But the number 3 is there just because we decide to calculate digits in base 10. We could encode Pi in binary instead, and since it doesn't repeat it necessarily will never be a point where there will never be another 1 or a 0, right?
But it's also true that pi may not contain every _possible_ sequence of decimals, no matter what base you pick. Like the Riemann hypothesis, it seems very likely and people have checked a lot of statistics, but nobody has proven it beyond a (mathematical) shadow of doubt.