New Approach to ZZ-d

[porkynator]

It is almost a year since I published this post; that approach isn't bad, but I wasn't fully satisfied. So I recently started working again on ZZ-d, and tonight I finished. Now I am satisfied with this method, I think it can be suitable for speedsolving (although probably useful only for OH) and I think it deserves a new thread (unlike the old approach).

What's new?
With my old method, you permuted corners by doing an average of 9 moves after building the first 3x2x1 block. With this new method you will achieve the same result by adding fewer moves (I haven't calculated anything this time, but the average movecount should be around 5 and the worst case 7) while completing the first 3x2x1 block. It may be only 1 move better than the old method, but some of the new permuting algs are super-fast (like U R' or R U R') and I think they are way better for OH. Moreover, with this new method you solve CP before finishing the first block, which is how zz-d was originally meant.
There are 24 different patterns to recognize and 18 algorithms (1 to 3 moves long) to learn. This isn't a big problem, but it more difficult than my old approach.

Before we begin...
...I want to "expand" my old method.
If you have built a 2x2x1 block on LBD and the LFD corner is already placed (not caring about orientation) you may want to use my old approach to solve corners' permutation now. But there's a problem: your LF edge may be stuck on RF, RD or RB after you are done with the permutation. This is a problem. But I've "generated" more algorithms, so that you can choose which one to use to avoid the edge getting stuck. Here we go:
For the "nothing to do" case you can do any R* move to free your edge.
For the L' U R U' L case you can also use U L' U R' or R2 L' U R2.
For the L' U R2 U' L case you can also use R2 L' U R or L' U' R.

The method
First of all, place the DR corners on DR, as in the old method. Then, if the DLF corner is in place you use the "expanded" old method, otherwise you put it in ULB. Now you are ready to recognize the corners' pattern (you can do it by looking only at 3 corners, URB, URF and ULF).
In the spoiler the table with the cases.
Instead of numbers or letters I gave the 6 different cases the name of 6 random pokemons.

Spoiler

[TABLE=width:,500]
[TR]
[TD]Pattern[/TD][TD]DR corners OK[/TD][TD]DR corners SWAPPED[/TD]
[/TR]
[TR]
[TD]Picture 1[/TD][TD]Pikachu Case[/TD][TD]Squirtle Case[/TD]
[/TR]
[TR]
[TD]Picture 2[/TD][TD]Bulbasaur Case[/TD][TD]Machamp Case[/TD]
[/TR]
[TR]
[TD]Picture 3[/TD][TD]Pidgey Case[/TD][TD]Dragonite Case[/TD]
[/TR]
[TR]
[TD]Picture 4[/TD][TD]Machamp Case[/TD][TD]Bulbasaur Case[/TD]
[/TR]
[TR]
[TD]Picture 5[/TD][TD]Pikachu Case[/TD][TD]Squirtle Case[/TD]
[/TR]
[TR]
[TD]Picture 6[/TD][TD]Dragonite Case[/TD][TD]Pidgey Case[/TD]
[/TR]
[TR]
[TD]Picture 7[/TD][TD]Pidgey Case[/TD][TD]Dragonite Case[/TD]
[/TR]
[TR]
[TD]Picture 8[/TD][TD]Bulbasaur Case[/TD][TD]Machamp Case[/TD]
[/TR]
[TR]
[TD]Picture 9[/TD][TD]Machamp Case[/TD][TD]Bulbasaur Case[/TD]
[/TR]
[TR]
[TD]Picture 10[/TD][TD]Dragonite Case[/TD][TD]Pidgey Case[/TD]
[/TR]
[TR]
[TD]Picture 11[/TD][TD]Machamp Case[/TD][TD]Bulbasaur Case[/TD]
[/TR]
[TR]
[TD]Picture 12[/TD][TD]Pidgey Case[/TD][TD]Dragonite Case[/TD]
[/TR]
[TR]
[TD]Picture 13[/TD][TD]Machamp Case[/TD][TD]Bulbasaur Case[/TD]
[/TR]
[TR]
[TD]Picture 14[/TD][TD]Pidgey Case[/TD][TD]Dragonite Case[/TD]
[/TR]
[TR]
[TD]Picture 15[/TD][TD]Squirlte Case[/TD][TD]Pikachu Case[/TD]
[/TR]
[TR]
[TD]Picture 16[/TD][TD]Dragonite Case[/TD][TD]Pidgey Case[/TD]
[/TR]
[TR]
[TD]Picture 17[/TD][TD]Squirtle Case[/TD][TD]Pikachu Case[/TD]
[/TR]
[TR]
[TD]Picture 18[/TD][TD]Bulbasaur Case[/TD][TD]Machamp Case[/TD]
[/TR]
[TR]
[TD]Picture 19[/TD][TD]Pikachu Case[/TD][TD]Squirtle Case[/TD]
[/TR]
[TR]
[TD]Picture 20[/TD][TD]Dragonite Case[/TD][TD]Pidgey Case[/TD]
[/TR]
[TR]
[TD]Picture 21[/TD][TD]Bulbasaur Case[/TD][TD]Machamp Case[/TD]
[/TR]
[TR]
[TD]Picture 22[/TD][TD]Squirtle Case[/TD][TD]Pikachu Case[/TD]
[/TR]
[TR]
[TD]Picture 23[/TD][TD]Pikachu Case[/TD][TD]Squirtle Case[/TD]
[/TR]
[TR]
[TD]Picture 24[/TD][TD]Squirtle Case[/TD][TD]Pikachu Case[/TD]
[/TR]
[/TABLE]

