# ZZ-blah

#### blah

##### brah
Note: The contents of this thread have changed a lot over the course of the day because of several miscalculations and a few new ideas that came along the way. If you just want the important stuff in this LL approach, read all the underlined and bolded text in this entire thread

I think I've just had an idea that may very potentially become mainstream in a few months/years if it's as impressive as it appears to be. What do I mean by this? Somehow, I feel that I've missed a point that makes this method as stupid as all the other methods that claim to be able to beat Fridrich, but I can't figure out what that point is, yet. So I'll post it here for someone to find out the flaw

Here's what the method is all about:
1-Look LL with 108 algorithms

It starts with ZZF2L. There is no need for phasing at the end of F2L. Then you do 1-Look LL. That's all there is to it.

How it works: During LL, 5/6 of the time, you can AUF such that 2 adjacent edges are solved. Why do an extra phasing step?

Simple proof: Let's name the edges 1, 2, 3 and 4 respectively in clockwise order, doesn't matter which edge you start from. Here are all the possible LL edge permutations after F2L: 1234, 1243, 1324, 1342, 1423, 1432*. Need I say more? I'll talk about the 1432 case later on.

So what happens after this? You either get the 1234 case, or 1 of the other 4 cases. If you get the 1234 case, do pure CLL. If you get any of the other 4 cases (I actually just see them as 1 case with 2 adjacent edges solved and the other 2 swapped), do one of the 240 algs.

Actually, there's more. If you don't do LL corner control, you'll end up with 12*9*3 = 324 1LLL cases to memorize. If you do LL corner control with the Winter/Summer Variations to ensure that there's at least 1 corner oriented, you'll end up with 12*20 = 240 1LLL cases to memorize. For the Winter Variation, it's just a matter of choosing between RU'R' and URU2R'. For the Summer Variation, you need to learn 1 more extremely short alg, and choose between that and RUR'.

Oh, and about that 1432 case, you can learn all 167 cases (got this figure from Michal Hordecki) for ZZLL, but I'd just do COLL and EPLL, it only happens 1 in 6 times anyway. And it probably isn't too hard to find a way to detect this at the end of F2L to avoid it once this method gets the recognition and development it needs.

So, anybody found the flaw in this entire proposition yet? If not, I'm gonna start generating algs

Edit: I corrected everything, I originally did a miscalculation and thought only 108 algs were needed. I recalculated and realized that we need 240 algs. But never mind that. This method's still useable, check out the next 2 posts.

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#### blah

##### brah
Better idea: Do LL corner control such that you end up with ZERO corners oriented, this way you have even fewer algs to learn. 12*6 = 72 algs, that's fewer than OLL and PLL combined.

Edit: This method is getting ridiculously promising, someone please point out a flaw somewhere before I get really addicted to it.

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#### blah

##### brah
Wait, I was stupid. It's not 108 algs. It's 12*20 = 240 algs.

But that's history, I like the zero corners oriented approach better now

Edit: The zero corners oriented approach is better! Case recognition is so easy because all the non-U colors are on U.

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#### blah

##### brah
I've generated 24/72 RUL 3-gen algs for the Double Sune/Antisune cases. They're just ZBLL algs really. But I haven't been able to find ZBLL algs for Double Sune and Pi cases online because I guess no one's learned them yet. And it's really not that hard to learn. If you already know COLL, then you would know 8 of these 24 cases already. I guess all 72 could be easily learned in less than a month. Or half a month if you're hardcore.

Basically, whatever I've proposed so far is just a reduced version of ZBLL simply by doing LL corner control (I've just realized this myself!) And also a different recognition method*. I'll post these corner control algs (a few Winter/Summer Variation algs) once I'm done with them, I'm about 50% done now.

*Actually, the only ZBLL recognition method I know is the one used by Jason Baum/Dan Harris. I think the one I suggested has the potential to be as fast as that, I hope

#### Ellis

##### Member
How difficult is it to control LL corner orientation to zero every time? And about the 1432* case, are there still separate algorithms for that?

