# [SIMPLE] LL Variant (Revamped 'Fish & Chips')



## mDiPalma (Aug 10, 2017)

*tl;dr - efficient 'Fish and Chips' with 27-alg 'Fish' selected from short, ergonomic, well-known algs ... followed by L3C 'Chips' (commutators)*

Hello again. I am back with another EO-solved LL variant that tugs the pareto front lower still, albeit leveraging some cheap commutator tricks. It is called...





As you can tell, [SIMPLE] is a modern version of the 'officially' unpublished LL approach from the Snyder Method.
As such, the first step is to solve the LL edges and one LL corner ('Fish').
The second step is a corner commutator ('Chips').

*The advantages of [SIMPLE] are: *

Extremely low movecount. It is only 2.2735 moves worse than FULL ZBLL, but it only takes 27 algs (most of which you already know, see "ALGS" below). This confirms the "mathematical advantage" that Snyder constantly brags about on his website.
Reasonably low alg count. For less algs as OCLL (2nd look of 2-look OLL) & PLL, this variant saves 4.8565 moves.
High algorithm familiarity. Of the 27 algs, most cubers will only have to learn the effects of 10-12 NEW ones. Many are OLLs/PLLs you should already know.
Algorithms selected for ergonomics/speed (see "ALGS" if you don't believe me). High frequency of sunes.
It's cool and good.

*The disadvantages of [SIMPLE] are:*

It requires EO to be solved before the LL (ZZ/Petrus/CFOP with edge control).
It takes a shift in mindset to discretize the LL in this way (orienting and permuting pieces at the same time).
Second step requires a working knowledge of commutators (or just knowledge of the L3C algs).
You might trip over all the fangirls flocking for your autograph.

*[SIMPLE] is superior to the currently published alg-sets for 'Fish and Chips' by virtue of algcount (9 fewer), movecount (1.7728 fewer), and ergonomics, but it only considers LL cases with oriented edges.*



Spoiler: ALGS



We don't need 36 algs for this set because some algs solve multiple cases.
Algs were selected to balance coverage, movecount, and ergonomics. Some of the algs are not even optimal.

Here they are arranged in numerical order. Numerical order is assigned in no particular order.


```
#    Name            Moves                                STM        Edge Effect        Should you already know this?
-------------------------------------------------------------------------------------------------------------
1    Sune            R U R' U R U2 R'                     (7)        "adj 2-swap"       Ya
2    Antisune        R U2 R' U' R U' R'                   (7)        "adj 2-swap"       Ya    
3    Backsune        R' U' R U' R' U2 R                   (7)        "adj 2-swap"       Ya
4    Backantisune    R' U2 R U R' U R                     (7)        "adj 2-swap"       Ya
5    R-Niklas        R U' L' U R' U' L                    (7)        none               Ya
6    L'-Niklas       L' U R U' L U R'                     (7)        none               Ya
7    Bruno (pi oll)  R U2 R2 U' R2 U' R2 U2 R             (9)        "adj 2-swap"       Ya
8    Backbruno       R' U2 R2 U R2 U R2 U2 R'             (9)        "adj 2-swap"       Ya
9    Diag1           r U2 R' F R' F' R2 U2 r'             (9)        "adj 2-swap"       Most will
10   Diag2           R U' L' U' L U' F2 D R' D' F2 U' R'  (13)       "adj 2-swap"       Nope
11   Op-T            r U' r U2' R' F R U2' r2' F          (10)       "opp 2-swap"       Nope
12   Uperm a         M2 U' M U2 M' U' M2                  (7)        "adj 2-swap"       Ya
13   Uperm b         M2 U M U2 M' U M2                    (7)        "adj 2-swap"       Ya
14   Hperm           M2 U M2 U2 M2 U M2                   (7)        none               Ya
15   Zperm           M2 D S2 D' S' M2 S                   (7)        "opp 2-swap"       Ya
16   Op-pi           F U R U' R' S U R U' R' f'           (11)       "opp 2-swap"       Most will
17   T8              r U R' U' L' U l F'                  (8)        none               Ya
18   L8              F R' F' r U R U' r'                  (8)        none               Ya
19   Twisty          R' F U' F' U' R F U' R' U' R F'      (12)       none               Nope
20   Ice             F U' L2 D2 B R2 u R' u R2            (10)       "opp 2-swap"       Nope
21   Tooroo          R U2 R' U2 L' U R U' R' L            (9)        "adj 2-swap"       Nope
22   Rootoo          L' R U R' U' L U2 R U2 R'            (9)        "adj 2-swap"       Nope
23   Fruffy          F R U R2 F R F' R U' R' F'           (11)       "adj 2-swap"       Nope
24   2manyR2         R' U2 R2 U2 R2 U' R2 U' R2 U R       (11)       "adj 2-swap"       Nope
25   L9              R' U2 R' D' R U2 R' D R2             (9)        none               Ya
26   MikePence       F B' R2 U R2 U' R2 F' U' B           (9)        "adj 2-swap"       Nope
27   ecnePekiM       B' U F R2 U R2 U' R2 B F'            (9)        "adj 2-swap"       Nope
```

