  Electroweak Baryogenesis (EWBG) is a compelling scenario for explaining the
matter-antimatter asymmetry in the universe. Its connection to the electroweak
phase transition makes it inherently testable. However, completely excluding
this scenario can seem difficult in practice, due to the sheer number of
proposed models. We investigate the possibility of postulating a "no-lose"
theorem for testing EWBG in future e+e- or hadron colliders. As a first step we
focus on a factorized picture of EWBG which separates the sources of a stronger
phase transition from those that provide new sources of CP violation. We then
construct a "nightmare scenario" that generates a strong first-order phase
transition as required by EWBG, but is very difficult to test experimentally.
We show that a 100 TeV hadron collider is both necessary and possibly
sufficient for testing the parameter space of the nightmare scenario that is
consistent with EWBG.
