Comment by witty_username

If we model the stock market as a random walk/Weiner process and I got the math right, I think you're almost certainly going to make money (if you stop when you reach a given profit threshold), but you will have arbitrarily large drawdowns. This is similar in terms of the risk/return profile to the martingale betting system. https://en.wikipedia.org/wiki/Martingale_(betting_system)