Equal case coverage can be made by replacing some cases with their inverses, if your ergonomic preferences require it. For example, Op-pi can be replaced by it's inverse.

Most ZBLL cases can be reduced to a commutator in many different ways. The shortest way can be found by using this little application:

http://homepages.rpi.edu/~dipalm/simple.html





Spoiler: How to learn this method:



The hard part of this method is NOT learning the algs - it's learning what the algs truly do. You may know certain algs as OLLs, but now you must learn how they affect piece permutation.

So, to learn this method, study what each alg above does to the cube for both edges and corners.

Apply them when you think you need to. Use your brain - this is a rubix's cube forum, not /r/abortion.

Here are some other generic tips,
-Remember: you can reduce the candidate algorithms by the current edge case you have.
-Note how many cases are each type of 'Edge Effect'
-Use the EPLLs to slot edges around an oriented LL corner.
-Use Twisty to rotate a corner if edges are solved
-R-Niklas places the FUR sticker into UBR (like an R move)
-L'-Niklas places the FLU sticker into ULB (like an L' move)
-T8 case puts FLU to UBR, use your brain to figure what L8 does (the inverse)
-Only 8.07% of LL states are covered by a single algorithm, the rest can be reduced to L3C in multiple ways. Try using algs that give better L3C.





Spoiler: 'Exact' frequency-normalized movecount:





```
AUF      =  0.7500 stm
'Fish'   =  7.3102 stm
'Chips'  =  9.3333 stm
AUF      =  0.7500 stm
-------------------
LL TOTAL = 18.1435 stm
[LS/LL   = 25.1835 stm]
```

(If you rotate instead of AUF before 'Fish', the movecount drops 0.75)





Spoiler: Comparison with other variants:



This variant is *objectively *better than most variants.










Spoiler: Chances



You will skip the 'Fish' step of [SIMPLE] 4.78% of the time.
You will skip the 'Chips' step of [SIMPLE] 3.70% of the time.
To put that in perspective, PLL skips happen 1.39% of the time.

36% of the time, the 'Fish' can be done with a sune. (What edge case will this be? Use that to your advantage)





Spoiler: Example solves:



Below are 5 example solves with various methods. Click them for the alg.cubing.net.

*Petrus*
U B2 R2 U' F2 L2 D' B2 U2 B2 U R' B D U F2 D' R F2
F' L2 R F B2 U2 R' // 3x2x2
y R' U2 R F' L' U' L U F // eof2l-1
U R U2 R' U R U' R' // f2l
l' U' L U R U' r' F // [SIMPLE] 'Fish' T8
U y F R' F' r U R U' r' // [SIMPLE] 'Chips' commutator
=17 move LL

*Freefop (with edge control):*
D B2 U R2 D L2 B2 U2 R2 U2 F2 R' B R U L B2 L2 D R2 U
U B' U R U D L x2 // 3/4 cross
R2 F R' U' R' // finish cross
L U2 L2 U' L2 U' L' // pair 3
R' U' R U R' U R y U2 F R' F' R // pair 4 and eo
R U2 R' U' R U' R' // [SIMPLE] 'Fish' antisune
y2 F R' U2 R F' R' F U2 F' R // [SIMPLE] 'Chips' commutator
=17 move LL

*ZZ:*
B2 R F' R2 F2 L2 U2 D L' F2 R2 D' L2 U L2 F2 R2 D R2 D
D B2 U F' // eoline
R L' U R L2 U L2 // square
U' R U' R' U' L' // block
R U R' U2 R' U' R2 U R // block
y' R U2 R' U' R U' R' // [SIMPLE] 'Fish' antisune
y R' U L U' D' F2 D R2 U2 L' U R' U2 // [SIMPLE] 'Chips' commutator
=20 move LL

