# ZZ-blah



## blah (Jan 20, 2009)

*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 (Jan 20, 2009)

*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 (Jan 20, 2009)

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 (Jan 20, 2009)

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


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## Ellis (Jan 20, 2009)

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 (Jan 20, 2009)

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


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## blah (Jan 20, 2009)

Ellis said:


> 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 *



Ellis said:


> 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!



Ellis said:


> 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 (Jan 20, 2009)

Lt-UnReaL said:


> 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.


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## blah (Jan 20, 2009)

@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 (Jan 20, 2009)

blah said:


> 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*
> ...


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.


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## blah (Jan 20, 2009)

krazedkat said:


> 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.


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## AvGalen (Jan 20, 2009)

blah said:


> krazedkat said:
> 
> 
> > 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.
> ...


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?


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## Lofty (Jan 20, 2009)

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


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## blah (Jan 20, 2009)

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.

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*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? 

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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 (Jan 20, 2009)

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

is there a list for all the algos needed?


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## Lofty (Jan 20, 2009)

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.


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## JohnnyA (Jan 20, 2009)

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 (Jan 20, 2009)

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*)


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## krazedkat (Jan 20, 2009)

blah said:


> krazedkat said:
> 
> 
> > 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.
> ...



240 algs. not 100....


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## JohnnyA (Jan 20, 2009)

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


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## blah (Jan 20, 2009)

krazedkat said:


> 240 algs. not 100....



Clarified. It's exactly 108 now.


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## mpohl100 (Jan 20, 2009)

whoah
this method rocks
I'll start ZZ right now to learn EOline and then I'll try my best on intuitive Corner control.
The big big big advantage of no corners oriented is that you only have to look at the 4 top stickers which is awesome for recognition.
You rock man!!!!!

I can't wait for a complete list of algorithms.

Thanks in advance

Michael


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## Stefan (Jan 20, 2009)

blah said:


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





mpohl100 said:


> The big big big advantage of no corners oriented is that you only have to look at the 4 top stickers which is awesome for recognition.


I don't get it. How do you have eight corner stickers on U?


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## mpohl100 (Jan 20, 2009)

StefanPochmann said:


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


Well Stefan,
I think you are intelligent enough to understand what he wants to say ;-)


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## krazedkat (Jan 20, 2009)

blah said:


> krazedkat said:
> 
> 
> > 240 algs. not 100....
> ...



Much easier ...


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## Stefan (Jan 20, 2009)

mpohl100 said:


> Well Stefan,
> I think you are intelligent enough to understand what he wants to say ;-)


Apparently not. Yes, it reduces the number of cases, which probably makes it easier. But the way it makes it easier that you're talking about is not clear to me. I can only recognize OLL and PLL. Should I be able to recognize CLL to understand the benefit you're talking about?


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## blah (Jan 20, 2009)

mpohl100 said:


> The big big big advantage of no corners oriented is that you only have to look at the 4 top stickers which is awesome for recognition.



Exactly. I think I've already mentioned this, or I may not have, can't keep track of what I've posted and what I haven't with all the double/triple/quadruple posting in this thread 

But there's even more to the "zero corners oriented" approach than just this. 2 more advantages, in fact.

Firstly, it has the fewest algorithms among all the "n corners oriented" groups (n < 4 ), because it includes the Double Sune case, which has fewer algs than any other cross-OLL case because of its symmetry.

Secondly, corner control is much easier than the traditional way, because you have multiple algs to choose from. What do I mean by this? In classical/traditional corner control methods, you control the corners such that they are all oriented in ONE specific direction, so you would need different algs for all 54 COLS cases (excluding mirrors). For my approach, you would control corners such that they are all NOT oriented in a specific direction, in other words, corner control becomes sort of a "one-to-many function" instead of a "many-to-one function", so you have lots of freedom in applying and choosing algs, because you're fine with either 4 (do PLL in this case) or 0 corners oriented, whereas in the traditional approach, your only goal is to have 4 corners oriented.

Just to make the second point clearer in case it was too confusing, in the traditional approach, take for example the Winter Variation, you can only apply R U' R' and U R U2 R' to 2 specific cases, whereas in my approach, these 2 simple "algs" (I really wouldn't call them algs) can be applied to 14 out of 27 cases - that's more than half the total number of cases!


