My wife explains it thusly:
"If you write it out as an algebra problem, you always end up with a multiple of nine, no matter what the initial digits are. The value of the actual number, because of place value, is 10a + b. The number you subtract when you add the digits is just a + b. No matter what the digits are, the result is a multiple of nine, and if you look at the chart they show you at the end, every multiple of nine has the same symbol. It only LOOKS random. There's no trick -- it's just math!"