Who throws the dice for you?

[Heywood]

That's fine....except we know physical local variables are not there. So the "gap" can only be filled by something non physical....non local.

Inserting "nothing" is burying your head in the sand and pretending there isn't problem to explain.

Uh, no. non-local doesn't mean non physical in the sense that it can't be observed.

Nothing is not burying your head in the sand. It is a recognition that collective properties may have fundamental building blocks that can not be subdivided and does not derive from anything finer.

What are the constituent parts of a fundamental particle? Nothing. The fundamental particle derive its properties from nothing other than its own existence. "What about the particle gives it its property" stops having meaning when one reachs the most fundamental particle.

At certain level, randomness may be a fundamental property of the the most basic building block of the universe. Nothing in the building block gives it that property. The property is intrinsic to the building block itself.

It may be that some or all building blocks in the universe is infinitely divisible. But our best mathematical description of what we see suggest that is not the case. The universe appears to not be infinitely divisible in any of its basic properties. At some level, nothing deeper is there.

ummm.....no. Randomness isn't a property of matter. Randomness is a property of events.