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.
