With 2 hypothesis: die is fair/die is 100% loaded, a single roll doesn’t discriminate at all.
The key insight is that you have to combine Baysean and Frequentist theories. The prior is heavily weighted towards “the die is fair” such that even 3 or 4 of the same number in a row doesn’t push the actionable probability all the way to “more likely weighted” but as independent observations continue, the weight of evidence accumulates.
With 2 hypothesis: die is fair/die is 100% loaded, a single roll doesn’t discriminate at all. The key insight is that you have to combine Baysean and Frequentist theories. The prior is heavily weighted towards “the die is fair” such that even 3 or 4 of the same number in a row doesn’t push the actionable probability all the way to “more likely weighted” but as independent observations continue, the weight of evidence accumulates.