I appreciate the clarity in code — I'm asking for `betamaxinv` I think?

    >>> betamax((3, 14), (4, 12))
    0.29448379324802676

    >>> betamaxinv(0.29, allowed_error=0.01)
    [((3, 14), (4, 12)), ...]

I assume the results of `betamaxinv` are not unique, and so perhaps there need to be constraints, or return a family of results. I don't know. I'm trying to wrap my head around how OP got A ~ Beta(2,13) and B ~ Beta(3,11) without just brute forcing numbers into `betamax`.