Here's the basic question: I want to walk into a casino with a given bankroll and keep betting on red or black on a roulette wheel, each time betting, probably, 75% of however much money I have on hand (net of wins or losses). I plan to stop when I reach my goal or lose it all. My question is, what is the probability of reaching my goal?
Just to make my strategy clearer: Say I walk into the casino with $1,000. My 1st bet would be 75% of that, or $750. Say I win that first bet; the casino pays me, therefore, my bet back plus $750. So, now, getting ready for the 2nd bet, I have a bankroll of $1,750. My 2nd bet would be 75% of that, or $1,312.50. If I should lose that 2nd bet, then I'd be down to a bankroll of $437.50 (i.e., $1,750 - $1,312.50) , and my 3rd bet would be 75% of that, or $328.13. Etc., Etc.
I'l elaborate and define terms in the next post. I'd do so here, but if I make this first one too long, nobody will read it.