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## blah (Jan 20, 2009)

StefanPochmann said:


> But the way it makes it easier that you're talking about is not clear to me. I can only recognize OLL and PLL. Should I be able to recognize CLL to understand the benefit you're talking about?



I can't tell if you're pretending not to understand in order to point out some flaw in my sentence, or if you really don't understand.

In case it's some flaw in my sentence, maybe I should've said "Case recognition is so easy because all the U stickers are not on U." Other than that, I can't really think of anything else 

In case you really don't understand (since you mentioned you can only recognize OLL and PLL, I take it that you can't recognize COLL?), the answer to your question would be: Yup.

For CxLL recognition, I think most people look at the non-U-colored stickers to look for color patterns, instead of tracing where each piece goes. (Similar to how PLL recognition is mostly done by identifying blocks, instead of manually tracing where each piece belongs.)

When all 4 corners are misoriented, the U face would only have non-U-colored stickers on the corners, which makes recognition almost instant. When, for example, only 2 corners are misoriented, I would have to look at the U-face stickers of the misoriented corners, then one of the non-U-face stickers of the oriented corners to identify the CxLL case, which is slightly slower.


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## mpohl100 (Jan 20, 2009)

StefanPochmann said:


> mpohl100 said:
> 
> 
> > Well Stefan,
> ...


Oh Stefan I am sorry.
I thought you would know all COLL cases and thus I assumed you knew how to recognize them. 
SO here is my explanation:
If you have the headlights case and both unoriented corners are facing you then you can just see two stickers. That's not enough for recognizing the case. So you have to do a y2 to see what case it is.
If all corners ar unoriented you can see four stickers on top and you can define the case by only these 4 stickers. THus you don't have to perform a cube rotation to recognize the case.
=> a very fast recognition for COLL case

AS I am already able to recognize which COLL I have to perform quite fast if no corners are oriented it won't take me much practice to be good at that.
I would just have to learn to recognize what edges have to be flipped in order to get a fast LL case recognition.

But I am not using COLL in normal solves if you are wondering. But I always know which corners switch places when I apply my OLL alg.

Michael

Edit:

This page might help you out if you don't understand what I meant:
http://www.cubewhiz.com/coll.html


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## blah (Jan 20, 2009)

mpohl100 said:


> I would just have to learn to recognize what edges have to be *flipped* in order to get a fast LL case recognition.



You mean swapped. There's no need to flip any edge.

*In case you didn't know, there's no need to use ZZF2L actually, Petrus F2L up to "Step 4a-and-a-half" is exactly the same thing.*

And I think it's worth mentioning that *this could very well be the ultimate weapon that can finally make Petrus users faster than Fridrich users!* I hope  I really wanna see some Petrus guys get sub-12 in competition with this 1LLL.


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## MHordecki (Jan 20, 2009)

That sounds pretty neat.

In my opinion, however, how much value is added there in comparison with ZZ.b? If I understand it correctly, you're basically doing 'corner orientation' phasing-esque step (as opposed to 'edge permutation' phasing in ZZ.b). Then comes an 1LLL. (yeah, there's quite different recognition, but only time will tell which of these two last slot approaches is faster).

One could use it, though, as an excellent transition tool between ZZ-VH and ZZ.a. I can imagine me using it to restrict LL to only these ZBLL categories that i know, and then proceeding, step-by-step, to the full speed ZZF2L.


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## mpohl100 (Jan 20, 2009)

blah said:


> mpohl100 said:
> 
> 
> > I would just have to learn to recognize what edges have to be *flipped* in order to get a fast LL case recognition.
> ...


I am a full fridrich user. I am sorry for that.
I think MGLS or ZBF2L is better for me to orient the edges of the last layer.
And I am sorry for the wrong term. I always mess that up ;-)

How long do you think will it take you to finish the algs?
I am keen on this method now. I want to learn it!!!!! Can't wait for it.


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## tim (Jan 20, 2009)

Why don't you start a new wiki article? This makes contributing algs easier.


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## blah (Jan 20, 2009)

MHordecki said:


> In my opinion, however, how much value is added there in comparison with ZZ.b? If I understand it correctly, you're basically doing 'corner orientation' phasing-esque step (as opposed to 'edge permutation' phasing in ZZ.b). Then comes an 1LLL. (yeah, there's quite different recognition, but only time will tell which of these two last slot approaches is faster).



Actually, I _have_ thought of the advantages this approach has over ZZ-b  Note that this "advantage" might not appear to be an advantage to everyone else, but at least it is to me.

