0.38 + -0.923 = -0.265 on a calculator for an expected value of -26.5 cents?

      Comment


      • #4
        (3/52)*$4=.231
        (1/52)*$19=.365
        (48/52)*(-$1)=(-.923)

        add those three up and you get -.327 which is an expected loss of 32.7 cents.

        I think you're forgetting to take off the $1 entry when you win. if you get paid $5... really, it's a $4 gain, as it costs you $1 to try. Same with the $20 return (it's really $19 due to the entry fee of $1).

        John (JWK24)
        Super-Moderator



        6 Time Bracelet Winner


        Comment


        • #5
          In the book Poker math that matters he doesn't take off the entry fee.
          If we do something simpler like the classic coin-flip and say you bet $1 to win $2 then doing it the way the book says it's:

          0.5*2 = 1
          0.5*-1= -0.5
          = +50 cents

          In the theory of poker he gives the same example and the EV is +50 cents if I take off the entry fee it would be:

          0.5*1=0.5
          0.5*-1=-0.5
          = 0

          So I don't get what i'm missing? Do you only have to take off the entry fee if there's more than two outcomes?

          Comment


          • #6
            Hate bumping but I need to know if i'm doing EV calculations right. I'm not great at maths so sorry if JWK24 method should be easy to apply to the coinflip example. If someone could workout the coinflip example again it would help me see where i'm going wrong.

            Comment


            • #7
              I'm not sure what book you're using... but the entry price absolutely must be taken into account.

              a coin flip where it costs $1 each and you win $2 has an EV of ZERO.

              John (JWK24)
              Super-Moderator



              6 Time Bracelet Winner


              Comment


              • #8
                Say you flip the coin 100 times and it hits heads 50 times and tails 50 times you would lose $1 50 times and win 2$ 50 times for a profit of $50 how can that have an EV of 0?

                Or did you think I meant you both put in $1 so the pool is 2$ Because that would be 0 EV you would just be trading back each others $1 stake. What i'm saying is you wager 1$ and if you win you get your stake which was one $1 plus another $1 if you lose you just lose your $1 stake.
                Last edited by Guyguyson; Sat Dec 22, 2012, 07:15 PM.

                Comment


                • #9
                  then you get $3 each time you win (if you want to end up with an EV of 50).... you have to take the entry price into account.

                  if each flip costs the same and the payout is 2X the buy-in, a coin flip has an EV of ZERO.

                  John (JWK24)
                  Super-Moderator



                  6 Time Bracelet Winner


                  Comment


                  • #10
                    Originally posted by Guyguyson View Post
                    Say you flip the coin 100 times and it hits heads 50 times and tails 50 times you would lose $1 50 times and win 2$ 50 times for a profit of $50 how can that have an EV of 0?

                    Or did you think I meant you both put in $1 so the pool is 2$ Because that would be 0 EV you would just be trading back each others $1 stake. What i'm saying is you wager 1$ and if you win you get your stake which was one $1 plus another $1 if you lose you just lose your $1 stake.

                    You must ADD your LOSS to your PROFIT

                    You are not doing this.

                    3 Time Bracelet Winner


                    Comment


                    • #11
                      Originally posted by Bill Curran View Post
                      You must ADD your LOSS to your PROFIT

                      You are not doing this.

                      Flip coin 100 times lose 50 times (-50) win 50 times (+100)

                      -50 + 100 = 50.
                      or
                      -100 + 100= 0

                      Or lets do this with pot odds.

                      Hero: 78s
                      Villan: AKo

                      Flop: Ah,4s,Js

                      Pot: 400 villan bets 100 = 500.
                      Pot: odds 5:1
                      Chance of improving: 4.2:1
                      Instant call.

                      .18*500=90
                      .82*-100= -82
                      = +8

                      If we do it your way:

                      Hero: 78s
                      Villan: AKo

                      Flop: Ah,4s,Js

                      Pot: 400 villan bets 100
                      Pot: odds 4:1 (-100 entry fee)
                      Chance of improving: 4.2:1
                      Instant fold.

                      0.18*400 (-100 entry fee)= 72
                      0.82*-100 = -82
                      = -10
                      Last edited by Guyguyson; Sat Dec 22, 2012, 08:47 PM.

                      Comment


                      • #12
                        You are totally missing the point about my last reply: You toss a coin 100 times...........OK 50 times are tails, you lose ......... = -$50 + $0 = (-$50) 50 times are heads, you win ......... = -$50 + $100 = (+$50) On each line, first number is cost to you, second number is your win, third number is your profit. overall Profit = (-$50) + (+$50) = $0 Hope this makes it clearer ? umbup:
                        3 Time Bracelet Winner


                        Comment


                        • #13
                          using the 78s scenario...

                          pot was 400, opp bet 100.. my pot equity is 100 (what I have to put in) / 600 (what pot will be once my chips are in it) = 16.7%

                          I have 9 outs, so my hand equity is 9 (number of outs) * 2% per out = 18%

                          so it's a call.

                          to get the EV...

                          78s on the flop has 35.275% equity from pokerstove.

                          .35275 * 600 = 211.65 chips on avg gained when I win the pot
                          .64725 * -100 = -64.725 chips from the call when I lose the pot
                          EV on the call is 211.65 - 64.275 = +147.375 chip EV from the call

                          John (JWK24)
                          Super-Moderator



                          6 Time Bracelet Winner


                          Comment


                          • #14
                            Guyguyson: you don't win $2 when you hit the coin -you only win $1.

                            Look at it this way: you flip twice and invest $2 to do so.
                            You win once, lose once, for a total payout of $2.

                            In the end, you didn't win.

                            If your math was right, and the flip would be +EV for 50 cts, then I would be winning money simply by not playing poker at all....
                            The Road to Fame and Fortune - Keeping track of my poker semi-career
                            Keep up to date: @Ov3rsight


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                            • #15
                              Originally posted by JWK24 View Post
                              using the 78s scenario...

                              pot was 400, opp bet 100.. my pot equity is 100 (what I have to put in) / 600 (what pot will be once my chips are in it) = 16.7%

                              I have 9 outs, so my hand equity is 9 (number of outs) * 2% per out = 18%

                              so it's a call.

                              to get the EV...

                              78s on the flop has 35.275% equity from pokerstove.

                              .35275 * 600 = 211.65 chips on avg gained when I win the pot
                              .64725 * -100 = -64.725 chips from the call when I lose the pot
                              EV on the call is 211.65 - 64.275 = +147.375 chip EV from the call

                              John (JWK24)
                              But you never took away your entry fee in the EV calculation...?

                              Comment

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