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I see. What if I wanted to maximise the expected profit, given that the chance of bankruptcy should not exceed 1%? Does that sort of problem become difficult to solve?

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Just always keep a cent in reserve. Then you can never go bankrupt and your average winnings are barely affected.

That's a good point.

Sorry for the late reply (don't know if you'll see this!) but I happened to be thinking about this again and the question popped into my head: what if I wanted to maximise a specific percentile (e.g. the 5th percentile) of my total winnings?

Fixing the percentile seems akin to the gambler's fallacy: since losses below a certain point don't matter, you just have to bet everything when you fall off, like you would if you thought after a big loss streak you were "owed" a win.

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