I'm assuming MWI, but noticing that NOT every source of "randomness" implies different branches.

Some things may, or may not, be interconnected in ways we don't see, and can't detect. (E.g. it's been shown that humans can learn to flip coins predictably etc.)

My point is to provably, with as high confidence as we require split the world into different branches, as opposed to having a pretty good chance but we don't know exactly how good of creating different branches.