If you were a frequentist, you would look for the maximum likelihood estimation of the number of faces, which is essentially the maximization of the term P(X∣θ)P(X|\theta)P(X∣θ) introduced above. Let’s take a second to go through this: if your die has nnn faces, then X∼U(n)X \sim \mathcal U(n)X∼U(n) and the probability to observe exactly this data is
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