I get similar numbers as bonanova and prime.
I did 1000 trials of playing 1000 games per trial.
Average final bankroll ~ $2E10
Median final bankroll = $0.49
Number of winning trials = 465
If you're on a Windows machine with a Java JDK installed (free to download from Oracle if you don't have it already): copy the code below and paste it into a txt file called LetItRide.java, then on a command prompt in that directory type javac LetItRide.java to compile it, then type java LetItRide to run it.
Spoiler for java code
Thanks for the code. I think I see what is causing the discrepancy between the simulation results. I made a mistake in transcribing the game probabilities...