*Petrus:*
U L2 D' B2 D' B2 U' F2 D B2 F2 L' B' L B2 D2 F' L D2 R2
z2 D' R2 D' B' L2 // 3x2x2
y U M' U M // eo
R U' R' U' R F U F' U R' // modern petrus hax - dont tell tao
R U2 R' U' R U' R' // [SIMPLE] 'Fish' antisune
d R U2 R D R' U2 R D' R2 // [SIMPLE] 'Chips' commutator
=17 move LL

*Petrus:*
B2 F2 U L2 D L2 F2 U2 L2 B2 U F' U L' F2 R U2 B U2 B U
B' U2 D B2 // 2x2x2
U' L U' L2 U F2 // 3x2x2
f U f' // eo
L U' L' U L2 U L' U' L2 U L2 // f2l
R U R' U R U2 R' // [SIMPLE] 'Fish' sune
U l' U' L U R U' r' F // [SIMPLE] 'Chips' commutator
=16 move LL


There were a lot of sunes for [SIMPLE] 'Fish', but that is how the cookie crumbles in this variant, boy.






Spoiler: Other Things



It was pointed out that the Zperm alg presented is UNCOMMON AND BAD. It can be executed M2 u' M2 u x' E M2 E' which I think is quite nice.

It turns out that the Zperm alg provides no additional coverage to the other 26 algs. Without it, all 1944 states can be reached in 7.56 moves. Therefore, it only serves to lower the movecount. If a more-common 9-move Zperm is used, the set movecount becomes 7.48 moves. This doesn't significantly affect the results, but I would like to include it for completeness.



Click here for an application to find a [SIMPLE] 'Fish' solution for a given LL case, if you need it . It should now give all possible solutions with these algs.


The objective of this project was to recreate a low-movecount, low-algcount, ergonomic LL variant that keeps the cube a "puzzle". It is basically the LL approaches created by Snyder/Petrus which I feel are very pure in nature. Their "mathematical advantage" over other variants is undisputable. I think these goals have been met. It also allows people with short attention spans, like myself, to learn all the algs before getting bored. 

Let me know what you think.


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## Pyjam (Aug 10, 2017)

DELETED


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## Teoidus (Aug 10, 2017)

can you compare to lookadoo method please


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## AlphaSheep (Aug 11, 2017)

This is the best fish set I've seen, although one or two algs could still be improved. Also, I already know 80% of these algs  

A hint for anyone thinking of learning this: the objective of the fish stage isn't just to to solve edges and one corner. You also need to try make sure you don't get a nasty pure twist case. You could ensure that one corner is always not permuted, but that's bad because it guarantees that you won't ever skip the chips stage. The better option is to learn to recognise which ZBLL case each fish alg solves so that you can always skip chips if you can. 

Also, it's tempting to pick the fish alg that gives the best L3C case, but you have to remember that a 7 move fish alg that leads to a 10 move comm is better than a 13 move fish alg that leads to an 8 move comm (in other words, Sune FTW).


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## Solvador Cubi (Aug 11, 2017)

Does this start at a point in the solve like where one would start the last 3 steps of a 4-Look Last Layer?
and then these 3 steps would be needed?
Orient Corners
Permute Corners
Permute Edges

I do a 4LLL and for those last 3 steps I use 9 algs for the 13 cases, around 27 moves or so.

Your example solves show 17-20 moves, but the graph shows 25.
What would you say the average is closer to?


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## mDiPalma (Aug 11, 2017)

Solvador Cubi said:


> Does this start at a point in the solve like where one would start the last 3 steps of a 4-Look Last Layer?



Yes, this would start after the 1st look of 4-Look Last Layer. It presupposes oriented edges. There are many methods that enforce this automatically (ZZ, Petrus, Heise, CFOP with edge control). Many experienced CFOP users orient edges before the LL so they can use more advanced LL sets.



> Your example solves show 17-20 moves, but the graph shows 25.
> What would you say the average is closer to?



And the graph actually compares "LS/LL" or "Last Slot + Last Layer" movecounts/algcounts, because many of those other methods on the chart are doing some interesting tricks during the last F2L pair. So this method takes ~18 moves for LL, but 25 moves if you also include the final F2L pair.

