Cube entropy

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Cube entropy

Postby arenol » Sat Aug 27, 2011 10:02 pm

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?
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Re: Cube entropy

Postby borginator2 » Sun Aug 28, 2011 7:20 am

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.
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Re: Cube entropy

Postby Sharkretriver » Sun Aug 28, 2011 11:44 am

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
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Re: Cube entropy

Postby Zeotor » Mon Aug 29, 2011 2:44 am

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.
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Re: Cube entropy

Postby Sharkretriver » Mon Aug 29, 2011 12:55 pm

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.
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