# Volunteers needed for cross solving study



## jazzthief81 (Feb 25, 2008)

Dear friends,

Some of you may remember this post:
http://games.groups.yahoo.com/group/speedsolvingrubikscube/message/430

In the study I did there I calculated some statistics for the 
required number of moves for solving the cross of a fixed color. 
Since most people always start with the same color, these figures 
give us a good idea of what the target should be for speedcubing.

Lately there have been some discussions on whether being color 
neutral is a big advantage for people who start with building the 
cross. Of course, it's easy to find single cases where the white 
cross can't be solved in under 8 moves but the yellow cross is 
already solved. But that doesn't tell us a lot about whether color 
neutrality is better compared to fixed color cross solving in the 
long run. 

That's why I'm currently redoing the same experiment for solving the 
cross on _any_ face. The intermediate results can be seen here:
http://www.cubezone.be/colorneutrality.html

I've done about 18% of the all the cases at the moment, and this took 
about 10 days. I plan to repeat this experiment for quarter turn 
metric (this current calculations use face turn metric), and I think 
it would also be interesting to investigate opposite cross solving 
and see where it is placed against fixed color cross solving and 
complete color neutral cross solving.

I'm very excited to know what the results will end up being, but I 
don't feel like waiting for another 2-3 months. That's why I was 
hoping that we could tackle this problem in [email protected] style and 
distribute the work over various machines. I've made a small client 
that is able to do generate all edge positions and solve them:
http://www.cubezone.be/colorneutralityathome.zip

Just download, extract, and launch run.bat and it will connect to a 
server and retrieve a package from it. A package in this case 
corresponds to all positions that have the same pattern of flipped/
unflipped edges. Once it has finshed processing a package, it will 
send the results to the server and retrieve a new one.

If you want to contribute to this study, feel free to download the 
client application and process some packages. It will take up 
virtually no memory or network bandwidth, but it will keep your 
processor busy all the time.

Thanks for your help.

Kind regards,
Lars


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## Stefan (Feb 25, 2008)

Very nice, I'm looking forward to those results as well. Especially quarter turn metric. 



jazzthief81 said:


> Of course, it's easy to find single cases where the white cross can't be solved in under 8 moves but the yellow cross is
> already solved.


Are you sure? Can you show one?


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## Mik (Feb 25, 2008)

The .bat file looks safe, opened it up in textedit and there's nothing bad.
Can't run those on Mac's though...


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## Bryan (Feb 25, 2008)

Does anyone know of a simple webpage where I could enter in the 4 cross pieces and have it tell me the optimal algorithm? I always have problems recognizing the 7 moves, and if I could have something that would always show me the answer, I could learn that way (as opposed to looking at three or four examples from a webpage).

I'm guessing CubeExplorer has this feature, but I wanted something a little more lightweight that I could access from work easily.


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## FU (Feb 25, 2008)

Bryan said:


> Does anyone know of a simple webpage where I could enter in the 4 cross pieces and have it tell me the optimal algorithm? I always have problems recognizing the 7 moves, and if I could have something that would always show me the answer, I could learn that way (as opposed to looking at three or four examples from a webpage).
> 
> I'm guessing CubeExplorer has this feature, but I wanted something a little more lightweight that I could access from work easily.



Johannes' optimal cross solver. Do a search on the forum for it.


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## jazzthief81 (Feb 25, 2008)

Mik said:


> The .bat file looks safe, opened it up in textedit and there's nothing bad.
> Can't run those on Mac's though...



You can, Mik. You can open a terminal and type:
sh run.bat

or you can rename it to run.sh and run it straight from the Finder. I will add a shell script to the zip file for convience.


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## Pedro (Feb 25, 2008)

I'm helping, Lars 

so...when I'm "tired" of doing it, I just close the client?
or do I have to wait until a package is finished?


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## jazzthief81 (Feb 25, 2008)

Pedro said:


> I'm helping, Lars
> 
> so...when I'm "tired" of doing it, I just close the client?
> or do I have to wait until a package is finished?



Yes, Pedro. 

You can just close it down at any time. At the moment the work it has done on the current package will be lost, but that's not a big deal. If a downloaded package is not being processed within one day, it will get sent to another person.