Edit: It looks like thats included. Sorry, I'm just trying to understand this. The LL is orienting and permuting all corners plus permuting 0-3 edges and its 72 cases?

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#### Lt-UnReaL

##### Member
The only down side to this is ZZF2L. EO-Line + cross will take forever to master.

#### blah

##### brah
How difficult is it to control LL corner orientation to zero every time?
I don't have the exact figures because I haven't yet finished generating all the algs, but this is what I've got so far: 35 out of 108 cases require 3 moves, the rest should average 7 to 8 moves. So on average, for full LL corner control, you'd be doing 3.xx (just an estimate, could be 2, could be 4) more moves than usual. I don't know how that appears to you, but to me, doing 3 more intuitive moves instead of learning 400 more algs is like a dream come true.

Look, here's the thing: You're gonna spend at most 1 second doing those 3.xx moves without having to think much. If you learn full ZBLL, you're gonna be spending about a second trying to recognize your LL case anyway. I'd pick the easier way out

And about the 1432* case, are there still separate algorithms for that?
I'll deal with that problem later. I really don't think it's that big an issue. Like I said, I (or someone else) will probably find a quick way to avoid that case at the end of F2L 100% of the time. If not, COLL + EPLL really isn't that bad, quick recognition and execution, and you get a 1/12 chance of skipping EPLL. Edit: Forget that last sentence, there are only 20 algs for this case - half the number of algs for COLL!

The LL is orienting and permuting all corners plus permuting 0-3 edges and its 72 cases?
Unbelievable? Believe it! Actually it's just 36 with mirrors. And since all my algs are currently RUL, mirroring should be very easy. This should be a dream method for OH, theoretically. But you got something wrong, the 1LLL is orienting and permuting all corners, plus permuting 2 edges or no edges.

For orienting + permuting all corners, and swapping 2 adjacent edges (probability: 2/3), you need 72 algs. For orienting + permuting all corners, and swapping 2 opposite edges (probability: 1/6), you need 20 algs. For orienting + permuting all corners, and leaving the edges untouched (probability: 1/6), you need pure CLL, which consists of 16 algs.

This gives a total of 108 1LLL algs.

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#### blah

##### brah
The only down side to this is ZZF2L. EO-Line + cross will take forever to master.
Agreed. I probably won't use it for 2H, but it has lots of potential for OH. Lofty, are you reading this?

By the way, cross isn't necessary, blockbuilding on either side of the line is just fine.

#### blah

##### brah
@Jason Baum and Chris Hardwick and anyone else who's learned part of ZBLL, if you're reading this, you can choose to stop learning full ZBLL and instead focus on improving recognition for the cases you already know. I think Chris knows all the T and U cases for ZBLL.

For example, in Chris' case, he can do LL corner control to ensure 2 adjacent corners are oriented everytime, then he can have a 1-look LL. Get what I'm trying to say? I think this is much better than having to learn all ~500 ZBLL algs and get confused or something.

But anyway, this is just my opinion. I am of course in no position to give advice to great cubers like you guys, but I sure hope my suggestion helps in one way or another.

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#### krazedkat

##### Member
I think I've just had an idea that may very potentially become mainstream in a few months/years if it's as impressive as it appears to be. What do I mean by this? Somehow, I feel that I've missed a point that makes this method as stupid as all the other methods that claim to be able to beat Fridrich, but I can't figure out what that point is, yet. So I'll post it here for someone to find out the flaw

Here's what the method is all about:
1-Look LL with 240 (corrected) algorithms

It starts with ZZF2L. There is no need for phasing at the end of F2L. Then you do 1-Look LL. That's all there is to it.

How it works: During LL, 5/6 of the time, you can AUF such that 2 adjacent edges are solved. Why do an extra phasing step?

Simple proof: Let's name the edges 1, 2, 3 and 4 respectively in clockwise order, doesn't matter which edge you start from. Here are all the possible LL edge permutations after F2L: 1234, 1243, 1324, 1342, 1423, 1432*. Need I say more? I'll talk about the 1432 case later on.

