Systems Archive 1
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Converting to Sharpe ratios or N0.
Posted by Kim Lee on 20 May 1998, at 4:07 p.m., in response to Level One Count Win Rates, posted by T-Hopper on 19 May 1998, at 2:03 a.m.
If the mean is mu and the standard deviation is sigma per 100 hands then the required bankroll is W = 10*sigma^2*ln(100)/(2*mu). The ROI is mu/W = .2*ln(100)*mu^2/sigma^2. The Sharpe ratio is mu/sigma = sqrt(ROI/.921), and Don Schlesinger's Desirability Index is 100 times this quantity. BRH's number of hands to double is N0 = 100*sigma^2/mu^2 = 92.1/ROI.
Example: The high-low double deck ROI is .00367. The Sharpe ratio is .0631, Don's Desirability Index is 6.31. Brett's N0 is 25,096.
If the Sharpe Ratio is 10% higher for an advanced system then you will win 10% betting at the same level. But you should optimally bet 10% more. Consequently you will win 1.1*1.1-1 = 21% more. The ROI already incorporates this adjustment. Thus THT wins .395/.367 = 1.076 times as much as high-low.
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