It's the same advantage ELS has over F2L (in my opinion). If you insert the last F2L pair the normal way, you'd have to trace 2 pieces. If you do ELS, you'd have to trace 1 edge piece, and at the same time, observe the orientation of the LL edges that don't "move around".

Similarly, I don't like the concept of phasing as much as corner control because phasing involves tracing pieces. Corner control involves observing the orientation of "fixed pieces", and besides, my U stickers are the brightest colors on my cube anyway, whereas my FBRL stickers are relatively darker colors, making them harder to trace. I simply prefer observing to tracing. That's all.

As for, the 1LLL, my approach already has fewer algs than ZZ-b does  Does that count as an advantage? However, ZZ-b's 1LLL has an advantage in that edge permutation is _much_ more easily identified, making recognition for ZZLL _as fast as_ COLL.

I really can't decide which is better  Like you said, time will tell (provided there are enough people who use these methods ).


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## Stefan (Jan 21, 2009)

Geez, we need an "I'm serious" antismiley that I can use to make it clear I'm in no way kidding or hiding something.

I still don't understand how four stickers are enough to determine the case. If I see let's say a red sticker, it could still be either the yellow/green/red corner or the yellow/red/blue corner. Does that not matter?

And no, I really can't recognize CLL (or CxLL or whatever you call it). Not quickly without thinking, at least. I guess I should finally learn that...


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## blah (Jan 21, 2009)

StefanPochmann said:


> Geez, we need an "I'm serious" antismiley that I can use to make it clear I'm in no way kidding or hiding something.


As a matter of fact, we do  We need an "I'm being sarcastic" antismiley too 



StefanPochmann said:


> I still don't understand how four stickers are enough to determine the case. If I see let's say a red sticker, it could still be either the yellow/green/red corner or the yellow/red/blue corner. Does that not matter?


Nope. Doesn't matter. Take a look at this: http://www.stanford.edu/~leyanlo/coll.htm

Scroll down to look at the Pi and H cases.

I'll go through every case just to help you understand. Now take a look at the 6 Pi cases. If you AUF them the same way everytime (in Leyan's case, he AUFs such that the Pi's head is on R, and its two legs run along F and B, try to understand what I just described, think Greek letter), then look at the U face, you'll notice color patterns.

On Leyan's page, they're in this order:
Pi1 Double vertical bars
Pi2 Cross
Pi3 Right vertical bar
Pi4 Left vertical bar
Pi5 "Slash"
Pi6 "Backslash" (his image is wrong, it's supposed to be just a backslash, the other two colors should be different, not both green)

It doesn't even matter what colors the bars are, nor does it matter whether they're F or B or R or L stickers. Get it?

In case you need more clarification, the H cases on Leyan's page are in this order:
H1 Double vertical bars
H2 Double horizontal bars
H3 Vertical bar
H4 Horizontal bar

Get it now?


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## mazei (Jan 21, 2009)

Wow. And you were developing this for how long already?


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## Johannes91 (Jan 21, 2009)

blah said:


> StefanPochmann said:
> 
> 
> > I still don't understand how four stickers are enough to determine the case. If I see let's say a red sticker, it could still be either the yellow/green/red corner or the yellow/red/blue corner. Does that not matter?
> ...


I haven't ever understood that claim, either, even though I used to use that recognition system (now I prefer "free-style").

Look at H1 and H2 on that page. The 4 stickers on U-face alone aren't enough, you're ignoring the fact that you know where the yellow stickers are. You could say that "only 4 of the 8 non-U-coloured corner stickers are enough", but that's kinda obvious.


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## bamman1108 (Jan 21, 2009)

ZZ-b

ZZF2L:
EOLine
Blockbuilding of one side
Finishing F2L + phasing (i.e. permuting two opposite LL edges)

ZZLL:
ZZLL - 1-look LL

The regular ZZ-b method has 167 algorithms, which is fewer, so recognition should be easier as well. I'd like to see both methods side-by-side when this method is ready.


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## AvGalen (Jan 21, 2009)

blah said:


> StefanPochmann said:
> 
> 
> > Geez, we need an "I'm serious" antismiley that I can use to make it clear I'm in no way kidding or hiding something.
> ...



What about ' and ' ?


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## mazei (Jan 21, 2009)

Which one is the "I'm serious" antismiley?