Keep in mind that the name of this method is misleading, it is certainly one of the more advanced LL approaches. I would not recommend it for beginners.


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## AlphaSheep (Aug 11, 2017)

Solvador Cubi said:


> Does this start at a point in the solve like where one would start the last 3 steps of a 4-Look Last Layer?
> and then these 3 steps would be needed?
> Orient Corners
> Permute Corners
> ...


The graph includes extra moves for solving the last F2L pair so that it can be fairly compared to other variants that have different approaches. For solving the same as the 3 steps you describe, this variant averages 18 moves.

Edit: Ninja'd


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## Solvador Cubi (Aug 11, 2017)

Are you calling me a beginner!?!  j/k I consider myself between a beginner and speedsolver anyway.

Thanks for the extra explanation. Those move counts are impressively low... ~18 moves for the equivalent of 3LLL, nice!


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## phreaker (Aug 13, 2017)

Any chance for the algs with B, M. S and E moves, so those of us who enjoy OH can play along.


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## Pyjam (Aug 15, 2017)

DELETED


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## Pyjam (Aug 16, 2017)

DELETED


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## genericcuber666 (Sep 2, 2017)

I'm so lost.
I understand fish is permuting edges and a corner so is chips just solving the last 3 corners? also were are the algs for chips?

Also if fish and chips is better than coll/epll based on your graph, what was holding it back?


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## shadowslice e (Sep 2, 2017)

genericcuber666 said:


> I'm so lost.
> I understand fish is permuting edges and a corner so is chips just solving the last 3 corners? also were are the algs for chips?


The algs for chips are intuitive as they are just 3-cycles though you could just look up the BLD algs for those cases.


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## Pyjam (Sep 2, 2017)

DELETED


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## Pyjam (Sep 18, 2017)

For people interested by *Fish & Chips* for the simple cases where a pair is already formed.

Here are my *Fish* algs.

There are only 4 cases (when squares are excluded) (8 with symmetrical cases).

You identify the case by compairing the corner sticker on F with the edge on F then with the edge on R (or L for symmetrical cases). You get: O= (opposite / equal), OA (opposite / adjacent), A=, or AO.

I provide 2 algs per case. This has for fonction to avoid a Sune/Anti-Sune in outpout, because those cases are difficult to identify and solve (you could get Nikas, Anti-Niklas, or 3 corners twisted). I use the OLL case to choose between the 2 algs (for the sake of simplification, the orientation doesn't matter).

My grips are noted between accolades {} in red. Those are not moves!






Warning: You will often get 2 corners twisted in output.

Enjoy


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## HamzaZaidi (Oct 9, 2020)

I can't open the application. Is there a list of the best algs for each case?


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## PapaSmurf (Oct 9, 2020)

Probably? Just figure it out, all of the algs themselves are good at the worst.


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## xyzzy (Oct 10, 2020)

Some better algs than what's in the OP:

>10 Diag2 R U' L' U' L U' F2 D R' D' F2 U' R'
R U D' R U R' D R2 U' R U R2 U2 R'

>16 Op-pi F U R U' R' S U R U' R' f'
Any of the RU 2-gen versions.

>20 Ice F U' L2 D2 B R2 u R' u R2
r2 U' F U' R2 F' U2 r2 U F' (solves the inverse case; regripless starting from thumb on top)
L' U' L U' L' U' R U' L U' R' U' R U' R'


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## PetraPine (Oct 10, 2020)

I really cant understand from the post what the actuall steps are, it doesnt state it anywhere,
could you please explain them?


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## PapaSmurf (Oct 10, 2020)

F2L and EO (so ZZ, Petrus, LEOR etc.), use an alg to solve all but 3 corners, use a comm for the rest. Just a better version of fish and chips.


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## curiosity (Oct 10, 2020)

arguably the tastiest cubing method


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## trangium (Nov 8, 2020)

I decided to generate my own algs for this set, although I called it EP+1. There are 25 EP+1 cases, five of which are also L3C cases. and 23 L3C cases, for a total of 43 algs. Only about 5% of cases can be reduced to L3C in only one way, so try to use algs that avoid pure twists or give better L3C.



Spoiler: EP+1



The probabilities are if someone always uses the first alg in the table for the edge case that reduces to L3C. The average movecount for EP+1 is 8.249 STM, although it could be lower since some higher-movecount algs are prioritized over some lower-movecount algs.

