  We regard binary black hole (BBH) merger as a map from a simple initial state
(two Kerr black holes, with dimensionless spins {\bf a} and {\bf b}) to a
simple final state (a Kerr black hole with mass m, dimensionless spin {\bf s},
and kick velocity {\bf k}). By expanding this map around {\bf a} = {\bf b} = 0
and applying symmetry constraints, we obtain a simple formalism that is
remarkably successful at explaining existing BBH simulations. It also makes
detailed predictions and suggests a more efficient way of mapping the parameter
space of binary black hole merger. Since we rely on symmetry rather than
dynamics, our expansion complements previous analytical techniques.
