Let's say that I have a bankroll B, and that I bet 1 unit at a time on a wager with expectation E and variance V. What is my RoR before achieving a target K, where K>B? Has this been done? Is it in a book. An approximation formula is fine.

Also, how does the answer change if I bet, instead of 1 unit per round, some other amount f?

Thanks in advance. I know this is a hard question.