  Alice is a charismatic quantum cryptographer who believes her parties are
unmissable; Bob is a (relatively) glamorous string theorist who believes he is
an indispensable guest. To prevent possibly traumatic collisions of
self-perception and reality, their social code requires that decisions about
invitation or acceptance be made via a cryptographically secure variable bias
coin toss (VBCT). This generates a shared random bit by the toss of a coin
whose bias is secretly chosen, within a stipulated range, by one of the
parties; the other party learns only the random bit. Thus one party can
secretly influence the outcome, while both can save face by blaming any
negative decisions on bad luck.
  We describe here some cryptographic VBCT protocols whose security is
guaranteed by quantum theory and the impossibility of superluminal signalling,
setting our results in the context of a general discussion of secure two-party
computation. We also briefly discuss other cryptographic applications of VBCT.
