  By constructing explicit supersolutions, we obtain the optimal global
H\"older regularity for several singular Monge-Amp\`ere equations on general
bounded open convex domains including those related to complete affine
hyperbolic spheres, and proper affine hyperspheres. Our analysis reveals that
certain singular-looking equations, such as $ \det D^2 u = |u|^{-n-2-k} (x\cdot
Du -u)^{-k} $ with zero boundary data, have unexpected degenerate nature.
