I encountered a real life example where I have a 2% edge in a "gambling game". There isn't any real money involved, just bragging rights among friends. It's a scratch ticket that costs 100 points to buy. There is a 2/3 chance to win 153 points and a 1/3 chance to lose the initial 100.
I understand the law of large numbers and how over the long run, values tend to trend up or down depending on the odds. If I had infinite points, this would be a no brainer as I would continue to make money as long as I kept playing.
However, unlike a casino, I have limited funds and realize the chance of going bankrupt if I have a series of unlucky runs.
I'm trying to find a formula that calculates the chance of me going broke depending on my initial investment. I want to see how many points I should save up to have a x% probability of that happening. If anyone could point me in the right direction, I'd really appreciate it!