Suppose you are denied experimentation and denied extremely powerful computer (e.g. you can only do <100 simulated trials but want reasonable accuracy), or need high accuracy in limited time. I was more interested about what you do when you are to try to analytically solve something like this, finding probabilities for the 3 distinct sides.
The point here is that you want to go for physically justified stuff, and anything not physically justified that you are doing anywhere, is same in principle as wilfully putting cognitive bias into your calculations, and is just plain wrong, no philosophical stuff here, you'll end up losing games vs someone who solves it better. Maybe you guys need "Overcoming Bayes" blog.
The point here is that you want to go for physically justified stuff, and anything not physically justified that you are doing anywhere, is same in principle as wilfully putting cognitive bias into your calculations, and is just plain wrong, no philosophical stuff here, you'll end up losing games vs someone who solves it better.
Statisticians, by and large, don't lose sleep over this problem. Even in your not-quite-fair die problem, the calculations involved are really hard. It wasn't made explicit in my comment but I wasn't even assuming that opposite s...
I've had a bit of success with getting people to understand Bayesianism at parties and such, and I'm posting this thought experiment that I came up with to see if it can be improved or if an entirely different thought experiment would be grasped more intuitively in that context:
I originally came up with this idea to explain falsifiability which is why I didn't go with say the example in the better article on Bayesianism (i.e. any other number besides a 3 rolled refutes the possibility that the trick die was picked) and having a hypothesis that explains too much contradictory data, so eventually I increase the sides that the die has (like a hypothetical 50-sided die), the different types of die in the jar (100-sided, 6-sided, trick die), and different distributions of die in the jar (90% of the die are 200-sided but a 3 is rolled, etc.). Again, I've been discussing this at parties where alcohol is flowing and cognition is impaired yet people understand it, so I figure if it works there then it can be understood intuitively by many people.