  This work is devoted to the study of a novariational class of singular
elliptic equations ruled by the infinity Laplacian. We provide optimal
$C^{1,\beta}$ regularity along the singular free boundary, where in particular,
the optimality is designed by the magnitude of the singularity. By virtue of a
suitable penalization scheme and a construction of radial super-solutions,
existence and non-degeneracy properties are provided where fine geometric
consequences for the singular free boundary are further obtained.
