Bad construction on two accounts. First, the example is formally describable as is, to the limits of description allowed by mathematics given the parameters provided. Second, the knowledge of the situation is not perfect by definition, so your assertion to the contrary is invalid. We have no visibility inside the blackbox and the appplication of mathematical induction to that state is intractable (the given severe finite limits you placed on induction is how we derived the strict probabilistic version in the first place). If we did have internal visibility, we would be able to predict the outcome -- again, by definition.
Unpredictable is very, very different from random mathematically, even though they look the same to an observer with a sufficiently poor inductive model. You have posited a scenario where they are mathematically equivalent as far as a formal description is concerned, but one could adjust the parameters of the scenario so that this is not the case.
I don't think you understood his description. Edsheppa's experiment is in essence identical to the two slit experiment. While I'd argue both experiments are formally deterministic, if you divide the system into quantum system and measuring apparatus, the result is as completely random as anything a physical system could provide; in fact, any algorithm that purported to predict the result to better than 50% accuracy would violate the uncertainty principle.
By definition of what? Knowledge? Perfection?
...so your assertion to the contrary is invalid. We have no visibility inside the blackbox... If we did have internal visibility...
On the contrary. There is no black box, I have completely described the physical situation. An experimenter could construct this apparatus. What is it you find unclear?