  We discuss the effects of the black holes' spin-multipole structure in the
orbital dynamics of binary black holes according to general relativity,
focusing on the leading-post-Newtonian-order couplings at each order in an
expansion in the black holes' spins. We first review previous widely confirmed
results up through fourth order in spin, observe suggestive patterns therein,
and discuss how the results can be extrapolated to all orders in spin with
minimal information from the test-body limit. We then justify this
extrapolation by providing a complete derivation within the post-Newtonian
framework of a canonical Hamiltonian for a binary black hole, for generic
orbits and spin orientations, which encompasses the leading post-Newtonian
orders at all orders in spin. At the considered orders, the results reveal a
precise equivalence between arbitrary-mass-ratio two-spinning-black-hole
dynamics and the motion of a test black hole in a Kerr spacetime, as well as an
intriguing relationship to geodesic motion in a Kerr spacetime.
