Not quite.
You should worry about things to the extent you can change your expected utility.
There's maybe a million to one chance of drawing some particular hand at poker night, and there's also a million to one chance that there will be some disaster (earthquake, zombies, flood). One of those doesn't matter very much and you can't do much about it anyway, the other you can do very much to prepare for and actually make a large expected difference.
Your rule will work if you are well-calibrated to one possible cause of death and you are wondering how much time to spend on another, given that you know the probabilities. If the events (and therefore utilities) are not as comparable, it's best to just use decision theory in some form.
It may be 'best' to use decision theory - but I've found that it can take more time trying to figure out what a decision theory says about an everyday choice than that choice makes a difference of. So I'm hoping that some variation of this rule-of-thumb allows for a reasonable compromise - while it doesn't always apply, the cases where it does allow you to reap most of the benefits that applying a full-fledged decision theory would, while requiring significantly less mental processing time.
Or maybe it's not useful that way at all - in which case, I'd like to find that out here if I can, before I start relying on it too heavily.
Does something like this seem to you to be a reasonable rule of thumb, for helping handle scope insensitivity to low probabilities?
There's a roughly 30 to 35 out of a million chance that you will die on any given day; and so if I'm dealing with a probability of one in a million, then I 'should' spend 30 times as much time preparing for my imminent death within the next 24 hours as I do playing with the one-in-a-million shot. If it's not worth spending 30 seconds preparing for dying within the next day, then I should spend less than one second dealing with that one-in-a-million shot.
Relatedly, can you think of a way to improve it, such as to make it more memorable? Are there any pre-existing references - not just to micromorts, but to comparing them to other probabilities - which I've missed?