Given any problem, one should look at it, and pick the course that maximising one's expectation. ... what if my utility is non-linear

You're confusing expected outcome and expected utility. Nobody thinks you should maximize the utility of the expected outcome; rather you should maximize the expected utility of the outcome.

Lets now take another example: I am on Deal or No Deal, and there are three boxes left: $100000, $25000 and $.01. The banker has just given me a deal of $20000 (no doubt to much audience booing). Should I take that? Expected gains maximisation says certainly not!

Yes, and expected gains maximization, which nobody advocates, is stupid, unlike expected utility maximization, which will take into account the fact that your utility function is probably not linear on money.