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## AvGalen (Jan 21, 2009)

mazei said:


> Which one is the "I'm serious" antismiley?


1) Turn on your camera
2) Stick out your tongue (hint)
3) Invert those actions
4) Publish the video and provide us with the link


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## Lofty (Jan 21, 2009)

Yes, its assumed that you can near instantaneously distinguish between the Pi and the H cases and so all that is left is the U face to determine the case. Most people don't look to see where the corners are going but just have memorized the relation of colors. 
After doing COLL for awhile recognizing is very very easy so then you would just have to make it slightly harder by then also looking at two of the edges.


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## blah (Jan 21, 2009)

blah said:


> *If you AUF them the same way everytime* (in Leyan's case, he AUFs such that the Pi's head is on R, and its two legs run along F and B, try to understand what I just described, think Greek letter), then look at the U face, you'll notice color patterns.





Johannes91 said:


> I haven't ever understood that claim, either, even though I used to use that recognition system (now I prefer "free-style").
> 
> Look at H1 and H2 on that page. The 4 stickers on U-face alone aren't enough, you're ignoring the fact that you know where the yellow stickers are. You could say that "only 4 of the 8 non-U-coloured corner stickers are enough", but that's kinda obvious.



Think you kinda missed that point


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## blah (Jan 21, 2009)

Lofty said:


> After doing COLL for awhile recognizing is very very easy so then you would just have to make it slightly harder by then also looking at two of the edges.



I think I'm abandoning my original ZBLL recognition method. It's stupid.

COLL recognition followed by edge recognition sounds way faster. And _is_ way faster


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## Matthew (Jan 21, 2009)

blah said:


> Lofty said:
> 
> 
> > After doing COLL for awhile recognizing is very very easy so then you would just have to make it slightly harder by then also looking at two of the edges.
> ...




Bingo - I think that recognition in your method (with MH we called it's as ZZ-g variation temporary) is the same as in ZZ-b - first You do AUF, then recognition orientation -> coll -> edge permutation (the edge permutation recognition is topic to another conversation) - and then you your algorithm... 

But... you said that you prefer to observate, non tracking - i can't consent with this - in zz-b you have only to look at two of edges - and you do an intuitively alg.. in zz-g - you look at orientation of four corners... IMO the recognition and execution of this "algs" will be the same...

And.. I don't have yet the detailed statistics (I can have it's tomorrow), but as I remember, algs for Pi-orientation (double-sune) are longer that in other orientations.. but I must check this


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## blah (Jan 21, 2009)

Matthew said:


> (with MH we called it's as ZZ-g variation temporary)


Why not ZZ-blah?! ' (note the prime after the smiley, which means it's an antismiley - it's a sarcastic mad smiley, if you know what I mean  Credits to AvG for the antismiley concept  (note the absence of a prime after this smiley))



Matthew said:


> But... you said that you prefer to observate, non tracking - i can't consent with this - in zz-b you have only to look at two of edges - and you do an intuitively alg.. in zz-g - you look at orientation of four corners... IMO the recognition and execution of this "algs" will be the same...


Well, if you really wanna know, it really doesn't bother me at all that you can't consent with this  I'm happy with it - fewer algs, instant COLL recognition, and I look at the orientation of 3 corners, not 4, the last one is trivial. And in ZZ-b, you have to look at all 3 edges before you decide which 2 to look at, don't twist the facts. You just made 3 vs 3 sound like 4 vs 2. There are better ways to promote your method you know 



Matthew said:


> And.. I don't have yet the detailed statistics (I can have it's tomorrow), but as I remember, algs for Pi-orientation (double-sune) are longer that in other orientations.. but I must check this


Ouch. You really hate ZZ-blah () don't you?

At the end of all this, I really think ZZ-b vs ZZ-g is just gonna be like OLL/PLL vs CLL/ELL - neither can be proven to be faster than the other, it just depends on the number of users, if any


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## Matthew (Jan 21, 2009)

blah said:


> Why not ZZ-blah?! ' (note the prime after the smiley, which means it's an antismiley - it's a sarcastic mad smiley, if you know what I mean  Credits to AvG for the antismiley concept  (note the absence of a prime after this smiley))



I said it is temporary - we can call it zz-g but all we knows that You are the inventor...




> Ouch. You really hate ZZ-blah () don't you?



