The Anna Karenina principle is named after the opening sentence in the
eponymous novel: Happy families are all alike; every unhappy family is unhappy
in its own way. The Two Envelopes Problem (TEP) is a much-studied paradox in
probability theory, mathematical economics, logic, and philosophy. Time and
again a new analysis is published in which an author claims finally to explain
what actually goes wrong in this paradox. Each author (the present author
included) emphasizes what is new in their approach and concludes that earlier
approaches did not get to the root of the matter. We observe that though a
logical argument is only correct if every step is correct, an apparently
logical argument which goes astray can be thought of as going astray at
different places. This leads to a comparison between the literature on TEP and
a successful movie franchise: it generates a succession of sequels, and even
prequels, each with a different director who approaches the same basic premise
in a personal way. We survey resolutions in the literature with a view to
synthesis, correct common errors, and give a new theorem on order properties of
an exchangeable pair of random variables, at the heart of most TEP variants and
interpretations. A theorem on asymptotic independence between the amount in
your envelope and the question whether it is smaller or larger shows that the
pathological situation of improper priors or infinite expectation values has
consequences as we merely approach such a situation.Comment: Final corrections (fingers crossed