It is by definition not random. The Antihydra is generated by a fixed computable map, so it is compressible and would fail some effective statistical tests. You can't get true randomness via a deterministic algorithm; any computable infinite sequence fails Martin‑Löf randomness.

That said, empirically and in all current analyses, the Antihydra's parity behaves as if it were roughly fair over long spans (neither a proven odd nor even bias), and the short-range statistics look pseudo-random. Non-halting is overwhelmingly plausible... but a concrete proof seems out of reach.