I think you are conflating a little bit randomness and complexity. Scott Aaronson in "Quantum Computing since Democritus" cites a study that shows that when pe

I think you are conflating a little bit randomness and complexity. Scott Aaronson in "Quantum Computing since Democritus" cites a study that shows that when people are asked to generate a random sequence the sequence that they write looks _more complex_ than a truly random sequence. For example, when generating a sequence of coin tosses people would try to avoid long sequences of heads of tails, making the probability of those sequences lower than in a truly random sequence. I decided to try and test this using your game. I generated the results for all three tests using random.org, and ended up somewhere between 10th and 20th percentile of complexity.