This article discusses rationality gaps triggered by self-referential/cyclic choice, the latter being understood as choosing according to a norm that refers to the choosing itself. The Crocodile Paradox is reformulated and analyzed as a game—named CP—whose Nash equilibrium is shown to trigger a cyclic choice and to invite a rationality gap. It is shown that choosing the Nash equilibrium of CP conforms to the principles Wolfgang Spohn and Haim Gaifman introduced to, allegedly, guarantee acyclicity but, in fact, does not prevent (...) self-referential/cyclic choice and rationality gaps. It is shown that CP is a counter-example to Gaifman's solution of the rationality gaps problem. (shrink)