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Similarly, if I state my goal is either to double my money or go bust on just-dice, the chance that I double my money with one bet is 49.5%. If I bet 1/10th of that on the same bet until I either double my money or go bust, the chance is higher I go bust (not going to waste my time in R to tell you the odds...)
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This is what I plan on doing. Figuring the odds for a given gain using martingale. For the same risk I'm sure it is less than making a single bet. The math is not easy. I've done simulations and the probability distribution function is complicated. I'm going to use the simulation to figure the odds.
I stated before that I thought that martingale had a smaller expected value than a single bet. That thinking was not only wrong but the utility of EV for what I'm trying to show isn't even correct.
Here is what is correct. The expected profit = -(house edge)*sum(every bet). This is true no mater what bet sequence you use.
Betting on the house side is the way to have a positive profit.
What exactly do you mean by "expected profit"? How exactly are you calculating it? Is it the expected profit per sequence or per roll? The expected value is a weighted average - what are your weightings and their associated probabilities?
Not hassling, just interested - you haven't provided enough information for me to know what you mean.