  We provide a variety of cases in which two factorizations have Hurwitz orbits
of the same size. We begin with prototypical results about factorizations of
length two, and show that cycling elements or flipping and inverting elements
in any factorization preserves Hurwitz orbit size. We prove that "double
reverse" factorizations in groups with special presentations have Hurwitz
orbits of equal size, and end with applications to complex reflection groups.