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## Stefan (Feb 25, 2008)

jazzthief81 said:


> It will take up virtually no memory


That might explain why it takes so long. Are you actually solving each case instead of looking up the distance for each cross?

And wow, I just saw there were already 16 cases found which take 8 moves! I was thinking about betting there won't be any.


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## jazzthief81 (Feb 25, 2008)

StefanPochmann said:


> jazzthief81 said:
> 
> 
> > It will take up virtually no memory
> ...



No it looks up the the 6 possible crosses in a precalculated table and takes the minimal distance.


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## Stefan (Feb 25, 2008)

Alright... sorry about that. I very much overestimated the memory the tables would take.


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## KoenHeltzel (Feb 25, 2008)

Hey Lars,

Interesting study.. i'm in.

Greets, Koen


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## jazzthief81 (Feb 25, 2008)

StefanPochmann said:


> Alright... sorry about that. I very much overestimated the memory the tables would take.



Yeah, it's just 6 times 190080 entries.

Where the applications spends its time is generating a cube from the edge case with a given number and then calculating 6 indices from that.


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## Johannes91 (Feb 25, 2008)

Do you reduce symmetric positions? If not, that would be one way to speed it up.



StefanPochmann said:


> And wow, I just saw there were already 16 cases found which take 8 moves! I was thinking about betting there won't be any.


And here's one where each 2x2x2 blocks requires 8 moves: B' F R D' U B2 R2 B' L' R D F2 U L2 R2 D' R2 D'.

Now, who wants to do a complete calculation like this for 2x2x2 block?


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## Stefan (Feb 25, 2008)

Ok, two suggestions to maybe make it faster, although I know that'd might be a lot harder to implement. So I don't suggest to do these, I'd just like to throw them out as ideas.

1) Orientation as inside loop. Then from one cube to the next, you'd just have to flip edges, which probably means only flipping some bits in your six indices, right? And if you used Gray code (for the "first" eleven bits), that would even be just two bits (one from the Gray code, plus the remaining twelfth bit), so very little change between two cubes.

2) Symmetries... i.e. somewhat only do about 1/48 (or 1/96 thanks to inverses?) of all cases. Not sure how to do this, though. Scares me.


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## AvGalen (Feb 25, 2008)

Johannes91 said:


> Do you reduce symmetric positions? If not, that would be one way to speed it up.
> 
> 
> 
> ...


That scramble should be considered "illegal" for FMC 

The client is running on my pc now. Too bad it requires a "cmd" and a "java" window to stay open.

I hope you will do the same for a 2x2x2 block and after that for a cross OR 2x2x2 block. Maybe a scramble will come up that requires 8 moves for both cross AND 2x2x2


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## Stefan (Feb 25, 2008)

AvGalen said:


> I hope you will do the same for a 2x2x2 block


That'd be *a lot* harder (and this is a huge understatement).


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## Johannes91 (Feb 25, 2008)

StefanPochmann said:


> AvGalen said:
> 
> 
> > I hope you will do the same for a 2x2x2 block
> ...


Indeed...



AvGalen said:


> Maybe a scramble will come up that requires 8 moves for both cross AND 2x2x2


Once this calculation is done, it shouldn't be too hard to go through all the 8-movers and see if it's possible to place the corners in a way that requires 8 moves for 2x2x2 blocks, too. But I can't believe such a position exists.


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## jazzthief81 (Feb 25, 2008)

StefanPochmann said:


> Ok, two suggestions to maybe make it faster, although I know that'd might be a lot harder to implement. So I don't suggest to do these, I'd just like to throw them out as ideas.
> 
> 1) Orientation as inside loop. Then from one cube to the next, you'd just have to flip edges, which probably means only flipping some bits, right? And if you used Gray code (for the "first" eleven bits), that would even be just two bits (one from the Gray code, one from the remaining twelfth bit), so very little change between two cubes.



Indeed, this would speed it up. The good thing about putting the orientation as the outside loop, is that we get all the statistics grouped by orientation pattern for free. The correlation with the flip of the edges is quite interesting. It also gives us a nice and workable amount of packages to distribute. 



StefanPochmann said:


> 2) Symmetries... i.e. somewhat only do about 1/48 (or 1/96 thanks to inverses?) of all cases. Not sure how to do this, though. Scares me.



