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