I have been wondering about the following question for a while. Consider the martingale strategy for roulette, where you bet on a color, such as red. If you put \$1 on red and win. You walk away, or bet another on \$1. If you lose, you double your bet and put it on red. That way if you win, you win back your previous investment, plus the \$1 payout from the original wager. If you lose, you double your bet and try again. Obviously with a finite amount of money this strategy will eventually bankrupt you.
Now consider the augmented strategy, where after a certain number of losses, you accept the loss and rather than keep doubling your bet you start over at \$1. For example, after 4 losses in a row, you would have \$15 Invested ;1+2+4+8. Now rather than keep doubling you start the system over.
So the question becomes are you able to hit on 15 reds before you hit on 4 blacks in a row. Runs of black less than 4 are obviously allowed.
In roulette there are 38 equally likely outcomes, 18 red, 18 black, 2 green.