So what happens after this? You either get the 1234 case, or 1 of the other 4 cases. If you get the 1234 case, do pure CLL. If you get any of the other 4 cases (I actually just see them as 1 case with 2 adjacent edges solved and the other 2 swapped), do one of the 240 algs.

Actually, there's more. If you don't do LL corner control, you'll end up with 12*9*3 = 324 1LLL cases to memorize. If you do LL corner control with the Winter/Summer Variations to ensure that there's at least 1 corner oriented, you'll end up with 12*20 = 240 1LLL cases to memorize. For the Winter Variation, it's just a matter of choosing between RU'R' and URU2R'. For the Summer Variation, you need to learn 1 more extremely short alg, and choose between that and RUR'.

Oh, and about that 1432 case, you can learn all 167 cases (got this figure from Michal Hordecki) for ZZLL, but I'd just do COLL and EPLL, it only happens 1 in 6 times anyway. And it probably isn't too hard to find a way to detect this at the end of F2L to avoid it once this method gets the recognition and development it needs.

So, anybody found the flaw in this entire proposition yet? If not, I'm gonna start generating algs

Edit: I corrected everything, I originally did a miscalculation and thought only 108 algs were needed. I recalculated and realized that we need 240 algs. But never mind that. This method's still useable, check out the next 2 posts.
That is what I've been working on -.- except that mine was full with over 1000 algs (No ZBF2L).... This is a good idea BUT, as with my method, there are probably way too many algs. for anyone with a NORMAL memory to memorize.

#### blah

##### brah
That is what I've been working on -.- except that mine was full with over 1000 algs (No ZBF2L).... This is a good idea BUT, as with my method, there are probably way too many algs. for anyone with a NORMAL memory to memorize.
How is 100-ish "way too many"? Any normal person who's been Fridrich-ing for a while wouldn't find 100 algs daunting at all.

#### AvGalen

That is what I've been working on -.- except that mine was full with over 1000 algs (No ZBF2L).... This is a good idea BUT, as with my method, there are probably way too many algs. for anyone with a NORMAL memory to memorize.
How is 100-ish "way too many"? Any normal person who's been Fridrich-ing for a while wouldn't find 100 algs daunting at all.
100-ish is "way too many" for me. After 3 years of speedcubing I have reached the point where I went to more competitions than I know algorithms. I guess I should have learned at least 1 PLL during my travelling so I would at least know all PLL's by now.

Any normal person who's been Fridrich-ing
Normal persons don't Fridrich

But seriously, this method looks like it really has the potential to give 1 look last layers. Could you give a couple of example solves?

And is there a list of algs?

#### Lofty

##### Member
Hmm yes I am reading this
This makes me very upset that I only put a couple weeks into ZZ adn then gave up... my only problem is that I can already get WR times OH with the Fridrich method (plus edge control+COLL+other little tricks) so thats very discouraging to learning a new method. (Plus I do have some kind of life lol). I feel like this could be a good intermediate step between this and something like full ZZ or ZB. Another problem is that you just can't brute force a bunch of RUL algs and find the best algs... you would have to generate huge lists for each case then try and optimize them for finger tricks. I guess with only 36 plus mirrors this is not too big of a task.
I have a list of 2GLL algs generated already if you need those cases. I generated them all but I didn't find the best algs of the lists yet for most of them. I dont even remember if I am still hosting them or if I ever hosted them. I know I was working at the table of 2GLL at once point... Idk. Maybe I can learn some new algs

#### blah

##### brah
Scramble from CubeMania: B U' R F' D2 L2 D R U' B' U L B2 U' F2 R F2 U L' U B L' D' F U
EOLine: y' L' D F R' L2 y (5)
First block: R2 U L' U R U R' (7)
Second block: L2 U' L U' L2 U L (7)
First slot: R' U R U2 L U L' (7)
Second slot setup: R' U2 R U (4)
LL corner control: R' U' R (3) (kind of "lucky")
1LLL: (no AUF required) y L' U2 L U2 L' U L U2 L' U L U2 L' U' L (15)
Total move count: 48

This was REALLY easy. EOLine and LL corner control were both easy.

