Is it somehow clear?
Yes, and it's simpler than that: every bet has an expected return of 99%, so the sum of all bets has an expected return of 99%, however you bet.
It's easy enough to run a simulation and find an approximation for a particular p and N. I'm looking for an analytical answer.
Great! I was fearing you were in the gambler's fallacy :-)
May I ask you why you are so interested in the busting probability of funny martingales?