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  • ROI Question

    Hello,

    I've been struggling with a seemingly simple ROI problem and would like someone else's opinion. The situation is as follows:

    You have $27 and are faced with a multiple choice question containing 4 choices and 1 correct answer. If you win, you get $82. If you lose, you lose $19.50 of your $27 leaving you with $7.50.

    Initially I came up with the following answer:

    You have a 25% chance to get the correct answer giving you 3:1 odds. You will lose 27*4 = 108 in buyins (attempts) but gain 7.5 *3 + 82 = 104.5. This gives you an ROI = ((104.5 - 108)/108)*100 ~= -3.24%

    However, I later thought about it in this way:

    You gain $55 once but lose 19.5*3 = 58.5. This gives you an ROI = ((55-58.5)/58.5)*100 ~= -5.98%.

    My question is, which way of thinking is correct? It's -ve ROI either way but it's nice to know how much you will be in the hole long term if you decide to go for it.

    Thanks in advance
    4 Time Bracelet Winner



  • #2
    You lose only $19.5 not your entire $27. If you win you net $62.5 (82 - 19.5).

    Play 400 times you will have net winnings of $6250 and entry cost of $7800 so you have a net loss $1550.

    This makes your ROI = -1550 / 7800 = -19.9%

    Comment


    • #3
      Originally posted by TrumpinJoe View Post
      You lose only $19.5 not your entire $27. If you win you net $62.5 (82 - 19.5).

      Play 400 times you will have net winnings of $6250 and entry cost of $7800 so you have a net loss $1550.

      This makes your ROI = -1550 / 7800 = -19.9%
      Sorry for the confusion but in this particular case, you always wager your whole $27. However, if you lose, you get $7.50 of it back. If you win you get $82. I know it's not normal to get anything if you lose, but this is an exception. So if you lose, you lose a net 19.50 but if you win, you gain a net $55 from your original $27 wager.

      Herein lies my confusion. Do I count my $7.50 winnings (example 1) from wagering the $27 or do I just count my $19.50 loss (example 2)? It will make a difference in figuring out your actual ROI.

      Also, the number of times you run it won't change the ROI as long as it's a product of 4, as the ratio will remain the same.

      Thanks for your initial response
      4 Time Bracelet Winner


      Comment


      • #4
        Essentially you are investing $19.5 to win $74.5 with the odds 3:1 against.

        You average winning $18.63 each trial at a cost of $19.5 which equates to a net loss of $0.88 per trial.

        ROI -.88 / 19.5 = -4.5%

        Comment


        • #5
          Thanks for the reply. Your response led me to do some more digging and I was thinking about the problem in the wrong way. I should have been thinking EV, as ROI is what did happen and I'm trying to figure out what I can expect long term. I am in fact losing on average $0.875 per trial for an expected loss of ~4.5%.

          As for my ROI, I wouldn't know until I actually placed the bets.

          Thanks again
          4 Time Bracelet Winner


          Comment


          • #6
            Try looking at it in terms of money instead of percentages.. Evey 4 trials you lose $3.50 (profit 55 once, lose 19.50 three times or 58.50) so EV of -87.5¢ per trial. Of course this is assuming you dont know the answer to any of the questions.
            May the tinfoil protect you. MT

            Comment

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