More specifically, if the losing streak which gets you busted grows faster than the number of bets you have made so far (as the former obviously depends on your balance and its increase with time), statistically, you are unlikely to lose even over an indefinite time scale. Well, that's what I think but you may have a different opinion while everyone else is welcome to chime in on this
I didn't understand this part (and I even tried google translate help me on this!).
I know that the statistics tell that after each losing bet the chance for the next bet to be a winner increases
As rolls are independent of each other, the chances will always remain the same for each roll (unless you change the odds manually, of course). In other words, if you have 20 reds in a row, the odds to see red for the 21st time remain absolutely the same as for the first roll in the sequence (and any other roll in that sequence). It is the odds of seeing longer sequences that diminish with the length of the sequence
But that's not my point. My point is, an increase in your balance allows you to survive longer losing streaks, which should be obvious (provided everything else remains the same). So if the balance increases faster than the number of rolls you make (as more rolls means a higher chance to encounter a fatal sequence of reds), we can have a situation where you can play indefinitely long while odds for losing everything will actually be decreasing with time
That would be the case for one infinity (your balance) outrunning another (number of rolls)
OP the problem is that every strategy fails on long term, imagine you start gambling now with your strategy, gain some profit, then what to do?
You add winnings to your balance until you are satisfied with the results. Then you withdraw all and call it a day (or night, depending on your gambling preferences)
One amongst many revivals of the discussion =). I'd like to point out one big flaw of this idea though: that for your extended martingale, you need a casino able to take very high bets
It is more of a theoretical discussion as you will lose faster than your balance will get increased through winnings alone. Or you will be earning dust and basically wasting your time (but to each their own)