Absolutely true, but it scares me too and it would make things a lot more complicated to implement. Moreover, it would be hard to tell afterwards whether we didn't skip any positions. Doing it this way, if we can recognize the cube symmetries from the results at least we have some proof that it actually checked all edge cases.


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## fw (Feb 25, 2008)

If you would also add a text-based version (no GUI), I could run this in background on some servers..


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## jazzthief81 (Feb 25, 2008)

Johannes91 said:


> StefanPochmann said:
> 
> 
> > AvGalen said:
> ...



The only way I can think of is to go over all 43.252.003.274.489.856.000 cube positions and do 8 table look ups for each of them.


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## AvGalen (Feb 25, 2008)

fw said:


> If you would also add a text-based version (no GUI), I could run this in background on some servers..


Be very carefull about doing that. Servers are typically not meant to run privately made programs like this one. If these are your own servers, that might be ok, but never do that on your bosses servers without (written) permission


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## fw (Feb 25, 2008)

AvGalen said:


> Be very carefull about doing that. Servers are typically not meant to run privately made programs like this one. If these are your own servers, that might be ok, but never do that on your bosses servers without (written) permission



Dont worry, I am allowed to do that


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## jazzthief81 (Feb 25, 2008)

AvGalen said:


> The client is running on my pc now. Too bad it requires a "cmd" and a "java" window to stay open.


Yeah, the cmd window is a bit annoying. If you want it to disappear, edit the batch file to make it look like this:

start javaw ....

instead of this:

java ...

As for the application window itself, I thought it would be nice to get at least some feedback of what is happening.


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## mrCage (Feb 25, 2008)

Hi Lars 

Are you ultimately going to calculate an upper bound for the whole of CFOP?? Sounds like a daunting task to me 

I have seen some estimates .. ranging from about 55 - 60. But that was for average solves !!

- Per


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## Carson (Feb 25, 2008)

Will leave this running while I'm at work, but with my Athlon XP 2400+, I don't know how much help I'll be.


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## jazzthief81 (Feb 25, 2008)

Carson said:


> Will leave this running while I'm at work, but with my Athlon XP 2400+, I don't know how much help I'll be.



Any help is greatly appreciated. Thank you!


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## Bounb (Feb 25, 2008)

Excellent idea.

I very much like your approach to this - with the '@Home' style cumulative processing power program. I'll leave it running for a bit. Look forward to seeing the results


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## MiloD (Feb 25, 2008)

Johannes91 said:


> And here's one where each 2x2x2 blocks requires 8 moves: B' F R D' U B2 R2 B' L' R D F2 U L2 R2 D' R2 D'.



this is the ugliest scramble I have ever seen.


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## AvGalen (Feb 25, 2008)

MiloD said:


> Johannes91 said:
> 
> 
> > And here's one where each 2x2x2 blocks requires 8 moves: B' F R D' U B2 R2 B' L' R D F2 U L2 R2 D' R2 D'.
> ...


Really? Maybe you should try it on a 2x2x2  I think the WR can be broken with this scramble


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## AvGalen (Feb 25, 2008)

jazzthief81 said:


> AvGalen said:
> 
> 
> > The client is running on my pc now. Too bad it requires a "cmd" and a "java" window to stay open.
> ...


 
Actually, I think you should use this command:

```
start /belownormal javaw -cp colorneutralityathome.jar -Dmode=online -Daddress=78.21.73.117 -Dport=8080 cross.gui.CrossSolverMain
```
That way your system will be much more responsive for your daily work.


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## jazzthief81 (Feb 25, 2008)

AvGalen said:


> Actually, I think you should use this command:
> 
> ```
> start /belownormal javaw -cp colorneutralityathome.jar -Dmode=online -Daddress=78.21.73.117 -Dport=8080 cross.gui.CrossSolverMain
> ...



That's good feedback Arnaud, I didn't realize you could specify a priority like that. I will change it in the next version.


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## ShadenSmith (Feb 25, 2008)

I'm helping as well.


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## jazzthief81 (Feb 25, 2008)

StefanPochmann said:


> Very nice, I'm looking forward to those results as well. Especially quarter turn metric.
> 
> 
> 
> ...



