But even if you don't believe in many worlds, I think you do the same thing, unless you are not maximizing expected utility. (Unless chance is quantized so that there is a minimum possible possibility. I don't think that would help much anyway.)

Or unless your utility function is bounded above, and the utility you assign to the status quo is more than the average of the utility of dying straight away and the upper bound of your utility function, in which case Omega couldn't possibly double your utility. (Indeed, I can't think of any X right now such that I'd prefer {50% X, 10% I die right now, 40% business as usual} to {100% business as usual}.)