I hope this is an innocent question from an infrequent UA flier (3 economy segments this past year, 2 First segments and a couple of economy the previous year...)

I am about to book a UA flight (DEN-HDN on a 737) for this coming January. Looking at the seating plans, about 1/2 the economy cabin is E+. As I am not a UA Elite (have non-Elite status on BMI, but nothing "useful") and not intending to buy a full fare economy ticket, I realise that I cannot get these seats assigned to me.

However, I am also thinking that this flight is normally pretty full (when I have done it in the past), but I doubt that many of these passengers are "elite" or full fare either. So if the flight is pretty heaving, AND they need to fill those E+ seats with someone, how can you maximise your chances of getting allocated into an E+ seat? Or am I being overly optimistic here...

Any constructive advice much appreciated

Thanks,
Boo