# Formula for RoR with ROI and Capital to investment ratio.

1. Dec 27, 2011

### An Indiot

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?