The size of the orbit (that is, number of essentially equivalent grids) can be calculated using the orbit-stabilizer theorem: it is the size of the sudoku symmetry group divided by the size of the stabilizer (or "automorphism") group. Multipling the number of essentially unique grids (the number of orbits) with the orbit size gives the total number of grids with that stabilizer group size; summation then once again provides the total number of possible sudoku grids. "Automorphic" grids have smaller orbits so the probability that a random grid has a symmetry drops: from about 1 in 10,000 for essentially different grids to about 1 in 20,000 for all grids.