Curious about your result. If you average over many trials are your expected winnings positive? As I mentioned, I only did a small number of runs [about 100]. BTW - I like your title "Retired Expert"! I think that if you do a large number of runs, you eventually get to about 50%. I was quoting bonanova solution/answer, not my proposed strategy. Your strategy is not applicable, you can't bet more money than you have, if your current money is 50$, your original money is 100$, so 2*100-50 = 150$, which you don't have. Now I explain, my proposed strategy. Hidden Content yes, if you [and the house] are willing to bet micro, nano or pico dollars, then the game can go on forever. But your money is gone, so it is theoretically correct, but not very practical.