On the other hand objective randomness is a black box. You can describe how it behaves at the surface level (so functionally it is usable), but by definition you can't have a finite model of it, so what is inside? No answer by definition - something infinite.

So why X happens instead of Y?

1. Let's propose an unexplainable, unmodellable infinite entropy source under everything

vs.

2. X happens and so do Y, and one is observed at a certain probability due to anthropic principle - like this: https://www.youtube.com/watch?v=9R5OWh7luL4

The first is somehow psychologically less satisfying answer for me, although - of course - I accept that calculation works either way. The second at least not an unimaginable infinite, and in the end leaves me with less "why?".

MWI doesn't mean anything and everything can happen because there's infinite universes. The equations of quantum mechanics describe the ways that worlds can branch apart and the proportions of those branches.

Sorry if I'm underestimating your familiarity with MWI here; if I am, szemet has a much better response. I'm just a little concerned that some people in the thread don't realize MWI refers to something much more specific and grounded than what-if-multiple-universes, and I wanted to dispel that notion.

I hear a lot that MWI implies that everything that can happen does happen. What I find frustrating is that the obvious next interesting question then is 'well what can happen?', and people don't seem to talk too much about that.

The short answer is the Schrödinger equation.

If you want a more layman's explanation of what sort of things would cause a branch and how the branches would differ: one simple example is that when an excited atom emits a photon, it doesn't emit it in a random direction, instead there's a superposition of it emitting the photon across all paths away from itself. In many of these paths, the photon will interact with particles differently than happens with other paths, and the paths will decohere into different branches of the world with separate consequences from the photon hitting in a different place in each branch. In one branch, the photon could hit a particle in the air and affect its temperature and velocity by the tiniest amount. In another branch, the photon could instead hit a receptor in a person's eye and immediately trigger a reaction that would not have otherwise occurred.

Small differences between the branches could build up into bigger differences over time, especially when you consider the sheer number of concurrent interactions that are creating overlapping superpositions which decohere in many different ways. It could be that there's enough branches that most things that could have reasonably happened by chance do happen in some branch.

(If you're wondering how we could know in theory that the world may branch like this, it's because branches where particles take different paths but then later have all of their positions line up together interfere with each other. See the two-slit experiment.)

I would have thought that the answer to "what can happen" is pretty unequivocally the Schrödinger equation?