The New Method / Substep / Concept Idea Thread

[Neuro]

Instead of doing 50 samples, it would probably be less effort to work out the exact mean and SDs of move counts for each method. It would eliminate any uncertainty from having a limited sample size.

I provided the means and SD's in the document and also performed an ANOVA test to determine if any of them were truly different. ZZ-CT had the lowest mean, and of the top 3 lowest means ZZ-B had the lowest SD. However, ZZ-B's mean was only .05 greater than ZZ-CT's. Essentially the same thing with the SD's, where they were off by only ~.2. I concluded ZZ-CT on this preliminary test due to the extremely small deviation away from the "best" method and having what I believe to be much better recognition and OH potential.

I believe a larger size is necessary as not all of the plots are equally distributed, and some of them had extreme outliers which can of course affect the Mean and SD. I think that 20 is acceptable, but 50 will be more accurate. I hope this gives some reasoning behind my absolute madness (these tests take a VERY long time.) Also, I'd love to hear some opinions or secondary tests that should be performed on the methods. Hopefully someone benefits from this study at some point

 

[Shiv3r]

hey, so random Idea: CN ZZ is very possible if you're only Y axis neutral.
So here's what you do in inspection:
-Recog EO from one of the Y axis neutral anlges
-then glance around the Z axis(I rotate it but I don't think you need to) to see if there's an easy EOline(z rotations do not affect number of bad edges in any way)

You only need to do this twice, and only once if you find a good EOline your first time. and bonus: you don't need to recognize EO for every orientation, only 2 at most.
what do you think? I am heavily considering trying to get CN with ZZ just to use this.

I provided the means and SD's in the document and also performed an ANOVA test to determine if any of them were truly different. ZZ-CT had the lowest mean, and of the top 3 lowest means ZZ-B had the lowest SD. However, ZZ-B's mean was only .05 greater than ZZ-CT's. Essentially the same thing with the SD's, where they were off by only ~.2. I concluded ZZ-CT on this preliminary test due to the extremely small deviation away from the "best" method and having what I believe to be much better recognition and OH potential.

I believe a larger size is necessary as not all of the plots are equally distributed, and some of them had extreme outliers which can of course affect the Mean and SD. I think that 20 is acceptable, but 50 will be more accurate. I hope this gives some reasoning behind my absolute madness (these tests take a VERY long time.) Also, I'd love to hear some opinions or secondary tests that should be performed on the methods. Hopefully someone benefits from this study at some point

I think he meant mathematically calculate the averages according to the likelihood of each case and stuff like that.

 

[Teoidus]

Theoretical movecounts are already available and calculated by @mDiPalma

Interestingly they suggest conclusions different from @Neuro 's

 

[Mastermind2368]

When I first switched from CFOP to ZZ, I was doing a lot of EOCross, because I found block building hard. After my second comp, I was able to transition to full ZZ, and I can confidently say that either CFOP or ZZ is much better than a mix of both.

I did EO-Line, then EO cross, rather then thinking about the other two pieces when doing EO-Line.

 

[Neuro]

So here is something pretty cool that I came up with for OH

1: Roux FB
2: z or z' and build 2x2x3 block <U,u,R/L>
3: F2L minus 1 corner
4: Ribbon style orientation (idk the ergonomics of this but it's probably similar to that of OH OLL)
5: TTLL

Basically its CFOP-y Pootris (seriously is there a better name for this? if not there really, REALLY needs to be one) The method has pretty good ergonomics (and IMO CFOP OH really isn't that bad) with some really nice steps at the end of the solve.

Solve here, 42 moves. I'm a right handed OH user so I catered to that demographic.

 

[Sue Doenim]

Take a look at the square 1 world record.
Scramble: 0,5/-3,0/1,1/0,-3/-3,-3/2,-4/-5,0/0,-3/0,-3/0,-3/2,-2/0,-4/4,-4
Solve:
y2
CS: 2,-2/0,4/-2,-1/0,-3/
CO: 0,-2/
EO: 3,-3/-1,-1/
CP: Skip
EP: -2,4/5,-1/-3,0/1,1/-3,0/2,-3
It's a fluke, due to low movecount. Easy CO, best EO (other than skip), CP skip. We need a method where this isn't just luck. The chance of just nice EO and CP is 1/144, I believe. With a Roux style F2B, movecounts like this are not uncommon (maybe that's a bit of an exaggeration, but it certainly ha better chances than in Vandenburg). This would be compounded if you used non-matching blocks, but that is a bit of a stretch. If you build a layer minus 1 edge, the solve could be finished with the same case count as TTLL+PLL, but recognition would be better due to being able to recognize CP from any angle, among other things. We need to make this a thing.

