  Due to the attractor mechanism, the entropy of an extremal black hole does
not vary continuously as we vary the asymptotic values of various moduli
fields. Using this fact we argue that the entropy of an extremal black hole in
string theory, calculated for a range of values of the asymptotic moduli for
which the microscopic theory is strongly coupled, should match the statistical
entropy of the same system calculated for a range of values of the asymptotic
moduli for which the microscopic theory is weakly coupled. This argument does
not rely on supersymmetry and applies equally well to nonsupersymmetric
extremal black holes. We discuss several examples which support this argument
and also several caveats which could invalidate this argument.
