## Cube entropy

General discussions and topics

### Cube entropy

I have a general impression that ha 25-30 move scramble (3x3x3) is not quite enough to separate all pieces from each other. When I scramble randomly myself with 40-50 moves, I find it more difficult to find a good start.
As a result, I started thinking whether it is possible to find some kind of metric that calculates how well a cube is scrambled.

A possible metric would be to calculate the entropy of the cube. Entropy is a well defined metric within mathematics and chemistry and should be suitable way to calculate how well a cube is scrambled. A solved cube has entropy 0, and grows the more unordered the cube is.

Has anyone looked into this?
arenol

Posts: 9
Joined: Sun Jul 10, 2011 9:47 pm

### Re: Cube entropy

I never bother with scrambles. I just mess it up without looking for about 20 seconds.
Please take off topic discussion off this forum. Thanks.

borginator2

Posts: 1544
Joined: Tue Sep 30, 2008 8:07 am
Location: Cheshire, UK

### Re: Cube entropy

right now it's just the computer showing 20 or 21 move scrambles (WCA regulations)
now of course hand scrambling would require more moves because it's not as random
you can display the distance that it would take to solve the scramble, but most scrambles should have distance 18
lol, here to help ^_~
Sharkretriver

Posts: 367
Joined: Thu Jul 14, 2011 10:11 pm

### Re: Cube entropy

I think how well a cube is scrambled depends on how it's being looked at. Someone may look at a certain scramble from a speedsolving perspective and begin to see one solution. However, someone else may look at the same thing from a fewest moves perspective and begin to see a different solution.

It would probably be difficult to calculate a cube's entropy. If a computer program determined it, then it would have to consider lots of different methods. It would do this so that the scrambled cube wouldn't be biased toward one approach.

Zeotor

Posts: 359
Joined: Thu Jan 13, 2011 5:12 am

### Re: Cube entropy

Zeotor wrote:I think how well a cube is scrambled depends on how it's being looked at. Someone may look at a certain scramble from a speedsolving perspective and begin to see one solution. However, someone else may look at the same thing from a fewest moves perspective and begin to see a different solution.

It would probably be difficult to calculate a cube's entropy. If a computer program determined it, then it would have to consider lots of different methods. It would do this so that the scrambled cube wouldn't be biased toward one approach.

Good point. I've gotten scrambles that would be great for 3OP but average for speedsolving.
lol, here to help ^_~
Sharkretriver

Posts: 367
Joined: Thu Jul 14, 2011 10:11 pm