No - I like the idea, but now I'm learning zz-b and I will stay with this 

About the stats - i quickly generate it's for shortests alg for ever cases in zbll/zz-b/zz-blah

HTM:
ZBLL - 12.14 moves
ZZLL (v.b) - 12.62 m.
ZZ-Blah (OLL Pi+H) - 12.51 m.

QTM:
ZBLL - 15.96 m.
ZZ-b - 16.08 m.
ZZ-blah - 16.34 m.

The average of move count is nearly the same - so... beatlle between zz-b and zz-blah will be so exciting


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## blah (Jan 21, 2009)

Matthew said:


> blah said:
> 
> 
> > Why not ZZ-blah?! ' (note the prime after the smiley, which means it's an antismiley - it's a sarcastic mad smiley, if you know what I mean  Credits to AvG for the antismiley concept  (note the absence of a prime after this smiley))
> ...


I think you got it wrong... A sarcastic mad smiley, my friend, is a smiling smiley (this guy right here ---> ) who's pretending to be mad, and ends up looking like this guy here ---> '

I didn't invent anything  I just stole ZZF2L, F2LL and ZBLL and added 54 of my own algs  This is a Dutch-French-Malaysian-Polish (I don't mean to offend anyone here, so I just arranged it in alphabetical order) hybrid method. Talk about globalization  Now if only someone from the USA could contribute...  Then we could call it the Tricontinental method! Sounds epic for a method name 


Matthew said:


> > Ouch. You really hate ZZ-blah () don't you?
> 
> 
> 
> ...



May I know how you generate such stats? I've had to painstakingly, excruciatingly, manually paint one cube after another on Cube Explorer to generate my algs. And I have a 512 MB RAM. I hate this piece of junk, it crashes when Cube Explorer starts searching for 18 move algs  (not an antismiley)

Edit: Actually, Tricontinental method sounds absolutely retarded  But at the moment it's still a Bicontinental method, which sounds even more retarded.


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## MHordecki (Jan 21, 2009)

Matthew's actually got all ZBLL cases (with corresponding solutions, of course) stored in his private database, so it's a matter of a few queries to compute these statistics 

PS. 'Tricontinental' sounds absolutely awesome for me


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## blah (Jan 21, 2009)

12.51 seems a little low. From all the algs I've generated so far, I was expecting 14.xx.

Is 12.51 for optimal solutions?


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## Asheboy (Jan 22, 2009)

Right, so does the LL need 108 or 240 algorithms?


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## blah (Jan 22, 2009)

108. Actually, now I'm not too sure of this figure again. I just calculated, I didn't count, if you know the difference. Better ask someone who has a complete list of ZBLL to confirm this. But it should be somewhere around this number though. Can't be too far off


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## Matthew (Jan 22, 2009)

When I said inventor I mean that you are the inventor of variation - not of all zz-method 


12.51 is for the shortest algs - for more fingershortcuts friendly algs this will be ~14




blah said:


> 108. Actually, now I'm not too sure of this figure again. I just calculated, I didn't count, if you know the difference. Better ask someone who has a complete list of ZBLL to confirm this. But it should be somewhere around this number though. Can't be too far off



IMO 112 (with mirrors and inversions) - 72 for Pi-Orientation and 40 for H-orientation 

And my last question - if you are going to oll-skip with the last slot - what would you do?


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## JohnnyA (Jan 22, 2009)

Can you post some examples of corner control. I can do it, but its very slow.


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## blah (Jan 23, 2009)

Matthew said:


> IMO 112 (with mirrors and inversions) - 72 for Pi-Orientation and 40 for H-orientation


Yeah that should be it. I guess you're a reliable source since you have an entire database.



Matthew said:


> And my last question - if you are going to oll-skip with the last slot - what would you do?


PLL. Why?



JohnnyA said:


> Can you post some examples of corner control. I can do it, but its very slow.


Got some bad news for you: Me too  I hadn't had the time to sit down and spend an hour or so to go through all 27 cases yet. Kinda busy with my non-cubing life at the moment. But don't worry. I'll post something here as soon as I've produced some results


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## Matthew (Jan 23, 2009)

blah said:


> Matthew said:
> 
> 
> > And my last question - if you are going to oll-skip with the last slot - what would you do?
> ...




So in your method are 133 algs - no 112  And question is how long are algs for corners control - I think the longest sth around 7 moves - but we will se when you generate it's


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## mazei (Jan 23, 2009)

Well most probably he is going to generate 2-gen algs for Corner Control i guess, since he is kind of obsessed with 2-gen algs. Not that I'm against it but I wouldn't mind it if he created some 1-LLL algs that are not 2-gens but well, maybe I should contribute instead of just complaining. I'll try to help blah.


