Volunteers needed for cross solving study

[jazzthief81]

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.

 

[jazzthief81]

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

 

[Dene]

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!

 

[AvGalen]

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.

 

[jazzthief81]

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.

 

[Dene]

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.

 

[AvGalen]

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.

 

[Dene]

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.

 

[ExoCorsair]

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.

 

[Dene]

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 .

 

[Johannes91]

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

Worth *what*?

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.

 

[Stefan]

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.

 

[jazzthief81]

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

 

[Bryan]

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.

 

[jazzthief81]

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).

 

[Stefan]

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.

 

[Stefan]

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?

 

[Johannes91]

Johannes, how many cubes did you try?

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