I can not for the life of me figure out how this can be done try it for your self. I tried 8 times and each time it showed me the correct symbol. http://www.mysticalball.com/
Here is the not so secret secret behind those types of sites. It's just a matter of mathematics using multiples of 9. When you get to the page, pay attention to the symbols at the multiples of 9 numbers IE: 0, 3, 9, 18, 27, 36, 45, 72 ... you will find that while the symbol is different each time you refresh the page, the actual symbol next to those numbers are the same.