In the next spoiler I listed 3 algs for each case. Note that 3 algs are enough to cover all possible "last edge saving" cases.

Spoiler

Pikachu Case L' U2 R2 or L' U R' or L' U' R
Squirtle Case R2 or R' U R' or L' U R
Bulbasaur Case R or R' U' R or R2 U' R'
Machamp Case R' or U R' or R U' R
Dragonite Case U' R2 or U2 R or R U' R2
Pidgey Case R U R' or R U' R' or R2 U' R or Do nothing (yay!)

Once you performed the permuting algorithm, you can solve the remaining pair of the left block using only L and U moves (you can obviously use also L2, L', U2 and U'). After completing the first block this way, you can solve the whole cube 2-gen (using only R and U moves).

UPDATE
When one of the DR corners is in DLF setup moves can be long. So I decided to find algorithm even for this case(s). I only did it for when the two DR corners are in DLF and DBR, thinking that when one of them is in DFR recognition can be so bad that you may just want to R' to see the hidden corner.
Considering that when DRF is in DLF the DR corners are OK, and that when DRF is in DBR they are swapped, you can use the same recognition system (thinking of the corner in DRF as if it was in DFL) and apply these transformations:

Pikachu becomes Machamp and Machamp becomes Pikachu.
Squirtle becomes Dragonite and Dragonite becomes Squirtle.
Bulbasaur becomes Pidgey and Pidgey becomes Bulbasaur.

Minor Update
The mysterious "Charmander Case" did not actually exist: it was a Bulbasaur case. I don't know how it happened, maybe I was setupping the case in a wrong way, but it seemed to me that the Bulbasaur algs did not work for that one. But they did. So, no more Charmander and all makes way more sense now.
Thanks to collins for finding this out.
______________________________________________
I haven't tried this method yet, but I hope I can find enough time to learn it.
What do you think about this approach to ZZ-d? Was it a waste of time for me to think of it or will it be called the "not-missing-anymore"-link?
______________________________________________
EDIT (2021-03-10): all of the pictures broke because I let my old website die, so I re-uploaded them. Since the forum now has a 20 image per post limit I replaced them with links. It's probably better if you refer to the pdf attached below.
______________________________________________
EDIT 2 (2021-03-16): N's-cvt proposed a better recognition system that relies on looking at just 3 last layer corners, see this file and his post.

 

[mDiPalma]

This is very good. I completely understand it! Excellent explanation!

I'm going to learn all the cases right now. It's like using visual memory for 3x3 BLD corners.

What do you plan to call it? ZZ-Grumpig?


Edit: You should also sort the cases by the destination of DLF. For example, group cases 1, 2, 7, 13, 16, and 22 together. It seems to make it easier to learn.

 

[mDiPalma]

Sorry for the double post.

I learned a few cases and filmed a 41.25 without the algorithm table! UWR?

You can hear me muttering the Pokémon in the background. My family must think I'm crazy. :fp

Your move, Porkynator! :tu

Edit: 38.65

Edit2: 33.89. it might be a better idea to organize the algorithms in groups of whichever pokemon they involve. A lot of the N and V shaped cycles, for example, involve Machamp/Bulbasaur. It might help for memorization.

Edit3: 32.48

Edit4: 25.95 on camera. EPLL skip. This is a very good method. I like starting with the same 2x2x1 block every time. It makes transitioning from EOL to F2L very easy. By the way, whenever I get DLF solved, I do L' U L U, just to practice the harder cases.

Do you think there is a better Last-Block/Last-Layer combination than Block+2GLL? Is there some direct-solving method for the last 13 pieces that doesn't involve building an F2L block first?

What about solving the 2x2x1 at DRB and another at ULB (any U-layer 2x2x1)? Then the cube is reduced to 7 pieces instead of 8. There would be less cases. But I do not know how the efficiencies will compare.

