Graph

Effect of OverHead on Risk of Ruin

by

MathProf

The following graph illustrates Risk of Ruin, given that a certain amount of oberhead F must be meet. It illustrates the Effect of different unit sizes on the Bank which is required to maintain a given level of risk r. The parameter on the horizontal axis is is ExpectedValue/OverHead (m/F), which is proportional to unit size. When this is 2, we will have our optimum unit size in the sense that our required Bank will be a minimum. On the vertical axis, we plot the required Bank, normalized so that a value of 1 represents the minimum Bank.

ROR Graph


When the betting units is large, so that EV is large relative to F, our graph is nearly linear, as it is in the classical RoR sitution, when there is no overhead. However, note that as we decrease the unti size, our required Bank levels off as we reach the optimal level and then increases percipitously thereafter. When EV=F, our required Bank is actually infinite.

The actual size of the minumum Bank is given by the following formulas:

Formulas for Optimal Bank (given Overhead) 


     Bank   =  -2 * ln(r) * F * [ s/m ] 2     

     r      =  exp (  - [ m/s ] 2 B / [ 2 * F ] )      

  where   F  =  Fixed Expenses (Overhead) in $/Hour.
          m  =  Mean Earnings ($/Hr)
          s  =  Standard Deviation
          s2  =  Variance($/Hr)

  Assumming optimal betting:   m = 2 * F



May Your Earnings Always Exceed Your Expected Value!