OK, I have to admit that I wrote this down without really thinking about it. The point I was trying to make is that it's easy to find cases where your normal cross is quite hard and on another face it's (almost) solved.

But because you insist, Stefan, here it is and it wasn't difficult to find :
B2 D L2 R2 U R2 D' L2 R' F' D' L R2 B2 F' D2 L' F2 D U2


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## Swordsman Kirby (Feb 25, 2008)

jazzthief81 said:


> StefanPochmann said:
> 
> 
> > Very nice, I'm looking forward to those results as well. Especially quarter turn metric.
> ...



Scrambles like that tell us that color neutrality is great.


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## jazzthief81 (Feb 25, 2008)

fw said:


> AvGalen said:
> 
> 
> > Be very carefull about doing that. Servers are typically not meant to run privately made programs like this one. If these are your own servers, that might be ok, but never do that on your bosses servers without (written) permission
> ...



In that case, you can download the client application again. I've added a text-only mode for running in headless environments.

The client application now also starts at the lowest priority right away. 

Kind regards,
Lars


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## jazzthief81 (Feb 25, 2008)

Swordsman Kirby said:


> jazzthief81 said:
> 
> 
> > StefanPochmann said:
> ...



Now try this one:
D2 L' D2 F2 R' D2 B2 F2 R2 B' D U F L' R' B U2 F2 D2 R2


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## Lucas Garron (Feb 26, 2008)

jazzthief81 said:


> Swordsman Kirby said:
> 
> 
> > jazzthief81 said:
> ...


I happen to think I found a fast, easy cross on these scrambles upon trying them. I might not even mind having an average of 12 solves with such crosses.


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## Lofty (Feb 26, 2008)

I'm on my second packet 
And I would be interested in doing it for 2x2x2 blocks, though I'm only opposite color neutral and not even sub-40 OH with Petrus it still leaves me all the 2x2x2 blocks to pick from.
We should do a similar thing with ZBLL. I would love a massive table with tons of algs to pick from for each case divided up into LUR, RUD, RUF, optimal, etc.


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## cuBerBruce (Feb 26, 2008)

mrCage said:


> Hi Lars
> 
> Are you ultimately going to calculate an upper bound for the whole of CFOP?? Sounds like a daunting task to me
> 
> ...



I don't think coming up with an upper bound for the whole of CFOP is a daunting task. Finding the best (lowest) upper bound for the whole of CFOP might be, but first you would have to define exactly what you mean by that.


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## Dene (Feb 26, 2008)

This is awesome, Lars! Way to go! The OPness of colour neutrality is finally coming to show!! I may as well have my little input here, in saying that I can almost always find a case where on edge is already oriented and another 2 are extremely easy, for a cross. This isn't certain, but I generally come to expect a good cross on at least one face. COLOUR NEUTRALITY FOR LIFE!!!


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## Stefan (Feb 26, 2008)

jazzthief81 said:


> But because you insist, Stefan, here it is and it wasn't difficult to find :
> B2 D L2 R2 U R2 D' L2 R' F' D' L R2 B2 F' D2 L' F2 D U2


Darn. I was of course hoping there isn't any. After all, there are just 102 cases for eight moves white cross, and it had to be one putting the white edges in F2L only. Figured there's a good chance this is impossible. Darn.


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## AvGalen (Feb 26, 2008)

It looks like it will be finished within the next 2 days. What will be next?

I think all big conclusions can already be drawn from the current results. The rest of the crunching will just provide us with meaninglessly exact numbers and hopefully some fun scrambles.


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## jazzthief81 (Feb 26, 2008)

StefanPochmann said:


> jazzthief81 said:
> 
> 
> > But because you insist, Stefan, here it is and it wasn't difficult to find :
> ...



Well I never really looked into the 102 worst cases a lot. These are the patterns that can occur for cross on bottom:

4 edges in D slice: 10 cases
3 edges in D slice, 1 edge in E slice: 8 cases
1 edge in D slice, 3 edges in U slice: 20 cases
1 edge in E slice, 3 edges in U slice: 16 cases
1 edge in D slice, 1 edge in E slice, 2 edges in U slice: 8 cases
4 edges in U slice: 40 cases


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## Bounb (Feb 27, 2008)

Should be done in one or two days we're at 60% now. Looking forward to the analysis.


