  We revisit the no-hair theorems in Einstein-Scalar-Gauss-Bonnet theory with a
general coupling function between the scalar and the Gauss-Bonnet term in four
dimensional spacetime. In the case of the old no-hair theorem the surface term
has so far been ignored, but this plays a crucial role when the coupling
function does not vanish at infinity and the scalar field admits a power
expansion with respect to the inverse of the radial coordinate in that regime.
We also clarify that the novel no-hair theorem is always evaded for regular
black hole solutions without any restrictions as long as the regularity
conditions are satisfied.
