Abstract: ETH holds that an eigenstate is statistically indistinguishable from a random vector – the reasoning underlying the LMRS criterion for BPS chaos, available only at finite N and weak coupling. Berry’s random-wave conjecture is the same randomness read in position space: where the semiclassical limit is an irregular phase space, the eigenfunction is locally a Gaussian random superposition of plane waves. We propose it as the semiclassical counterpart of that criterion in the supergravity regime. Across a family of smooth, horizonless supergravity backgrounds ordered by decreasing supersymmetry and increasing throat depth, chaos of probe waves by this measure grows steadily as the geometry approaches a black hole. Geodesics run the other way, becoming more regular in the very same limit – not a contradiction but a mixed phase space, whose chaotic sea the waves see and whose regular islands the geodesics see. We also study the Renyi entropies of the dual CFT states, which do not follow the same ordering. We close with work in progress on momentum-fractionated superstrata of Bena, Martinec, Turton and Warner, whose duals carry fractional spectral flow and are natural candidates for fortuitous states at finite N — the states the finite N criteria cannot reach.