It is critical to note our blog host's aberrant beard growing genetics. All hairs on his face grow from left to right creating an upward sweeping motion. (Should it bother Kirk's wife that I know this?)
Cool puzzle, what really threw me off track was that it (meaning I) was wrong one time.
The answer is always a multiple of 9. Any two digit # is 10a+b where a and b are integers between 0 and 9. So any two-digit number you pick yields 10a+b-(a+b) = 9a, or a multiple of 9. All the multiples of 9 have the same symbol; you'll always be looking at one, so that symbol will always come up. What throws you is that each time you reset the game, another symbol is associated with the multiples of 9, so you think that it's choosing among different possibilities. But it ain't. In case you wanted to know.
Yup. I did the math too in a little perl program.
Pretty clever!