Keltham is in favor of people understanding things using calculus and continuous distributions, to be clear.  So long as they can also understand the ideas in terms of a countably infinite collection of individual hypotheses each with probability 1/INF.  You don't want to start identifying either representation or methodology of analysis with the underlying idea!

Which idea is just: a metahypothesis where any fraction from 0 to 1 seems equally plausible on priors.  Those get updated on observations of LEFT and RIGHT, that have different likelihoods for different propensity-fractions; the allocation of posterior probability over fractions changes and gets normalized back to summing to 1; that changes the new predictions for LEFT and RIGHT on successive rounds, having updated on all of the previous rounds.

Keltham will now go up to the wall and spend a bit of time figuring out how to derive the rest of the Rule of Succession, which there's no simple or obvious way to prove using calculus known to anyone in this room anyways.

Thankfully, they know what all the correct answers have to be!  Using much simpler combinatoric arguments, about new balls ending up randomly ordered anywhere between the left boundary, all the LEFT balls, the 0 ball, all the RIGHT balls, and the right boundary.

Eventually Keltham does succeed in deriving (again) (but this time proving it using dubious infinitary arguments, instead of clear and simple combinatorics, so they can see what's happening with priors and posteriors and likelihoods behind the scene) that indeed:

If you start out thinking any fraction of LEFT and RIGHT between 0 and 1 is equally plausible on priors, and you see experimental results going LEFT on N occasions and going RIGHT on M occasions, the prediction for the next round is (N+1)/(N+M+2) for LEFT and (M+1)/(N+M+2) for RIGHT.

(Continued in "my fun research project".)