So I didn't really look into this any significant detail after my last post, but I did calculate the EV assuming the following strategy:
Play one hand of 100 units (I'm assuming table max is 100x table min). If you win, you collect your winnings and quit. If you lose, you play your 500 hands and collect your 30% loss rebate. If you push, you play another hand at 100 units until you win or lose. I modeled this last rule by simply ignoring the pushes entirely and recalculating the probabilities, starting with the win/loss combinations given
here at the WizardOfOdds website.
I found that playing this strategy will improve our EV from +0.97 units to +15.68 units, although I'm sure we can do better. Note that our improvement with this strategy is roughly 15 units, and we made a 100 unit bet, which loses about half the time, and earns a 30% rebate when it loses. I suspect that if we use a stop win equal to our stop loss for our big bets, we may see that our EV is approximately 15% of our stop. If, for example, we were flipping coins instead of playing blackjack, our EV for the big bets alone would be 0 with an equal chance of hitting either stop. The losses would be discounted 30%, so in this case our EV would be exactly 15%. The effects of our minimum bet grind portion of this play become relatively insignificant compared to the 100 unit bets, so I think we can ignore those when it comes to figuring out the optimal strategy.
As far as bankroll, the results of our big bet will dominate our overall result, and our edge is about 15% of that bet, with very roughly the same variance associated with one hand of 100 units. If your bankroll is such that you are comfortable betting 100 units on a single hand of blackjack with a 15% edge, you should be comfortable with this first draft strategy.
Can anyone point me toward something to tell me how to figure out the odds of reaching +X before -Y when flipping a coin (hitting stop win before stop loss)? I think I'm not looking for anything related to a normal distribution because we will be dealing with a small number of trials. I think binomial distribution might not be it either since the number of trials is not fixed. Any suggestions? Been a while since stats class...
I think we're getting somewhere
Edit:
I probably should explain my methodology thus far. It's nothing too sophisticated, but it does what I want it to do.
First, to calculate the value of the rebate, I calculated the EV and SD for a series of 500 bets of 1 unit. I then created a table. The first column was possible results, from about -7SD to +7SD, broken into very small chunks (0.5 units). The next column is the Z score for that result, or how many standard deviations it would be from the EV. Third, I used the NORMSDIST function. The fourth column multiplies the result (first column) by the probability (calculated from the third column). The fifth column contains an if statement that returns 70% of the fourth column if negative or 100% if positive. I then simply summed the fifth column to get the EV.
To calculate the EV of the strategy I gave above, I started with the same spreadsheet. Using the Wizard's chart for win/loss distribution, I took each of the losses, multiplied by 100 units, and added that to my starting disadvantage of -2.5 units. I then input that (negative) number in my previous spreadsheet and read the EV, given that I started at -100 units, or -200 or -800, etc. I used those conditional EVs along with the Wizard's win/loss distribution to calculate the final EV. See attachment for that final calculation.