What does it mean for a Rubik's cube to be perfectly scrambled, and how do you reach it? Without doing a checker board

Can you picture the perfectly scrambled cube? A Rubik's Cube that's perfectly scrambled? How would it look? Is it even possible?

The quest for the Perfect Scramble is now upon us, and I challenge you puzzlers to find the state that is "perfectly scrambled" and how to do this scramble, starting with a solved cube, in minimum moves.

But first, before you can even begin to figure it out, mathematically prove it, or even brute force it, you must define it. What exactly is a perfectly scrambled cube? there's 6 faces to the cube, and 9 squares on each one, so how do you define the perfect scramble?

The perfect scramble is the scramble farthest away from the perfect cube. What would that look like?

The quest for the perfect scramble is upon you. It's up to you to solve this Rubik's crisis! Can you do it?

Answer

The "most scrambled cube" is any configuration that requires the greatest number of rotations to solve the cube using a perfect algorithm.

Although unknown, this algorithm is hypothetically called God's algorithm and in fact the maximum number of rotations, called God's number has been found to be 20.

The list of such 20-move cubes is given here.

---

To define the "most scrambled-looking" cube, consider any legal cube configuration where:

1. each face displays all six colours


2. for each face: upon blacking out the cells of any $n$ colours, $n \leq 4$, the resulting $3\times 3$ grid must exhibit no horizontal, vertical, diagonal, or anti-diagonal symmetry


3. no line of 3 identically-coloured cells may appear horizonally, vertically, diagonally, or anti-diagonally on any face

Alternatively, we might gauge scrambledness via empirical observation as follows:

1. 
   

   Given the population, $H$, of all capable human beings on Earth, let $S$ be a subject drawn from $H$, and conduct the following experiment $\forall\; S \in H$:

   
   
   
   
   
   1. 
      

      Explain the nature and objective of the Rubix cube to subject $S$, and provide a "play" cube for familiarization purposes.

      
      
   
   
   2. 
      

      After a minimum of 5 minutes of continuous play, present $S$ with a complete set of 43,252,003,274,489,856,000 rubix cubes, one per each legal state of the contraption. For every unique subset of 3 cubes, have $S$ rank the cubes in order of increasing scrambledness per his/her subjective preference.

      After each evaluation, tally $0$ for the cube ranked "least scrambled", $2$ for the cube ranked "most scrambled", and $1$ for the remaining cube.

      
      
   
   
   
   


2. 
   
   

   After all subjects in $H$ have completed all tallies for all subsets of all possible cube states, assign to each cube state a datum $s$ that is the sum of all numbers tallied on the state. $s$ will be a non-negative integer $<$ 1.7$\times$10⁶⁹.

   
   


3. 
   

   Let $s_{\rm max}$ be the $s$ datum of greatest magnitude computed in step 3. Let $C$ be the set of all Rubix cube states for which $s = s_{\rm max}$. We conclude that any cube $c \in C$ is "maximally visually scrambled" with 95% certainty.