If a phone game shuffle and a physical noise source both look messy, what makes only one useful for security against someone who knows the code?

Answer: Unpredictable hidden inputs

Even-looking output pattern — An even-looking pattern is not the same as security. A deterministic shuffle can spread cards or numbers across the screen in a way that looks fair, yet someone who learns the algorithm and state may still predict the next result. NIST SP 800-22 treats statistical tests as a first screen, not as proof that a generator is safe for cryptography.

Unpredictable hidden inputs ✓ — Security cares about what an adversary cannot know or reconstruct. A physical noise source can add fresh unpredictable input, so the next value is not just the visible end of a known recipe. That is why encryption systems feed randomness from outside the deterministic computer, rather than trusting messiness on the display.

Longer visible sequences — Longer output can make a sequence feel more random, but length alone does not create unpredictability. A short secret seed can deterministically generate a huge stream, and if the seed and algorithm are exposed the stream can be rebuilt. The decisive question is not how much you see, but whether the hidden input is unknowable.