I wonder how many "data scientists" around don't know what a normal distribution is or what's the chance of throwing 6 in a die right after throwing a 6 on the first time.
That's an odd effect of Bayes' rule that I never considered.
This isn't true. You probably have a higher prior for it being unfair towards 6 or 1 (and how much depends on the scenario).
However, if for example, you have priors for it being potentially unfair towards every number equally, 1 throw only changes the posterior probability of whether it is biased towards that number but not whether it is unfair. In case of unequal priors for which numbers it might be biased (e.g. 0.01 chance of it being biased towards 6/1 and 0.001 for 2, 3, 4, 5 and 0.976 for unbiased) getting a number changes all those probabilities yes but for example if you get a 3 the chance of bias there gets higher but mostly at the expense of the probabilities for bias for the other numbers - which get lower (I am too lazy to calculate the posteriors).
All in all, you should know beforehand what your posteriors are going to be for any case based on any outcome and if you know that any one probability (like that of it being fair) is definitely going to lower no matter the outcome then that should be your current prior for that case.
What is with the poisonous gate-keeping in the data science field/community? Is it a bunch of PhDs stuck doing marketing, bitter that people in the business domain are competing with them?
What do you care if a "data scientist" doesn't know what a normal distribution is? Are you worried about them as competition? If that person is getting hired in a role over you, maybe you should look in the mirror or be happy you dodged a bullet at said company. Easy.
I realize you're being facetious, but I always think back to that post here where someone asked how to become a data scientist and one of the replies said you needed to be able to code all the algorithms from scratch in C, C++, CUDA etc etc. Hilarious.
The purpose of data science is solving problems with the help of data. Everything else is semantics. In the real world most of the value comes from pretty simple solutions. Most people aren't working for Google X. Most experiments aren't critical. Uncertainty is acceptable. The inane trivia --which I liken to stupid whiteboard coding challenges-- becomes less important as the tooling improves. Better get used to it, or the ambitious analysts and BI people will eat your lunch.