  We propose a classification of BPS states in holographic CFTs into monotone
and fortuitous, based on their behaviors in the large $N$ limit. Intuitively,
monotone BPS states form infinite sequences with increasing rank $N$, while
fortuitous ones exist within finite ranges of consecutive ranks. A precise
definition is formulated using supercharge cohomology. We conjecture that under
the AdS/CFT correspondence, monotone BPS states are dual to smooth horizonless
geometries, and fortuitous ones are responsible for typical black hole
microstates and give dominant contributions to the entropy. We present
supporting evidence for our conjectures in the ${\cal N}=4$ SYM and symmetric
product orbifolds.
