Can a dialetheist stay regular?

For a dialetheist, it is rational to believe that true contradictions exist. However, we argue that a dialetheist faces a complex dilemma given some bridge principles for rational beliefs that connect possibility and probability, including the so-called ‘Regularity Principle’. Either her belief is not doxastically possible even for her, or she must assign positive credence to the proposition that dialetheia exists. The former makes her belief <i>prima facie</i> self-defeating. The latter seems to compel her to choose between several more fine-grained options, each of which seems undesirable for a regular and rational probability theory. It is unclear how a dialetheist would stay rationally regular, so we pose this challenge, seeking a response from a dialetheist.