Eh, even an expected value that's linear with respect to profits can end up with strange results like the St. Petersburg paradox. In general, naively maximizing it breaks down at the point where you stop being insensitive to the possible risks.

One possible resolution to that paradox is to recognise that money is not linearly proportional to 'value'.

If happiness is, e.g., log(money), then you can just adjust the game to have the payout be $2^2^n after the nth step. This cancels out the logarithm and recovers the paradox. The only way to get out of it with diminishing returns is to have happiness reach a finite asymptote.

When there is a decent probability that you may crash the financial system I'm nor even sure if a strictly monotonically increasing function is appropriate.