  We present a simple yet accurate numerical approach to compute the free
energy of binding of multivalent objects on a receptor-coated surface. The
method correctly accounts for the fact that one ligand can bind to at most one
receptor. The numerical approach is based on a saddle-point approximation to
the computation of a complex residue. We compare our theory with the powerful
Valence-Limited Interaction Theory (VLIT) (J. Chem. Phys. 137, 094108(2012), J.
Chem. Phys. 138, 021102(2013)) and find excellent agreement in the regime where
that theory is expected to work. However, the present approach even works for
low receptor/ligand densities, where VLIT breaks down.
