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I wonder... If you don't have access to randomness, e.g., you need to base your choice off some fixed program, and with some limited program length, in theory a perfect observer should be able to guess with certainty your next choices after some time, since there's only a fixed number of possible programs?

Of course this isn't of much practical use...

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Yes, the possible programs are enumerable, and you can start searching with the least complex programs and work your way up in complexity. Once you find a program that explains the available data, you cannot guarantee it will continue to explain possible future data, unless, like you mention, you constrain the program space to a finite set. What you're describing is generally how people make models of the external world.

Yes, and this is actually a challenge in cryptography; a random number generator relies on 'random' inputs to work properly, e.g. keyboard / mouse inputs, time of day, random electricity noise, lava lamps (https://blog.cloudflare.com/randomness-101-lavarand-in-produ...).

If these inputs or parts thereof are predictable, randomness decreases, making the cryptography ultimately weaker.

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