While shuffling a Rubik’s cube, I noticed that if my shuffling had a pattern I subconsciously assumed it isn't shuffled enough so I do couple more rotations.
But, knowing that pattern can and do appear on random processes I wonder what probabilistic properties a random shuffling of a Rubik’s cube say $n$ rotations have.
What is the average /maximal number of cubical of the same color laying on the same face, in expectation?
How does the entropy change was $n$ increases?
Any other interesting properties?