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## fw (Feb 27, 2008)

I think this whole thing is great. We should do this more often. I for myself have some CPU power, but almost never use it. And I think there are some other interesting cube-related problems which are unsolved just because it takes to long to calcuate the solution...


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## cuBerBruce (Feb 28, 2008)

fw said:


> I think this whole thing is great. We should do this more often. I for myself have some CPU power, but almost never use it. And I think there are some other interesting cube-related problems which are unsolved just because it takes to long to calcuate the solution...



I've done several large analyses related to 3x3x3 and 4x4x4. A lot of these involved the creation and reading of large data files, which would not make them be very well suited for WAN execution. I assume this one only sends distribution results back to the host (a small amount of data), so it's works well for this type of distributed computing.

I was wondering if Lars used some type of existing software package or tool to develop this client & server.

(By the way, I noticed I hit the jackpot the other night - orientation #777.)


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## jazzthief81 (Feb 28, 2008)

cuBerBruce said:


> I've done several large analyses related to 3x3x3 and 4x4x4. A lot of these involved the creation and reading of large data files, which would not make them be very well suited for WAN execution. I assume this one only sends distribution results back to the host (a small amount of data), so it's works well for this type of distributed computing.
> 
> I was wondering if Lars used some type of existing software package or tool to develop this client & server.
> 
> (By the way, I noticed I hit the jackpot the other night - orientation #777.)



Yeah, the amount of data sent back and forth is almost nothing. Retrieving a package is picking a number between 0 and 2047 and the result is the distribution of all the positions in that package (9 natural numbers).

I didn't use an existing library, just the Java API. It's all you need really. The server is a simple Java servlet that you can access through a URL.


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## jazzthief81 (Feb 28, 2008)

AvGalen said:


> It looks like it will be finished within the next 2 days. What will be next?



Next will be the same analysis in QTM, and then same thing again for opposite color cross solving.

After that we can debate about what other things would be interesting to investigate.



AvGalen said:


> I think all big conclusions can already be drawn from the current results. The rest of the crunching will just provide us with meaninglessly exact numbers and hopefully some fun scrambles.



Well, we could easily have made yet another good estimate, but now we will finally have the exact figures.


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## AvGalen (Feb 28, 2008)

jazzthief81 said:


> Well, we could easily have made yet another good estimate, but now we will finally have the exact figures.


If this was just about getting the exact figures I wouldn't have bothered. For me pi is simply 3.14, infinity is 999999999999999999999999 and 1/3 is 33%. With this logic I can be 100% sure that my logic is almost certainly wrong and/or correct.

For me this project is all about finding "weird" cases.

(p.s. I used to study applied physics)


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## jazzthief81 (Feb 28, 2008)

AvGalen said:


> With this logic I can be 100% sure that my logic is almost certainly wrong and/or correct.



I'm not even going to ask you to elaborate on this...


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## fw (Feb 28, 2008)

AvGalen said:


> infinity is 999999999999999999999999
> (p.s. I used to study applied physics)



Is that how all physicists handle math? If yes, that confirms some stereotypes I have heard of 

Just kidding...


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## Lucas Garron (Feb 28, 2008)

AvGalen said:


> If this was just about getting the exact figures I wouldn't have bothered. For me pi is simply 3.14, infinity is 999999999999999999999999 and 1/3 is 33%.


Incredible! You can solve some twistypuzzles from any of more than an infinite number states?


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## Johannes91 (Feb 29, 2008)

Lucas Garron said:


> AvGalen said:
> 
> 
> > For me pi is simply 3.14, infinity is 999999999999999999999999 and 1/3 is 33%.
> ...


Nah.

3x3x3 = 27
5x5x5 = 125
Megaminx is like a 3x3x3

They are all far from infinity!


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## AvGalen (Feb 29, 2008)

Johannes91 said:


> Lucas Garron said:
> 
> 
> > AvGalen said:
> ...


