How about this, maybe I'm too stoned but this method sounds not bad at all:
Instead of wasting time on the first 50 bets, what if we technically start on 50 bets?
If we "technically" start at 50 bets we must have a bankroll of 11739
By the way, I'm going to use my local currency, norwegian krone.
If I start with 11.739 kroner, (approx 1400 USD)
And we go 11739*1.10^10 we will have 30.448 kroner (approx 3600 usd i think)
Does it not sound fairly easy to win 10 times x 1.10?
And if we manage to do the run once, and start over, we have gained almost 2 fails before we go broke.
If we manage to do 4-5 runs we will have so high bankroll we can fail once in a while without affecting the bankroll