First, whether or not there is randomness anywhere has nothing to do with free will vs determinism. Things can be random but there is still no free will.
Second, and I’m suprised giraffe hasn’t popped into this one, the HUP (uncertainty principle) doesn’t say we are flawed in our measuring techniquies, or that measurement is impossible because to build a machine is impossible with that degree of accuracy, but that uncertainty is inherent in the system. Take the scientist out of the system and the uncertainty still is there. Someone asked for a good book, I always recommend “In Search of Schrodinger’s Cat” by John Gribbins. Or maybe Gribbin. Anyway, the title is right 
Now, onto pi. There is a formula for pi (in "The Joy of Pi by David Blatner) which will give you the nth digit of pi without calculating the previous n-1 digits. Tough titty, said the kitty, its in hex. To get the decimal equivalent you’ll need to have the previous n-1 digets. I’d love to reproduce the formula here, but message boards don’t allow for such formulas. 
If we are thinking “random” means “unpedictable” then the argument is much like we have now. But, if we clarify and say “rondom” means “impossible to predict, ever” then we might get somewhere.
Random events on our level are basically the chaos-theory type; ie-dependent on unmeasured conditions. Like lottery machines with little balls, or bingo things.
Pi, being an irrational number, doesn’t exist so long as we accept quantum theory.
Now I completely lost where I was heading…shit.