I'd imagined these terms would be self-explanatory from the post :-) The numbers refer to variants of the Born rule where the exponent doesn't necessarily equal 2. For example, see page 6 of this paper by Aaronson.

I'm unfamiliar with the terminology "2-sampling", "2-world", "3-world", etc. and a quick internet search has not turned up anything useful. Could you summarize what they mean or direct me to a place that explains them?

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.

This model is missing a plausible evolutionary explanation for how U and C may have evolved. That's a pretty gaping hole because if we don't constrain U and C to being plausible under evolution then they can be given whatever motives, responsibilities, etc. that are convenient to fit the model to existing data (see Psychohistorian's epicycle comment).