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Originally Posted by David Sklansky
If you martingale a fair coin bet starting with a dollar bet and an infinite bankroll, there is a 99.999999999......% chance that you will, at some point, be up a trillion dollars.
As you know, the same is true if you don't martingale, for example if you simply bet $1 per flip. That is, pretending there's a such thing as "being up a trillion dollars" when you already started with infinity.
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But if the coin will come up your side only 49.99% of the time, the chance you will EVER (even in an infinite number of years) be up a trillion dollars, is less than .000001%.
Nope, 100% if you martingale. You're 100% to win each dollar because there's a 0% chance of an infinite streak of losses. Repeat the process a trillion times and the combined chance of a trillion 100% outcomes is still 100%. Unlike when betting on a fair coin, martingaling makes a big difference when betting on an unfair coin (if one can't run out of bets to make).