Edit5: Some preliminary testing of that on cubeexplorer suggests an average movecount (in 2gen htm) of around 14.

But can you imagine doing a solve where the last algorithm is just R U' R' ?

Man, I wish you weren't on CEST. I feel like I'm talking to myself!

 

[porkynator]

What do you plan to call it? ZZ-Grumpig?

Nice idea!

Edit: You should also sort the cases by the destination of DLF. For example, group cases 1, 2, 7, 13, 16, and 22 together. It seems to make it easier to learn.

I will do something when I start learning it. But I also wanted to see if it's possible to recognize per CP case only looking at the corners on U, like 2-side PLL recognition. Well it is possible, but I don't know if it will be suitable for speedsolving.

it might be a better idea to organize the algorithms in groups of whichever pokemon they involve. A lot of the N and V shaped cycles, for example, involve Machamp/Bulbasaur. It might help for memorization.

I'll try also learning them by pokemon cases instead of by shape and which system is better.

Do you think there is a better Last-Block/Last-Layer combination than Block+2GLL? Is there some direct-solving method for the last 13 pieces that doesn't involve building an F2L block first?

I'd love to know it too. Possibly a reduction system <R,U> -> <R,U2> -> <R2,U2> can be more efficient, but it sounds awful for speedsolving. In my last FMC no time limit solve I solved 2x2x3 + EO + CP in 12, but couldn't find a decent ending. This might be the next thing I'll work on.

What about solving the 2x2x1 at DRB and another at ULB (any U-layer 2x2x1)? Then the cube is reduced to 7 pieces instead of 8. There would be less cases. But I do not know how the efficiencies will compare.

Edit5: Some preliminary testing of that on cubeexplorer suggests an average movecount (in 2gen htm) of around 14.

But can you imagine doing a solve where the last algorithm is just R U' R' ?

It doesn't seems like a big improvement from F2L+2GLL to me... but it can be an idea to start from (grammar?).

Man, I wish you weren't on CEST. I feel like I'm talking to myself!

When I finished the post it was 1 am here And I suppose it's like 4 am in New York now? (Too lazy to check).

 

[Hypocrism]

After you've permuted with DFL on UFB using the algs, and you don't have your DFL pair solved, how do you then go about solving it without mixing up the permutation of the remaining corners? After all you need to make L moves to solve that last DFL pair and once you use an L move you've changed the corner permutation..

There might be something very obvious that I'm completely missing.

 

[porkynator]

After you've permuted with DFL on UFB using the algs, and you don't have your DFL pair solved, how do you then go about solving it without mixing up the permutation of the remaining corners? After all you need to make L moves to solve that last DFL pair and once you use an L move you've changed the corner permutation..

There might be something very obvious that I'm completely missing.

You're right, there is a missing part that isn't obvious.
After you performed the algorithm, you have to solve the remaining left pair with only L or U moves. From this point you can solve the cube using only R and U.
I'm going to edit the first post, thank for noticing this.

 

[Hypocrism]

You're right, there is a missing part that isn't obvious.
After you performed the algorithm, you have to solve the remaining left pair with only L or U moves. From this point you can solve the cube using only R and U.
I'm going to edit the first post, thank for noticing this.

That definitely solves it, I should have been able to work it out!
Now I just need to decide whether phasing or corner perm is going to work better for me in learning ZZ

 

[porkynator]

Attention please!
I corrected a terrible mistake: the two charmander cases were actually different ones. So now there's a new case, the Mew Case.
There may be still some mistake in there; if anyone finds something wrong, please let me know.

EDIT: that new case was actually a pikachu case :fp
I've also added a missing ' in the third pidgey case

EDIT 2: One last (I hope) thing: the fifth case with DR corners swapped was listed as a Bulbasaur case, but was actually a Squirtle.

 

[mDiPalma]

I'd love to know it too. Possibly a reduction system <R,U> -> <R,U2> -> <R2,U2> can be more efficient, but it sounds awful for speedsolving. In my last FMC no time limit solve I solved 2x2x3 + EO + CP in 12, but couldn't find a decent ending. This might be the next thing I'll work on.

The hard part is going from <R,U2> to <R2,U2>. Do you have any ideas for this?

Attention please!
I corrected a terrible mistake: the two charmander cases were actually different ones. So now there's a new case, the Mew Case.
There may be still some mistake in there; if anyone finds something wrong, please let me know.

EDIT: that new case was actually a pikachu case :fp
I've also added a missing ' in the third pidgey case

EDIT 2: One last (I hope) thing: the fifth case with DR corners swapped was listed as a Bulbasaur case, but was actually a Squirtle.

I was wondering why some of my solves ended with COLL+EPLL. I just blamed myself, thinking I recognized the corner cycle incorrectly!