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## JohnnyA (Jan 23, 2009)

mazei said:


> Well most probably he is going to generate 2-gen algs for Corner Control i guess, since he is kind of obsessed with 2-gen algs. Not that I'm against it but I wouldn't mind it if he created some 1-LLL algs that are not 2-gens but well, maybe I should contribute instead of just complaining. I'll try to help blah.



The LL algs aren't 2-gen.


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## Matthew (Jan 23, 2009)

JohnnyA said:


> mazei said:
> 
> 
> > Well most probably he is going to generate 2-gen algs for Corner Control i guess, since he is kind of obsessed with 2-gen algs. Not that I'm against it but I wouldn't mind it if he created some 1-LLL algs that are not 2-gens but well, maybe I should contribute instead of just complaining. I'll try to help blah.
> ...



Only ZZ-d LL algs could be a 2-gen..


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## vrumanuk (Mar 27, 2009)

Is any work still being done on this method? It sounds very promising! I am planning to generate the algs for myself but am curious if you (blah) or anyone else is already in the process.


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## ostracod (Mar 27, 2009)

I agree, it seems like a fast variation with a decent number of algorithms. This is what I've observed between the variations:

ZZ-VH: Lots of moves, few algorithms; 6 OLL + 13 PLL = 19 algs.

Winter variation: Fewer moves (about 3), a tad faster, but more algorithms; 54 (or 27 for just R U' R' case) + 13 PLL = 67 algs (or 40)

The variation in this thread: The fewest moves, most likely the fastest, a hefty load of algorithms; intuitive corner orientation control + 1 LLL = 104, as is claimed in this thread (I don't know about mirrors/reversals :U)

I would say this variation is worth learning for sure. As you can clearly see, there is a trade-off for move count and algorithms to learn.

However, I'm doing my own little project of learning the full Winter/Summer variation (I like the seasonal theme X3). So far, I have learned 19 WV algs, and I know all the PLLs. Hopefully I will know all of WV by the end of the week. I've been learning about 2 per day; they're somewhat easy, mainly using L/U/R moves and only 8 long (they are optimal).

As I've posted in another thread, I have a collection of WV algs for whoever wants them:

http://web.mac.com/teisenmann/Tripod/winter.html

Looks like I'll need to generate Summer variation algs for R U R' cases SUNE! (PUN! HA HA HA. SUNE; SOON. GET IT? HA. HAAA...)


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## BatafCube (Dec 7, 2009)

Can you give me a link with the algs i am interested this days in 1LLL.And some help how will i get 0 corners oriented.

Thank's.


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## Athefre (Apr 20, 2010)

http://lh6.ggpht.com/_ktDMKpwYay8/Sw3HjNBwH8I/AAAAAAAAAD4/qYJzbl7HTfE/FullComplete.jpg

There's my Winter Variation image (not for regular F2L) and if you go from left to right, here are the ZZ-Blah solutions I've found:

1. (U) L'U2RU'R'U2L (Orients corners instead)
2. RU2R'
3. RU2R'
4. (U2) L'URU'M'
5. (U') RU'R'
6. RU2R'
7. L'URU'LU2R'
8. (U') RU'R'
9. (U') RU'R'
10. (U')RU'R' (Orients corners)
11. RU2R'
12. RU'R'URU2R'
13. (U') RUR'U'RU'R'
14. RU2R'
15. RU2R'
16. (U2) L'URU'M'
17. (U2) L'URU'M'
18. L'URU'LU2R'
19. (U) LU'RUL'UR' (Orients corners)
20. L'URU'LU2R' (Orients corners)
21. (U2) L'URU'M' (Orients corners)
22. (U') RUR'U'RU'R'
23. L'URU'LU2R'
24. (U') RU'R'
25. RU2R' (Orients corners)
26. (U') RUR'U'RU'R'
27. (U') RU'R'

4.77 average. There are probably shorter solutions.


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## jms_gears1 (Apr 20, 2010)

off topic, but does anyone know if esper (ostracod) even frequents this forum anymore?


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## miniGOINGS (Apr 20, 2010)

jms_gears1 said:


> off topic, but does anyone know if esper (ostracod) even frequents this forum anymore?



