Unlimited amount of money? - that's no fun...why else would they call it gambling?
Seriously, no matter what system is used in the long run, the ratio of money lost to money won will always approach the house edge.
Source: wizardofodds.com
The flat bettor has a bell curve with a peak at a loss of $1, and never strays very far from that peak. Martingale bettor would show a profit represented red curve, peaking at $51. On the far left shows there are times when you can't couldn't cover a bet and walked away with a substantial loss.