----------

Just to clarify, for 1LLL, I always AUF to solve 2 adjacent edges and then do a cube rotation to place the solved edges at UB and UL, then recognize the COLL case.

Edit:

Another scramble from CubeMania: F U' B' U' R2 U B2 U B2 U2 B' L B2 D R U B2 R D2 L2 D2 R' U' L2 U
EOCross: y L' F' R F R y' R L' U F2 (9)
First slot: U L2 U2 L' U' L U' L2 (8)
Second slot: R' U' R U2 R' U R (6.5)
Third slot: R U2 R' U' R U R' (6.5)
Fourth slot setup: U2 L' U L (4)
LL corner control: U' L' U L (4) (this skip happens 1/36 of the time )
PLL: AUF A perm (10)
Total move count: 48

Why did I have to get lucky for my first two examples?

----------

Third scramble: F2 R' B2 R U F R' D2 L' D' B2 U2 B2 D2 R2 D B L2 U L U' R' B U R
EOLine: y' U D' F B' L' U L2 y (7)
First block: L U' L2 R U2 L U L (8)
First slot: R L U2 L' (4)
Second block: R' U R' U' R U R' (7)
Second slot setup: U R' U' R (4)
LL corner control: U2 R' U2 R (4) (this is corner control, we choose to this instead of U' R' U R)
1LLL: U' U' L U' R' U L2 U' R L U2 L' U' L (13) (the first U' is an AUF)
Total move count: 47

This looks like a "normal" solve to me.

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#### vloc15

##### Member
wow..how does this method differ from ZZ-B? or from other ZZ variations?

is there a list for all the algos needed?

#### Lofty

##### Member
It differs because it forces zero corners oriented limiting the algs to only two of the ZBLL cases as opposed to ZZ which has phasing to control the edge permutation.
And from reading the msgs posted by blah it appears he is working on a list now. Alg lists don't just generate themselves.

#### JohnnyA

##### Member
Wow, is this two methods you have discovered in two days? Wow. This also intrigues me, especially the anti-intuitive corner control, it seems like you are disadvantaging yourself but you are actually improing your solve. Very nice!

Some side notes - how does your LL work, you say you recognise the COLL case but for this do you need two sets of COLL algs, one for when all 4 are solved and one where only the two adjacent edges are solved?

Also what is AUF - I understand the meaning but don't know the definition.

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#### blah

##### brah
Since there have been a few requests, I'll post some algs I've already generated for the Double Sune case. It's the case with the fewest number of ZBLL algs because of its high symmetry.

Explanation of naming:
DS: Double Sune (U stickers on R and L)
DA: Double Antisune (U stickers on F and B)
ULF corner: 1
URF corner: 2
URB corner: 3
ULB corner: 4
R: swaps 2 and 3
L: swaps 1 and 4
F: swaps 1 and 2
B: swaps 2 and 3
/: swaps 1 and 3
\: swaps 2 and 4
CW: 4-cycle clockwise
CCW: 4-cycle counterclockwise
S: 4-cycle 12431 (the line connecting 1243 looks like an S)
N: 4-cycle 14231 (the line connecting 1423 looks like an N)
H: 4-cycle 13421 (the line connecting 1342 is an X with a horizontal bar)
V: 4-cycle 13241 (the line connecting 1324 is an X with a vertical bar)

Note that all these algs also simultaneously swap the UF and UR edges (since it is impossible to have pure corner 2-swaps or 4-cycles).

DS-R
U L' U R' U' L U2 R U' R' U' R U R' U' R (16f*)
U2 R' U2 L U' R U' R' U' R U R' U L' U2 R (16f*)
L' U2 R U' L U' L' U' L U L' U R' U2 L U2 (16f*)

DS-L
R U R' U R U2 L' U R' U' L U2 R U2 R' U' (16f*)
L U2 R' U2 R U R' U2 L' U' R U2 L U2 L' U (16f*)

DS-F
U2 R U' L' U R' U L U2 R U' L' U R' L (15f*)
L U' R' U L' U R U2 L U' R' U R L' U2 (15f*)

