Interestingly, the author doesn't talk about Bayesian reassessment but that's what it is actually;).

Having an event (5 rolls in a row which gives 6) which has a different probability of occurring in two hypotheses:

A: the die is not loaded ---> 1/7000 probability of occurring

B: the die is loaded to always give 6 ----> probability 1 of occurring

fact that the hypothesis B must be reevaluated by a factor 7000 compared to A. 7000 is a lot but it depends on your initial estimate "the prior" on p (B) / p (A). In the example chosen, he took a prior of 1/1000, but suddenly the Bayesian revaluation factor transforms it into p (B) / p (A) = 7, i.e. 7 chances out of 8 that it is loaded and 1 chance in 8 that it is not loaded. Note that it depends on the prior which is quite subjective, this is the difficulty. If we are "much more confident" that the die is not loaded, for example we made it ourselves, say p (B) = 1 / 100, we can continue to play. If, on the contrary, we are wary from the start of the huckster like Tony (probability of 000/1 that he will be loaded for example), we will stop long before.

It is interesting to analyze the differences of opinion, including on this forum, based on prior and re-evaluations. For example, if you are sure that the pharmaceutical labs are lying to you and their results are faked, you will give much less importance to the results of a test than if you think the other way around. Any resemblance to real life situations would be pure coincidence

To pass for an idiot in the eyes of a fool is a gourmet pleasure. (Georges COURTELINE)

Mééé denies nui went to parties with 200 people and was not even sick moiiiiiii (Guignol des bois)