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

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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As you can tell, [SIMPLE] is a modern version of the 'officially' unpublished LL approach from the Snyder Method.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.

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.

Code:
#    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

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.

Code:
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)

This variant is objectively better than most variants.
zzlsllwsimple.png

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)

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.


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. :p

Let me know what you think.
 
Last edited:
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#4
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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#5
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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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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#7
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?
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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#8
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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#12
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?
 

Pyjam

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#15
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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