Consider the hardest configurations of the 2x2x2 Rubik's cube.  There are 276 configurations that requires 14 quarter turns to be solved optimaly.  How many of those have the front face entirely white?

(You should assume the white square with the Rubik's cube logo is always on the front face, as we did in the video.)

The 2x2x2 Rubik's cube has 3674160 possible configurations.  For 276 of those configurations, the optimal solve requires 14 quarter-turns.  (We consider that a half-turn counts as two quarter-turns.)

If I pick a random configuration out of the 3674160 possible configurations, what is the expected number of quarter-turns required to solve that configuration in the optimal way?  In other words, what is the average number of turns among the optimal solution of all possible configurations?

You can round your result to two decimal places.