 

[Teoidus]

So here is something pretty cool that I came up with for OH

1: Roux FB
2: z or z' and build 2x2x3 block <U,u,R/L>
3: F2L minus 1 corner
4: Ribbon style orientation (idk the ergonomics of this but it's probably similar to that of OH OLL)
5: TTLL

Basically its CFOP-y Pootris (seriously is there a better name for this? if not there really, REALLY needs to be one) The method has pretty good ergonomics (and IMO CFOP OH really isn't that bad) with some really nice steps at the end of the solve.

Solve here, 42 moves. I'm a right handed OH user so I catered to that demographic.

I'd argue you don't even need the z/z', can just build the 2x2x3 block <L,l,U> if you're right-handed.

I'm not sure how many moves ribbon takes, but this should give ~13 2x2x3, ~7sq, n ribbon, 15 TTLL => 35+n moves on average.
If ribbon is ~9-10 moves (which I could see it being) and my estimate for sq isn't too low, this would be pretty nice, averaging 45-46 moves.

Oh whoops, I didn't realize you have to solve the last F2L edge as well. In that case I think the movecount gets a little less appealing.

Take a look at the square 1 world record.
Scramble: 0,5/-3,0/1,1/0,-3/-3,-3/2,-4/-5,0/0,-3/0,-3/0,-3/2,-2/0,-4/4,-4
Solve:
y2
CS: 2,-2/0,4/-2,-1/0,-3/
CO: 0,-2/
EO: 3,-3/-1,-1/
CP: Skip
EP: -2,4/5,-1/-3,0/1,1/-3,0/2,-3
It's a fluke, due to low movecount. Easy CO, best EO (other than skip), CP skip. We need a method where this isn't just luck. The chance of just nice EO and CP is 1/144, I believe. With a Roux style F2B, movecounts like this are not uncommon (maybe that's a bit of an exaggeration, but it certainly ha better chances than in Vandenburg). This would be compounded if you used non-matching blocks, but that is a bit of a stretch. If you build a layer minus 1 edge, the solve could be finished with the same case count as TTLL+PLL, but recognition would be better due to being able to recognize CP from any angle, among other things. We need to make this a thing.

Maybe something like:

1. cubeshape
2. F2B
3. CLL + ULUR
4. EPLL

?

 

[Sue Doenim]

Maybe something like:

1. cubeshape
2. F2B
3. CLL + ULUR
4. EPLL

?

If you solve DB during F2B and use parity cubeshape, you can use one alg, basically HKPLL to solve the rest in a feasible number of algs. This is what I'm proposing. Your idea is probably fine, but has an extra look. Also, I had a 2-gen style HF thing I proposed a while back, and I want to ask you as the only person who really knows much about CP what you think of it.

HF+
1a) 1x2x3 on D (<R,U,F,r,u,f>)
1b) Attach DLF and solve CP
2a) E-slice edges -1
2b) Insert last E-slice edge and force arrow case
3) L5C
4) L5E
Example solve:
Scramble: F2 B2 U2 R2 L F U' D2 L' D' B D2 F' R2 U2 B L2 F2 R2 U2 B
Inspection- z2
Block- F' U' f2 E F2 R' (6/6)
CP- R U R' D R U' R' D' (8/14)
E-slice- U R U' R' u' U' r U r' u2 U r U r' (14/28)
Last edge + 3-flip- E' r U' r' (4/32)
L5C- R U2 R2 U2 R' U R2 U' R U2 R (11/43)
L5E- M' U M u' M' U2 M' U M U2 M' U M2 (13/56)
56 moves. This is around ZZ-VH movecount, isn't it?
Note: I don't actually know how to fix CP, I just tried stuff until I found something that worked; Last E-slice edge alg was intuitive; L5C was from cube explorer; L5E was just a cancelled U-perm, so if this is to become a method, we should have all L5E arrow cases.

 

[Teoidus]

Ah you're right. That sounds much better, solving the entire U layer + DF with 1 alg.

For the HF idea, I dunno if it's worth it to use something as advanced as CP. Usually the only advantages CP can give are slightly better ergonomics or a greatly reduced case count. In this case given that HF is sorta "high" movecount already, it doesn't seem to be worth much to reduce the case count and get a 2gen L5C.

 

[Neuro]

I'd argue you don't even need the z/z', can just build the 2x2x3 block <L,l,U> if you're right-handed.