I just realised that those numbers are actually pretty accurate :
1x1x1 = 1 (Start timer, touch cube, stop timer)
2x2x2 = 8 (That's about my average)
3x3x3 = 27 (Again, just about my average)
4x4x4 = 64 (I need to practise a bit more, but 1:04 should be possible)
5x5x5 = 125 (I am getting pretty close to 2:05)
megaminx is like a 3x3x3 only you do the same a couple of times (about 7 times slower for me, about 6 times for Erik so I guess that works)

I never realised this. Thanks for supplying such wonderfull math


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## jazzthief81 (Feb 29, 2008)

So it looks like it's going to be completed this evening and I would like to thank everyone once more for their contributions. This has been awesome. I had a quick look in the logs and the server received results from over 85 different machines.

I will a post some more detailed analysis about this study/experiment somewhere this weekend, but right now I'm in a bit of a hurry because I'm going to Rama's place (I heard something about a birthday party taking place ).

Kind regards,
Lars


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## DanHarris (Mar 1, 2008)

The study is now complete  You can view the data here - http://www.cubezone.be/colorneutrality.html

Some very interesting results! 40 positions at depth 8, and an overall weighted average of 4.8 turns, which I believe is a saving of around a move or so! 

I look forward to your analysis Lars 

Dan


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## Kenneth (Mar 1, 2008)

Can someone maybe create generators for the 8 turn crosses?

I would love to see how many turns I need to solve those


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## jazzthief81 (Mar 1, 2008)

Kenneth said:


> Can someone maybe create generators for the 8 turn crosses?
> 
> I would love to see how many turns I need to solve those



Yes Kenneth, I will do that as soon as I get back home on Sunday.


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## cuBerBruce (Mar 1, 2008)

Wait a minute... Isn't the "total" value 18000000 too high?

The error appears to be orientation #8, depth 1. It appears it should be 1.393.424 instead of 19.393.424.


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## jazzthief81 (Mar 1, 2008)

cuBerBruce said:


> Wait a minute... Isn't the "total" value 18000000 too high?
> 
> The error appears to be orientation #8, depth 1. It appears it should be 1.393.424 instead of 19.393.424.



Yes, you're right. This is one of the packages I processed before the server was put into operation and I added these figures manually and must have made an error.

It's been corrected now, and the total value is what we expect it to be.


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## jazzthief81 (Mar 5, 2008)

It has taken a little longer then expected, but I finally managed to
do the analyses for opposite color cross solving as well. You can find
the results of this and all previous studies here:

http://www.cubezone.be/crossstudy.html

The calculations for complete color neutrality in quarter turn metric
are still ongoing and people who are interested can still help:

http://www.cubezone.be/colorneutralityqtm.html

Kind regards,
Lars


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## Dene (Mar 5, 2008)

Depth/# cases/Distribution

8/40/0.00%	

Lol, 40 cases = 0.00%

I think this shows the power of colour neutrailty! A whole move less on average, those are nice odds. I hope you're all convinced to switch now  . Well done Lars!


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## AvGalen (Mar 5, 2008)

Only one move less on average doesn't convince me at all. Spending 15 seconds on an 6 move cross or 15/6=2.5 seconds on a 5 move cross? I would choose to do the extra move and spent the other 12.5 seconds on finding a finger-trick friendly way of performing those moves and seeing the next pair (or maybe x-cross)

For me this study has proven that color-neutrality is NOT worth it.


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## jazzthief81 (Mar 5, 2008)

AvGalen said:


> Only one move less on average doesn't convince me at all. Spending 15 seconds on an 6 move cross or 15/6=2.5 seconds on a 5 move cross? I would choose to do the extra move and spent the other 12.5 seconds on finding a finger-trick friendly way of performing those moves and seeing the next pair (or maybe x-cross)
> 
> For me this study has proven that color-neutrality is NOT worth it.



Yeah, I agree. It seems to make things a lot more complicated for very little gain.


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## Dene (Mar 5, 2008)

But that isn't realistic at all. The way I see it, 5 seconds to find a face with at leat one edge already oriented, 10 seconds to figure out the rest of the cross. I think I only take about 8 seconds observation on average. That leaves 7 seconds for optimising.

EDIT: And of course, move count isn't everything. As you say, you want it to be finger trick friendly, this is I think the main benefit of colour neutrality, in that, there is almost always an easy to execute cross, not just a short move-count one.


