> I think it would be a map/territory confusion to consider it a kind of actual randomness.

Even though it makes perfect sense to apply probability theory to it? We found a perfect coin, one that we know that you can't predict in advance even in principle, and you want to avoid considering it a kind of randomness? Why does the mechanism by which the universe implements randomness -- in this case via determinism -- matter?

The many worlds case I was responding to is different to the coin case you are taking about. In the MW case we know enough to see that the situation is not at all random. In your example you're postulating a coin that may well actually be random.

I don't understand what you mean here. I think "the many worlds case I was responding to" in your comment is justinpombrio's "which way you will see a photon go in a half-silvered mirror", but that's functionally identical to the "indexical coin flip" referred to by the LessWrong article, where the coin flip causes a bifurcation, landing heads in universe A and tails in universe B. From within the multiverse it is impossible to know ahead of time which universe you will observe, same as the photon example. It's "random" in the sense of being absolutely unpredictable (otherwise MWI would not be experimentally equivalent to alternative interpretations of quantum physics).

So, does indexical randomness fit your definition of "fundamental" randomness? And what did you mean when you said "a coin that may well actually be random" if it wasn't the indexical kind of coin?

> does indexical randomness fit your definition of "fundamental" randomness?

No, it does not. MW is determinsitic. The fact that you don't know which universe you will observe is a limit on your knowledge. It does not make the things actually random.

There are other interpretations of QM where there is literal randomness, independent of an observers knowledge.

By "a prefect coin", I was referring to a half silvered mirror.