I'm not sure how many moves ribbon takes, but this should give ~13 2x2x3, ~7sq, n ribbon, 15 TTLL => 35+n moves on average.
If ribbon is ~9-10 moves (which I could see it being) and my estimate for sq isn't too low, this would be pretty nice, averaging 45-46 moves.

Oh whoops, I didn't realize you have to solve the last F2L edge as well. In that case I think the movecount gets a little less appealing.

My estimate is 13 moves for 2x2x3, 9 for F2L-1 corner, 10 for ribbon orientation, and 15 for TTLL. Average movecount based on these estimates would be 47 moves, about the same as Roux. However, I believe tht lucky singles would be relatively common as 2x2x3 can be like 10 moves pretty easily (5 FB, 5 2x2x3) and TTLL/Ribbon orientation have really nice cases also. I may just use this and do Roux for 2H (maybe this for 2H as well b/c my F2L is actually pretty good.) I've basically decided I'm switching to Roux at this point but of course I'll continue to work on my ZZ variant sheet.

46 move solve, marked the most important parts of the solve w/ movecounts. Ugly but fast TTLL. I think being neutral between a z rotation and a rotation-less style is the best bet.

 

[Shiv3r]

My estimate is 13 moves for 2x2x3, 9 for F2L-1 corner, 10 for ribbon orientation, and 15 for TTLL. Average movecount based on these estimates would be 47 moves, about the same as Roux. However, I believe tht lucky singles would be relatively common as 2x2x3 can be like 10 moves pretty easily (5 FB, 5 2x2x3) and TTLL/Ribbon orientation have really nice cases also. I may just use this and do Roux for 2H (maybe this for 2H as well b/c my F2L is actually pretty good.) I've basically decided I'm switching to Roux at this point but of course I'll continue to work on my ZZ variant sheet.

46 move solve, marked the most important parts of the solve w/ movecounts. Ugly but fast TTLL. I think being neutral between a z rotation and a rotation-less style is the best bet.

This is basically what Kavin does for first and second block. weird how the fastest OH Rouxer is right-handed...

 

[Neuro]

That's where I drew inspiration from actually. I enjoy the rotation he uses. Right hand OH FTW!

 

[TDM]

weird how the fastest OH Rouxer is right-handed...

Why is it?

 

[Shiv3r]

Why is it?

Right-handers are in the Minority iirc.

 

[Hazel]

lil 3x3 method idea:
solve 2x2x2
EO
F2L using blockbuilding
LL

or you could also do 2x2x2 and EO at the same time, not too sure how hard it would be though

 

[TDM]

Right-handers are in the Minority iirc.

Roux solvers are also in the minority. Do you find it surprising that there are Roux solvers who are so high in the rankings?

 

[Thermex]

Roux solvers are also in the minority. Do you find it surprising that there are Roux solvers who are so high in the rankings?

No, because Roux is such a great method

 

[Neuro]

I calculated the # of cases for ribbon orientation (without accounting for AUF's)

There's 57 OLL's. Well that was easy

There are 8 possible EO cases, as well as 8 CO cases for both the plus and minus sets, so 2 sets of 64

64+64+57=185 algs

Still within reason as AUF's will probably cancel a decent number of cases out. I do suspect it's higher than the predicted 150 though.

 

[mDiPalma]

Also, I'd love to hear some opinions or secondary tests that should be performed on the methods. Hopefully someone benefits from this study at some point

Taking the means (taken from published algsets) and case frequency (for intuitive steps) into account, here is a good approximation of the relative movecounts of a few ZZ/Petrus LS/LL variants.

Method         Step 1        Step 2        Step 3         AUFS        Total        Alg Count
---------------------------------------------------------------------------------------------------------
ZBLL           7.04          13.5          ---            1.5         22.04        493
[color=green][b]CR             5.33          9.07          9              1.5         24.90       144 (72 w/ M)[/b][/color]
ZZ-b           10.07         13.76         ---            1.5         25.33        169
ZZ-CT          10.37         15.21         ---            2.25        27.83        197
COLL/EPLL      7.04          ~11.5         7.5            2.25        28.29        46
WV/SV          4.67          8.74          ~15            1.5         29.91        48
OLL/PLL        7.04          7.93          ~15            2.25        32.22        28

Here is a plot of movecount versus algcount for each variant and a least-squares linear regression.

 

[JTay]

Howdy all,
There's only 58 algorithms for each set of Ribbon Orientation (ROLL+ & ROLL-) when you account for symmetry. Add in the 72 from TTLL, and there are 188 new algorithms for someone who already knows full CFOP.

I should be able to make the algorithms soon, starting with the + cases, so expect those to come out in the next few days! It's my first time generating algs, so if anyone would like to help or can give any tips, that would be great!