I created an Excel spread sheet that computes the optimal stopping point for a loss rebate advantage play opportunity using the Loss Rebate Theorem (LRT). You can download it free of charge (and at your own risk) by clicking here:

Loss Rebate Theorem Excel Spread Sheet

Based on the recent Revel loss rebate promotion, the default settings are for 9/6 Double Double Bonus video poker, with an 800 unit bankroll, a 100% loss rebate and a wager size of $125. The house edge is -1.019217% and the standard deviation is 6.479582.

Here is an image of the default set up. The user inputs values in the green areas. The spread sheet completes itself from there:

loss rebate optimal strategy and return


Here are the details:

  • The player is assumed to play until he loses his entire bankroll or his current bankroll equals or exceeds the win-stopping point.
  • The player has no "time threshold." He keeps playing until he hits a bankroll stop point.
  • This spread sheet will fail if the optimal win-stopping point is more than 10,000 units above the number of units in the bankroll.
  • If no advantage play is possible, the spread sheet will indicate this with a warning message.

If you want to see the LRT behave badly, try using it on video poker with a small bankroll. Then, to see how accurate it can be in good conditions, try the spread sheet using the parameters that Don Johnson negotiated:

  • House edge = -0.00290361 (-0.290361%)
  • Standard deviation = 1.1417
  • Loss rebate percent = 20%
  • Wager size = $100,000

(House edge and standard deviation from Appendix 4 at wizardofodds)

When Don Johnson played, he was required to put at least $1M in the cage. With $100k wagers, his bankroll was only 10 units. This image shows the results of the LRT for a 10 unit bankroll for the game Don Johnson played:

Game Details

With the Don Johnson parameters, try various starting bankrolls until you determine the bankroll that maximizes Don Johnson's winnings. Then compare your results to those obtained in this post and this post. Then imagine how much fun Don Johnson must have had.
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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