It's just a question about what we perceive as random. It has nothing to do with the probability of the sequence being produced by a die, only with the probability of the sequence being produced by a human. A 20 20 20 sequence is not less random, it's just more likely to be produced by someone with incentive to cheat.
How did the researchers measure the "randomness" of a particular sequence in this experiment?
> Formally, the algorithmic (Kolmogorov-Chaitin) complexity of a string is the length of the
shortest program that, running on a universal Turing machine (an abstract general-purpose
computer), produces the string and halts.
I think we want (and expect) RNGs to produce sequences with high algorithmic complexity (which we regard as "random") and ignore the (almost impossible) possibility that they fail to do so.
An impossible to create modified RNG which always produces sequences with high algorithmic complexity would better meet our expectations of randomness, but would be less random because it could not produce uniform sequences (among others).
How did the researchers measure the "randomness" of a particular sequence in this experiment?
> Formally, the algorithmic (Kolmogorov-Chaitin) complexity of a string is the length of the shortest program that, running on a universal Turing machine (an abstract general-purpose computer), produces the string and halts.
Oh, interesting.