Last Activity: 03-09-2010 09:42 AM
Last Post: 12-05-2009 03:37 PM


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## ostracod (May 1, 2010)

Sorry that I am bumping this from the other page, but I thought it'd be appropriate to say that I am, in fact, still alive. Plus, here is a little surprise video from me:

http://www.youtube.com/watch?v=ETUsz9_CnCY

I know 3 minutes is a mediocre time for the 4x4, but people liked it...  I used reduction + ZZ. This allows me to fix parity BEFORE I solve as a 3x3.

I haven't been cubing a lot lately. Sorry to desert this forum. :| I think I do not have a suitable mind for speedcubing, but I have enjoyed thinking about the myriad of techniques and methods.


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## joey (May 1, 2010)

ostracod said:


> This allows me to fix parity BEFORE I solve as a 3x3.


Unless you have a nicer parity alg, this doesn't help..


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## miniGOINGS (May 1, 2010)

ostracod said:


> Sorry that I am bumping this from the other page, but I thought it'd be appropriate to say that I am, in fact, still alive. Plus, here is a little surprise video from me:
> 
> http://www.youtube.com/watch?v=ETUsz9_CnCY
> 
> ...



:!

I did not know that was you! Gears showed me that video, and I didn't realise it was you. He said that he had talked to you before.


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## nck (Jun 10, 2010)

Sorry for bumping but does anyone actually use this LL method?


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## Ordos_Koala (Jan 23, 2011)

It's nice idea, but i guess that when you'll do ZZ WV it will get even better... from start you have all edges oriented and with WV/SV you don't have to do any OLLs


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## oll+phase+sync (Mar 17, 2011)

Ordos_Koala said:


> It's nice idea, but i guess that when you'll do ZZ WV it will get even better... from start you have all edges oriented and with WV/SV you don't have to do any OLLs



You don't have OLL in this method too.

And deorienting corners should be easier (twice as easy  ) than orienting corners during last slot. 

You could also combine blah with Anti-MGLS : ELS + Anti-CLS ... (again ther are more nice Anti CLS cases than nice CLS cases)

But I have heard of no one mastering the disorinentation step as fast as ... let say: phasing


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## mariano.aquino (Aug 20, 2011)

is this thread alive?
i ve been following it, waiting for any news on zz-blah algorithm list...!
is this on wiki so that we can contribute...?


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## Akash Rupela (Aug 20, 2011)

this?
http://www.speedsolving.com/wiki/index.php/ZZ-blah


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## Athefre (Aug 20, 2011)

mariano.aquino said:


> is this thread alive?
> i ve been following it, waiting for any news on zz-blah algorithm list...!
> is this on wiki so that we can contribute...?


 
I posted a list of solutions on the previous page. A few orient all corners instead because it makes more sense for the case.


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## Egide (Jan 13, 2015)

Hi everyone, Just thought l'd share the algorithms l use to control corner orientation for ZZ-blah. Only 9 algorithms are needed when the last F2L pair is formed, the average movecount is 6.30 moves.

Here are the algorithms for when the case is a R U R' insert. The movecount is 7.11 moves.


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## guysensei1 (Jan 13, 2015)

Egide said:


> Hi everyone, Just thought l'd share the algorithms l use to control corner orientation for ZZ-blah. Only 9 algorithms are needed when the last F2L pair is formed, the average movecount is 6.30 moves.



Awesome! Is the average movecount the same everytime if we restrict it to other subsets of ZBLL? (Like U and T or Pi and sune or something?)


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## Petro Leum (Jan 13, 2015)

i skipped through the thread again after months, there are alot of different ideas in here....


did i get the concept right that you disorient the LL corners during the last slot, to reduce the Last Layer to only H and Pi ZBLLs?


shouldnt it be 112 algs then, and not 72?


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## guysensei1 (Jan 13, 2015)

Petro Leum said:


> did i get the concept right that you disorient the LL corners during the last slot, to reduce the Last Layer to only H and Pi ZBLLs?


Yep.


> shouldnt it be 112 algs then, and not 72?


Yep. Unless you take this substep 1 step further and force ZBLL（insert favorite subset here).


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## Egide (Jan 13, 2015)

l haven't checked the other subsets mostly because l found it better to aim for H and Pi, they have the easiest recognition.


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## mDiPalma (Jan 13, 2015)

A while ago, I made algs for the sune/antisune case.

