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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.
Expected profit is how much money you make on average, Total winnings - Total wagers.
I'm sorry, I'm still not getting it.
When you say "Expected profit is how much money you make on average", over what is it the average? Per roll or per sequence? Also "Total winnings - Total wagers" is not an average, it's a difference. So you've stumped me - I can't see how you're getting an average there.
Every bet will, on average, make -1% of the amount wagered. This is true no matter what the sequence. To get the total average profit just add up all the bets and multiply by -1%.
Not quite true - if you look a few posts above I derived the expected profit for both an unbounded and a bounded martingale sequence without house edge and it's not the sum of all bets, which is what I think you're saying it would be if there was no house edge.