Edit: 24.64

Edit2: 22.79

 

[elrog]

The hard part is going from <R,U2> to <R2,U2>. Do you have any ideas for this?

Since there are so few cases in <R2,U2> wouldn't it be more efficient to go straight from <R,U2> or <U,R2> to solved?

After you've permuted with DFL on UFB using the algs, and you don't have your DFL pair solved, how do you then go about solving it without mixing up the permutation of the remaining corners? After all you need to make L moves to solve that last DFL pair and once you use an L move you've changed the corner permutation..

There might be something very obvious that I'm completely missing.

Use key-holing before you do the other block? To preserve Edge orientation you must do an E2 instead of E'.

 

[mDiPalma]

I got a 20.34.

Since there are so few cases in <R2,U2> wouldn't it be more efficient to go straight from <R,U2> or <U,R2> to solved?

But since there are so MANY <R,U2> cases, it pays to reduce to <R2,U2>.

Use key-holing before you do the other block? To preserve Edge orientation you must do an E2 instead of E'.

The algorithms that Porkynator published "store" a solved permutation with respect to the left side. So when you use <LU> moves to solve the DFL pair, you do not destroy the corner permutation.

Keyhole would destroy cp, if I'm not mistaken.

 

[elrog]

Since there are so many <R,U2> cases and it is such a restricted move set, you'd basically have to make algorithms for each case to get it into the <R2,U2> group. So why not just solve it? I generated a couple of solved for the <R2,u> group and they were pretty long solutions. I'm not sure reducing like this is the best way to go.


Key-holing shouldn't mess up the CP if your key-holing edges. Example:
To place the FL edge to finish a 2x2x3 block (in the LD position) after you did CP and EO, you could place in edge in the UF position and preform Uw' R' Uw.


What if you solved two 2x2x1 blocks in the R and U layers then solved the rest with algs? You do have to build 1 more edge with your blocks, but you have more options for your blocks.

 

[mDiPalma]

Since there are so many <R,U2> cases and it is such a restricted move set, you'd basically have to make algorithms for each case to get it into the <R2,U2> group. So why not just solve it? I generated a couple of solved for the <R2,u> group and they were pretty long solutions. I'm not sure reducing like this is the best way to go.

There are 12 (6 unique) cases for the <R2,U2> move set. By reducing from <R,U2> to <R2,U2>, you can divide the amount of algs you need by a factor 12. And after the alg, you are only a max of 6 moves away from solved. That's reasonable.

Key-holing shouldn't mess up the CP if your key-holing edges. Example:
To place the FL edge to finish a 2x2x3 block (in the LD position) after you did CP and EO, you could place in edge in the UF position and preform Uw' R' Uw.

Doesn't this break EO?

What if you solved two 2x2x1 blocks in the R and U layers then solved the rest with algs? You do have to build 1 more edge with your blocks, but you have more options for your blocks.

Lol, scroll back like 10 posts.

 

[elrog]

There are 12 (6 unique) cases for the <R2,U2> move set. By reducing from <R,U2> to <R2,U2>, you can divide the amount of algs you need by a factor 12. And after the alg, you are only a max of 6 moves away from solved. That's reasonable.

It would only half the alg count if you worry about where the 1x1x3 blocks go, and if you don't recog is crazy bad.

If your looking for something reasonable, you should go with solving corners and then edges after getting the into the <R2,U> move set. Corners can be done intuitively leaving you with 5 edges requiring 60 algs.

Instead of Uw' R' Uw, it should be Uw2 R' U R Uw2

 

[mDiPalma]

Or after getting into <R2,U>, you could just solve the F2L and do an EPLL. But this is no more efficient than F2L+2GLL.

To be honest, the best approach is likely F2L+2GLL.

 

[porkynator]

Isn't it really bad when one of the DR corners happens to be stuck in DLF before when you have to setup it to DR? Yes, it is. But don't worry, I've found a solution and I've updated the first post!

 

[aznanimedude]

I don't always zz-d but when I do, I blame porkynator for making these approaches

 

[mDiPalma]

I hate to do this again, but...

If you place the DR corners and isolate the Left block pieces to the U and L faces before completing the first 2x2x1 block, you only need 2 algs for each pokemon case. Right?

 

[porkynator]

I hate to do this again, but...

If you place the DR corners and isolate the Left block pieces to the U and L faces before completing the first 2x2x1 block, you only need 2 algs for each pokemon case. Right?

I think so (I would have to check each case), but I also think it's way easier to just learn those 7 algorithms.

 

[TheNextFeliks]

Wow. I prefer this over other zz-porky a lot. Any tips for remembering which case is which Pokemon? Just learn them like algs?