if physics is based on a computational framework such as wolfram physics, but plausibly even if not, such that not all states the universe can be in produce the same number as next possible states;
in addition, if i am to follow to conclusion my current belief that moral patients count as different when they start being functionally different in terms of computation, and that exact copies morally count as a single person (as it makes not much sense to believe otherwise);
and if (as it seems to be the case) the universe values coherence and thus only a limited set of local outcomes can emerge from a given local situation, or at least outcomes are weighed by coherence;
then it makes sense to start caring about the amount of forking a given timeline goes through. which is to say: the amount of future states to be instantiated, be it directly next step or indirectly in the longer term.
in fact, if one calls what they care about moral patients, then we should care about the "forking bitrate" of moral patients. for example, we could want moral patients with a net negative future to be forked as little as possible, and moral patients with a net positive future to be forked as much as possible. considering forks are created over steps of time, and entropy seems to be a good measure for them, i think "bitrate" is an appropriate term for this; hence, forking bitrate.
if we're just talking about a place as small as earth, we can estimate that consequences rapidly ramificate around to all moral patients; and as such, it seems reasonable to think that the forking bitrate of all patients will tend to go about in the same direction.
so, if you see a quantum dice, should you throw it?
if you think the future of earth has expected net positive moral value, or has little enough suffering for your taste (depending on your moral framework), then yes: by throwing the (quantum) dice, you might be multiplying the amount of instances of that value by the number of possible outputs of the dice, by creating that many times more future timelines.
if not, then you shouldn't throw it.
(even in the absence of quantum effects, if one were to just move entropy around while phase space being conserved, moving the entropy from not-moral-patients to moral-patientss (or whichever thing you can about) still has that effect, i think)
this can probly be expanded to much larger-scale entropy control — and also, if superintelligences care about it (and if they're to be aligned, we might want them to) we can expect them to use it to maximize their value. even a paperclip maximizer can want to create as many timelines containing as many varied possible paperclips and arrangements thereof, if it is made to care about that.