The following spreadsheet extends the previous loss rebate theorem Excel spreadsheet (see this post) to include the risk of ruin (ROR):

Loss_Rebate_Theorem_Full_Solution_ROR

I've also added a table giving the house edge and standard deviation for some common games. The ROR percentage assumes continuous reinvestment.

About the Author
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received his Ph.D. in Mathematics from the University of Arizona in 1983. Eliot has been a Professor of both Mathematics and Computer Science. Eliot retired from academia in 2009. Eliot Jacobson