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Homework Help: Formula for RoR with ROI and Capital to investment ratio.

  1. Dec 27, 2011 #1
    Capital=All of your money.
    Investment= Portion of your money invested per unit ( day/month/hand/game)
    RoR= Odds that you will go broke
    RoR@X= Odds that your Capital will be less than Unit of Investment before reaching X.
    ROI= Return on investment, measured by percentage per unit of investment, represents your edge.
    Odds= Ratio of money invested to potential winnings.
    Equity= Portion of the potential winnings that is ours on expected value, affected by ROI. (1/2 for a coinflip 1/6 for dices etc…)
    Calculated by “Equity= Odds+ROI.Odds”

    This is only for calculating winner takes all scenarios.
    I have only figured so far formulas for situations where Capital=Investment.
    So if
    X= 2Capital
    Capital=1
    Investment=1
    ROI=3%
    Odds= ½

    Then
    First we calculate our equity
    1/2+3%/2 = 51.5%
    RoR@X= 100-51.5%= 48.5%
    So formula is
    RoR= 100%-(Equity)

    What would an appropriate formula that takes into consideration Capital to investment ratio be.
    I can only struggle to figure that there is a factor where the higher the ratio is the closer it will bring the edge to 100%:

    Following the same variables as before but:
    Equity=1/4


    Then I calculate the reverse of the equity.

    Feq= 1-1/4
    (? Is a mysterious operator)
    25%+3%?factor.Feq
    25%+ 99.999.Feq
    25%+ 99.999.3/4
    25%+ 75%
    25
    Somehow…
    My question is, what is the factor and how does it act?
    What would the formula be?
     
  2. jcsd
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