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## AvGalen (Mar 5, 2008)

Already oriented edges are just 1 indication. Just try L' F' R' B' L'. None of the D-layer edges are oriented, but it is a pretty easy cross (B R L F is nicer though)
Neutrality is better in theory, but at my level I need 15 seconds for 1 color. Opposite neutrality is a very nice compromise that prevents really bad starts.


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## Dene (Mar 6, 2008)

Well pish tush you. Maybe it would be no good "at your level" but I'm sure the likes of Harris Chan or Yu Nakajima could find use for it  , I know I certainly can.


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## ExoCorsair (Mar 6, 2008)

I pick one of three-four colors when doing cross on the 3x3x3, unless there's a blatantly obvious, very easy cross on another face (blue, orange). Once you're used to it, F2L times stay the same as F2L times on your normal color.

I don't really see much of a drawback to color neutrality, other than it takes time to practice.

Plus you can end with a cool LL color.


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## Dene (Mar 6, 2008)

ExoCorsair said:


> I don't really see much of a drawback to color neutrality, other than it takes time to practice.



It wouldn't if you learned it from the start, like me  .


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## Johannes91 (Mar 6, 2008)

AvGalen said:


> For me this study has proven that color-neutrality is NOT worth it.


Worth *what*?


jazzthief81 said:


> It seems to make things a lot more complicated


No, it really doesn't.

For me color neutrality is exactly that: color neutrality. It does not mean that I have to always check every possibility before choosing what to do, but that I don't care about colors, only patterns.

I don't see any reason to not be color neutral. But then again, I don't see any reason to program in non-functional languages.


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## Stefan (Mar 23, 2008)

Johannes91 said:


> I don't care about colors, only patterns.


But for color neutrality that does mean that the already solved part is part of the pattern, right? For a CFOP solver solving the F2L pairs this would mean he doesn't just look for the pattern of certain corner/edge pairs, but for patterns of certain corner/edge/cross triples. This seems harder.


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## jazzthief81 (Mar 23, 2008)

So the study was completed over a week ago and I finally managed to update my page:
http://www.cubezone.be/crossstudy.html

Once again thanks to all of you for helping me out. 

Kind regards,
Lars


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## Bryan (Mar 23, 2008)

I'm confused...for fixed in the QTM, depth 9 is 207. But for cross neutral, depth 9 in the QTM is 1,215. Shouldn't that number be smaller? 

It would be neat to see the source code for your optimal cross solver.


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## jazzthief81 (Mar 23, 2008)

Bryan said:


> I'm confused...for fixed in the QTM, depth 9 is 207. But for cross neutral, depth 9 in the QTM is 1,215. Shouldn't that number be smaller?



Percentage-wise it is smaller. For fixed color cross solving it's 207 cases out of 190,080 (with only 4 edges), for the color neutral cross solving it's 1,215 cases out of 980,995,276,800 (with all 12 edges).


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## Stefan (Mar 23, 2008)

I took Lars' numbers and did an estimation and comparison:
http://www.stefan-pochmann.info/misc/neutral_estimation.png

The first two columns are straight from Lars. The third column contains estimations for the neutral column, computed from the fixed column by assuming the different crosses are independent.

f_ = probability that one cross needs i moves
n = probability that C crosses need i moves (i.e. the best of the C needs i moves)

F and N are the cumulative versions:

F = probability that one cross needs i moves *or less*
N = probability that C crosses need i moves *or less*

Then for C-fold color neutrality:
N = 1 - (1 - F)^C)

Again, this assumes that the different crosses are independent, which they're not, for two reasons:
1) Pieces of one cross occupy positions in the cube that pieces of the other crosses then can't be at.
2) If two crosses share common pieces, the position in the cube of such a common piece is the same for both crosses.

You can see from my computations that this estimation works very well for opposite color crosses, and for full neutrality it's still quite good but considerable weaker. For opposite color neutrality only argument 1 applies, as two opposite crosses don't share common pieces. For full color neutrality argument 2 applies, too, and argument 1 applies much stronger._


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## Stefan (Mar 23, 2008)

Update: I added averages. Oh and I searched for Johannes' experimental results. For opposite color neutrality my computed estimations are better, for full color neutrality they're the same. Johannes, how many cubes did you try?


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## Johannes91 (Mar 24, 2008)

StefanPochmann said:


> Johannes, how many cubes did you try?


I'm not 100% sure, but probably 1e5.


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