Let's not confuse P(observed_rolls|used_dice) with P(used_dice|observed_rolls). P(observed_rolls|used_dice) is always the same, independent of observed rolls, a

Let's not confuse P(observed_rolls|used_dice) with P(used_dice|observed_rolls). P(observed_rolls|used_dice) is always the same, independent of observed rolls, assuming the dice are fair. But P(used_dice|observed_rolls) can vary, because other ways of generating rolls which are under consideration may be biased towards certain answers, and this allows you to perform inference. For example, suppose the rolls you will be shown were either generated by fair dice or by the program "always return 4" [4]. The rolls you are given are "4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4". Are you really thinking you'd make the same prediction for this sequence of rolls as you would for the sequence "1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1", or is there perhaps some SMALL INKLING OF A HINT as to which answer is correct? The simple fact of the matter is that, in the real world, if you see a sequence like "4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4" you can be surprisingly confident that it was not generated by die rolls. This is because there are plenty of other ways to get sequences and those other hypotheses didn't just pay a Bayes factor penalty of a trillion. Seeing the instructions as incoherent is the mistake of trying to over-isolate the study to the abstract mathematical realm, instead of the world people actually operate in. If someone tells you their luggage combination is 1234, do you really think it's meaningless to guess that it was the default combination as opposed to being generated by secure die rolls? Do you not form opinions about whether or not someone is using secure randomly generated passwords when you find out their password is "password2"? 4: https://xkcd.com/221/ https://xkcd.com/221/