Here's another example of how the utility maximization doesn't work by just calculating utilities of 2 futures then comparing.

There is a random number N on a paper in an envelope, it is entirely uncorrelated with your choice (not newcomb's paradox). You don't know the probability distribution or anything else about that number. You can choose between receiving $1000 prise if N>0 or receiving $1000 prize if N>1 . Obviously you should choose former; even though you don't know expected utilities of either choice you know one is greater than other (technically, greater or equal). (Also even if you are not decided yet what to do with $1000, considering that you will have option to give it up in the future, you can see that utility of future with you having $1000 is no less than utility of future with you not having $1000) . One doesn't simply compare reals to maximize utility. There's no need to assign some made up values to arrive at correct answers.

(The algebra drills at schools ought to help you understand that you don't need to assign made up values to unknowns)