They are all [RU] because it's intended for use with ZZ-d. [RU] movecount is 5.07 htm.

Here are the algs (with the cubewhiz case-numbering scheme)



Spoiler



01 [U2] R U' R' U R U2 R' (7) **** + **

02 [U2] R U2 R' (3) **
03 [U2] R U' R' U R U2 R'	(7) **** + **
04  R U R' U' R U' R' (7) *** + *
05  R U' R'	(3) *
06 [U2] R U2 R2 U2 R U R' U R (9) ** + sune
07  R U' R'	(3) *

08 [U2] R U2 R' (3) **
09  R U' R2 U' R U' R' U2 R	(9) * + sune
10 [U2] R U2 R' (3) **
11  R U' R'	(3) *
12  R U' R2 U2 R U R' U R	(9) * + sune
13 [U2] R U2 R' (3) **
14  R U' R'	(3) *
15 [U2] R U2 R' (3) **
16  R U R' U' R U' R'	(7) *** + *
17  R U' R' (3) *
18 [U2] R' U' R2 U' R2 U2 R	(7) *****
19  R U' R2 U' R U' R' U2 R	(9) * + sune

20  R U R'	(3) *
21  R U R'	(3) *
22 [U2] R U2 R' (3) **
23 [U2] R' U' R2 U' R2 U2 R	(7) *****
24 [U2] R U' R' U R U2 R'	(7) **** + **
25 [U2] R U2 R' (3) **
26  R U' R'	(3) *
27  R U R' U' R U' R'	(7) *** + *

avg	-	(5.07 htm [RU])






The discussion is here. 


it's better than zz-blah because sune zblls are typically more efficient than pi/H (plus you get those 7 movers every once in a while)


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## Egide (Jan 13, 2015)

l find it harder to recognise sune cases over H or Pi, but the low movecount is tempting.


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## mDiPalma (Jan 13, 2015)

yeah, this sune-LL is pretty good

i never really learned any of the algs (i was just looking for ways to break up the last ZZblock and 2GLL for ZZ-d), but maybe I should


one interesting analysis would be checking the longer sune-force cases to see if it's easier to force pi or something

then you could just learn the sune/antisune/pi zbll cases and be done.

it would probably lower the movecount a bunch, but raise the alg count a bit too


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## gewinnste (Jul 10, 2015)

I think that ZZ-b is better than ZZ-blah (why not ZZ-g? what's with the blah?). For phasing, you only need 6 algs with a move count of ~5 for both cases, built pair and split pair ready for RUR'-insertion - while for disorienting corners you need 17 (as it was shown on the previous page) with a move count of ~6.5.

As opposed to phasing, this is a full look, even with more algorithms than PLL, which only has 13 unique algorithms.

And all you get is learning only ~110 instead of ~ 160 cases, and the alg.s for ZZ-blah are even a bit longer than for ZZLL.

Also, you have to distinguish between 12 cases within the COLL cases, instead of only 4 which makes quite a difference in the recog time.

It could even be inferior to ZZ-WV because the recognition time for the LL could overcompensate the minute advantage of the step before in ZZ-blah.


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## oll+phase+sync (Jul 13, 2015)

I discovered the following 2-Step zz-blah Last-Layer simplyfication:

Edge-Permutation and Corner-Orientation can always be solved by doing a two SUNE combo. One of the 4 CPLLs (A,A,H,E) to solve the cube finaly.

How to find the SUNE combo? 
a) For corners: the first sune must set up a SUNE case.
b) For edges: make sure the first SUNE never phases the edges.
...
QUESTION: Has anyone a c) to complete this list, if not try and learn is the only way I can think of.

PUZZLE 1: can EP and CO be solved for each zz-b case (phased) by a SUNE combo?

PUZZLE 2: can EP and CO be solved for each zz Last-Layer case by a SUNE combo?


List of SUNES
Sune: R U R’ U R U2 R'
Anti: R’ U2 R U R' U R 
Back: R U2 R’ U’ R U’ R’
Invert: R’ U’ R U’ R’ U2 R

List of combos
*H:*
U Sune U’ Anti
Anti U Sune
Back Back
Anti Anti

*Pi*
Back U’ Back
Sune U’ Sune 
Back U2 Invert
Anti U2 Sune
Sune U2 Anti
Invert U2 back


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## shadowslice e (Jul 15, 2015)

Just out of interest, does anyone actually use this method as their main?


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