It was recently suggested that holographic BPS states can be divided into two categories: monotone and fortuitous. Various pieces of evidence suggest that monotone states correspond to horizonless microstate geometries, while fortuitous states are dual to supersymmetric black holes. In this talk, I will connect this classification to the fine-grained features of BPS states using concepts from quantum chaos. In concrete models such as the N=4 SYM theory, explicit calculations demonstrate that monotone states are only weakly chaotic, whereas fortuitous states can exhibit strong chaos due to an “invasion” mechanism. I propose using the N=2 SUSY SYK model as a toy model to explore many of these ideas.