My thoughts:

(Yes, Virginia, in this setting the fairness would be a mathematical property of the coin, not of our own ignorance.) In such a world, creatures who are too computationally weak to predict the Tape will probably evolve a concept of "probability",

I'm confused here -- if the coin's randomness really is fundamental, and not a property of our ignorance, then it doesn't make sense to say that a being is too computationally weak to predict it -- no amount of computational strength would allow prediction.

(I'm also confused at how the non-native speakers here so effortlessly use colloquialisms like "Yes, Virginia ...", which came from a famous "Yes, Virginia, there is a Santa Claus...", but whatever.)

Isn't Two a restatement of the anthropic explanation for the Born rule: we could only see this kind of universe if the Born rule were true? Other universes would permit "anthropic hypercomputation", which fundamentally changes the game, or fail to permit something we recognize as minds.