There's no way to predict what the next unsolved pi digit will be just by looking at what came before it. It's neither predictable nor deterministic. The very existence of calculations to get the next digit supports that.
Note: I'm not saying Pi is random. Again, the calculations support the general non-randomness of it. It is possible to be unpredictable, undeterministic, and completely logical.
Note Note: I don't know everything. For all I know, we're in a simulation and we'll eventually hit the floating point limit of pi and underflow the universe. I just wanted to point out that your example doesn't quite fit with pi.
As I said, you can't predict the next number simply based upon the set of numbers that came before. You have to calculate it, and that calculation can be so complex that it takes insane amounts of energy to do it.
Also, I think I was thinking of the philisophical definition of "deterministic" when I was using it earlier. That doesn't really apply to pi... unless we really do live in a simulation.