It's not just about the odds. You can convert any probability into odds if you like.
A 10/10 result for the claim that a losslessly compressed file sounds different from an uncompressed one will not convince anyone and no-one should believe that claim based on that evidence alone.
Beta(0, 0) could be interpreted as: either the trials always fail or they always succeed.This would make more sense e.g. for testing a whether a chemical reaction happens or not.0% everywhere except for the 100% at both extremes.Beta(0.5, 0.5) could be interpreted as: we don't know that it's possible for trials to both fail and succeed.But that gets you 6% from .45 to .55 and 20% from .9 to 1.This prior could make sense in a situation where you didn't know what kind of proportion between 0 and 1 you're dealing with (could be linear, could be logarithmic ...) and try to minimize the effects of the prior.And there are many other attempts at "objective" or "uninformative" or "diffuse" priors since the Jeffreys prior is not without problems can can even lead to inconsistent results, but that's a complex topic.
This does look incredibly interesting. Do you know of any books on this approach to statistics that are outside of any specific context and make an effort to substantiate it mathematically?