Determinism is well defined.
A deterministic system is one in which the future state at any time can be calculated by a complete knowledge of the state at some initial time and a recursive mechanism for calculating future states. Of course, even in a perfectly deterministic world, it would always be possible for us to have drawn our equivalence classes too broadly or too narrowly, resulting in discrepancies relative to our expectations. Therefore, it will never be possible to decide whether the world is causal or not. Your Pi example is not a difficult model to crack. Standard cryptography techniques would catch that easily.