DS-B
R L' U R' U R U' R' U2 L U' R U2 R' U' (15f*)

DS-/
U L U2 R' U R U2 R' L' U R2 U2 R' U' R U' R' (17f*)
U L' U' L U' L' U2 L2 U R' L' U2 L U L' U2 R (17f*)

DS-\
L' U R U' L2 U2 R' L2 U R U' L2 U' R' L' (15f*)

DS-CW
U R U2 R' U' R U R' U' R U' R' (12f*)

DS-CCW
R U R' U R U' R' U R U2 R' U' (12f*)

DS-S
U2 R' U' R U' R' U' L U' R U L' (12f*)
L' U' L U' L' U' R U' L U R' U2 (12f*)

DS-N
U R' U2 R L U2 R' U' L' U2 R U' L U' L' U (16f*)
U L U2 R' L' U2 L U' L' U2 R U' L U' L' U (16f*)
U' R U2 R' L' U2 R U' R' U2 L U' R U' R' U' (16f*)
U' L' U2 R L U2 L' U' R' U2 L U' R U' R' U' (16f*)
R' L' U2 L2 U' R U' R' U' L2 U2 R U' L2 U' L' (16f*)

DS-H
U' L U' R' U L2 U' R L U2 L' U' L (13f*)

DS-V
L U R U' L2 U' L2 U' L2 U2 R' L2 U' L' (14f*)

-----

DA-R
U R' U L U' R U' L' U2 R' U L U' R L' U (16f*)
U' L' U R U' L U' R' U2 L' U R U' R' L U' (16f*)

DA-L
U R L' U' L U' L' U L U2 R' U L' U2 L (15f*)

DA-F
R U' L U R' U2 L' U L U L' U' L U L' U' (16f*)

DA-B
U L' U' L U' L' U2 R U' L U R' U2 L' U2 L (16f*)
U' L' U2 R U2 R' U' R U2 L U R' U2 L' U2 L (16f*)

DA-/
R U R' U R U2 R2 U' R L U2 R' U' R U2 L' U' (17f*)
R' U2 L U' L' U2 R L U' L2 U2 L U L' U L U' (17f*)

DA-\
R L U L2 U R' U' R L2 U2 L2 U R' U' L (15f*)

DA-CW
U L' U' L U' L' U L U' L' U2 L (12f*)

DA-CCW
L' U2 L U L' U' L U L' U L U' (12f*)

DA-S
U R' U' L' U R2 U R2 U R2 U2 R2 L U R U' (16f*)
U' R' U2 R2 U R2 U R U L U' R U L' U R' (16f*)
U' L' U' R' U L2 U L2 U L2 U2 R L2 U L U (16f*)

DA-N
L' U R U' L2 U R' L' U2 L U L' U (13f*)

DA-H
U2 R U2 R' L' U2 R U L U2 R' U L' U L (15f*)
U2 L' U2 R L U2 L' U L U2 R' U L' U L (15f*)
R' U2 R L U2 R' U R U2 L' U R' U R U2 (15f*)
R' U2 R L U' R2 U' R2 U' R2 U2 R L' U2 R (15f*)
L U2 R' L' U2 L U R U2 L' U R' U R U2 (15f*)

DA-V
U R U R' U R U L' U R' U' L U (13f*)
U' L U L' U L U R' U L' U' R U' (13f*)

#### krazedkat

##### Member
That is what I've been working on -.- except that mine was full with over 1000 algs (No ZBF2L).... This is a good idea BUT, as with my method, there are probably way too many algs. for anyone with a NORMAL memory to memorize.
How is 100-ish "way too many"? Any normal person who's been Fridrich-ing for a while wouldn't find 100 algs daunting at all.
240 algs. not 100....

#### JohnnyA

##### Member
So, you do EOLine and ZZf2l, then on the last slot you do corner control to have no oriented corners. What do you do for corner control? Intuitive, or algorithms? An example of corner control would be nice. Then, you do a 1LLL which completes the corners and switches the last edge pair ... so how do you get the edge pair correct. Sorry for not quite understanding your first post