CasesProb.AdjR U R' U R U2 R'19.14%R' U' R U' R' U2 R14.20%R U2 R' U' R U' R'5.76%R' U2 R U R' U R4.53%M2 U M U2 M' U M24.12%M2 U' M U2 M' U' M22.88%R U R' U R U' R' U R U2 R'2.47%R' U2 R U R' U' R U R' U R2.47%F U R U2 R' U R U R' F'3.70%F R U' R' U' R U2 R' U' F'2.47%r U2 R2 F R F' R U2 r'2.06%R U2 R D r' U2 r D' R21.03%R2 D r' U2 r D' R' U2 R'0.21%R2 D R' U2 R D' R2 U' R U' R'0.82%R2 D' R U2 R' D R2 U R' U R0.41%R U R' U' R' F' R U2 R U2 R' F0.41%OppR' U' R U' R' U2 R2 U R' U R U2 R'12.55%R2 D r' U2 r D' R2 U' R U' R' 3.34%R' U' R U' R2 D' r U2 r' D R20.77%Solvedskip4.78%r U R' U' r' F R F'8.13%F R' F' r U R U' r'2.88%R U2 R D R' U2 R D' R2 0.31%R' U2 R' D' R U2 R' D R2 0.21%R' U2 D' R' D R U2 R' D' R D R0.05%R U R' U' R' F R2 U R' U' R U R' U' F'0.31%






Spoiler: L3C




LR U2 R' U2 R' U' R U R U' R' U2 R' U2 RR U2 R D R' U2 R D' R2F' r U R' U' r' F RR' U2 R' D' R U2 R' D R2F R' F' r U R U' r'TR U R' U R U2 R' U2 R' U' R U' R' U2 Rr U R' U' r' F R F'R' D' R' D R U2 R' D' R U2 D RR' F' r U R U' r' FR D R D' R' U2 R D R' U2 D' R'UR U2 R' U' R U' R' U2 R' U2 R U R' U RR2 D R' U2 R D' R' U2 R'R' U2 D' R' D R U2 R' D' R D RR2 D' R U2 R' D R U2 RR U2 D R D' R' U2 R D R' D' R'SR2 U R' U R U2 R U2 R U R' U R2 U R'R U' r' F R F' rF R' U2 R F' R' F U2 F' RASR U' R2 U' R U' R' U2 R' U2 R' U' R U' R2r' F R F' r U R'R' F U2 F' R F R' U2 R F'Ox R' U R' D2 R U' R' D2 R2x R2 D2 R U R' D2 R U' Rskip



Google Sheets with pictures per ObscureCuber's request: https://docs.google.com/spreadsheet...LYC6vVFXS91KJ_XZQFTeqE-R2U/edit#gid=256829182


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## PetraPine (Nov 8, 2020)

trangium said:


> I decided to generate my own algs for this set, although I called it EP+1. There are 25 EP+1 cases, five of which are also L3C cases. and 23 L3C cases, for a total of 43 algs. Only about 5% of cases can be reduced to L3C in only one way, so try to use algs that avoid pure twists or give better L3C.
> 
> 
> Spoiler: EP+1
> ...


It would be awesome if you created a google doc with pictures


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## trangium (Nov 9, 2020)

Recognition for the Adj swap cases can be difficult, simply because there are so many cases to choose from. So I also made a list of fixed corner algs: Put the swapped edges in UR and UF and solve the corner currently in UFR. There are 12 algs for this, and the average movecount is 9.83 HTM.


Spoiler: Fixed Corner Adj Algs




CaseOrientation of UFRPermutation of UFRU2 F U R U2 R' U R U R' F'TopUBLU R U R' U R U2 R'TopUBRU2 F R U R2 F R F' R U' R' F'TopUFRU2 R' U' R U' R' U2 RTopUFLU' r U2 R2 F R F' R U2 r'FrontUBLU' R' U2 R U R' U RFrontUBRU R U2 R D R' U' R D' R2 U R U2 R'FrontUFRU' R' U' R U' R' U R U' R' U2 RFrontUFLU F R U R' U' R' F' R U2 R U2 R'RightUBLR U R' U R U' R' U R U2 R'RightUBRR U2 R' U' R2 D R' U R D' R' U2 R'RightUFRR U2 R' U' R U' R'RightUFL


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