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ECE - New 3x3 Solving Method

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Thread starter #1
ECE, or E-slice edges, Corners, Edges is a solving method that focuses on many things that make a method great:
- ergonomics
- low movecount
- good lookahead
- quick execution

There are many variants of the ECE solving style. I will go over these variants and give my thoughts on each one and which one is better suited for different solvers.

The Original Variant:

Steps:

1. Solve 3 E-slice edges whilst simultaneously placing 3 oriented corners in the D layer
Moves: 5-9
Execution time: 2-3 seconds

2. Pair up the last E-slice edge with a corner and insert the pair whilst orienting the remaining corners on the cube through a CO method (WV, MGLS, etc)
Moves: 9-11
Execution time: 1-2 seconds

3. Separate corners into their layers and then permute them using 5 square-1 algorithms
Moves: 11
Execution time: 2-3 seconds

4. Solve the D layer edges whilst orienting the remaining edges
Moves: 12-15
Execution time: 3-4 seconds

5. Permute the remaining edges trough EPLL
Moves: 7
Execution time: 1 second

Total moves: ~47 STM
Theoretical execution time: 9-15 seconds

Pros:
- Easy to learn
- Low movecount
- Mostly ergonomic movesets
- Low algorithm count
- Effecient use of inspection time
- Placing D layer edge placement is tedious
- Lookahead from one step to the next is good

Cons:
- Bad recognition for second step
- Semi-difficult first step
- D layer edge placement is tedious

The L6E Variant:
This variant is simple and only slightly changes the last steps. This variant is better suited for Roux solvers.

Steps:

Steps 1 through 3 are identical to the Original Variant
Moves: 25-27
Execution time: 5-8 seconds

4. Place two opposite D layer edges whilst optimizing edge orientation for the following step (L6E)
Moves: 8
Execution time: 1-2 seconds

5. L6E with optimized edge orientation
Moves: 10-12
Execution time: 2-4 seconds

Total moves: ~45 STM
Theoretical execution time: 8-14 seconds

Pros:
- Mostly ergonomic movesets
- L6E finish is more effecient than the Original Variant's EPLL finish
- Lower movecount than the Original Variant
- Good lookahead
- L6E is very fast when edges are pre-oriented/easily orientable

Cons:
- L6E is occasionally slow despite being effecient
- This strategy requires more "looks" than the Original Variant

Broken Variant

The Broken Variant solves the first two layers quite differently and results in a PLL finish. This variant is better suited for ZZ solvers.

Steps:

1. The first step resembles EOLine, but the line is built on the left of the cube using the appropriate E-slice edges
Moves: 6-7
Execution time: 1-2 seconds

2. This step is identical to the first and second step of the Original Variant, but it will be significantly easier due to their being half of the E-slice pre-built
Moves: 12-15
Execution time: 2-3 seconds

3. Place the FD and BD edges
Moves: 3-4 moves
Execution time: 1 second

4. Finish the first two layers using R2, L2 or U moves.
Moves: 15-18
Execution time: 4-6 seconds

5. Permute the last layer
Moves: 11
Execution time: 1-2 seconds

Total moves: ~50 moves STM
Theoretical execution time: 9-14 seconds

Pros:
- Orienting edges at the beginning premotes effeciency
- Individual steps are faster than in the Original Variant
- Pre-oriented edges creates a faster first two layers

Cons:
- Higher movecount than the Original Variant
- First two layer strategy lacks freedom
- PLL is substantially slower than EPLL

The Permute-Last Variant

The Permute-Last Variant focuses on rapid turning that makes up for a higher movecount. CFOP users will enjoy this variant most.

Steps:

Steps 1 and 2 are identical to those of the Original Variant
Moves: 14-16
Execution time: 3-5 seconds

2. Build the first two layers without caring for corner permutation or D layer edge permutation. Do note that corner orientation does matter. Do note that it may be necessary to use slice moves to orient some D-layer edges, although this only occurs on certain occasions.
Moves: 12-15
Execution time: 2-4 seconds

3. Orient the remaining edges and separate them into their respective layers.
Moves: 6-9 moves
Execution time: 2-4 seconds

4. Permute the remaining layers in a two step system (Recognize both PLL cases, execute PLL, rotate, execute PLL)
Moves: 20-22
Execution time: 2-4 seconds

Total moves: ~55 STM
Theoretical execution time: 9-17 seconds

Pros:
- Ignoring initial permutation promotes fast turning and fluid execution
- The permutation step can be done in one look allowing for continuous movement

Cons:
- Reliance on fast turning ruins effeciency
- Permuting both layers requires a rotation unless one learns a new set of PLLs

EZD (Easy D-layer) Variant

This variant brings a slight change to the last steps that improves execution time for the lengthiest step of the Original Variant.

Steps:

Steps 1 through 3 are identical to the Original Variant
Moves: 25-27
Execution time: 5-8 seconds

4. Place the D-layer edges whilst orienting all edges without caring for edge permutation.
Moves: 8-12
Execution time: 2-3 seconds

5. Permute edges from both layers through a special set of algorithms I will generate.
Moves: 7-9
Execution time: 1-2 seconds

Total moves: ~43 moves STM
Theoretical execution time: 8-13 seconds

Pros:
- This variation is the most effecient
- Permuting multiple pieces at once can be done far more quickly
- Mostly ergonomic movesets
- Quicker D layer edges allows for better lookahead
- Permuting the edges of layers i surprisingly fast and using nice <UMD> algorithms

Cons:
- Admittingly EPLL is definetely faster than this variant's multi-edge permutation

The NoEO Variant

The NoEO Variant is once again a slight modification on the Original Variant's last two steps.

Steps:

Steps 1 through 3 are identical to the Original Variant
Moves: 25-27
Execution time: 5-8 seconds

4. Place the D layer edges.
Moves: 8-12
Execution time: 2-3 seconds

5. Solve the 4 remaining edges.
Moves: 10-11
Execution time: 1 second

Total moves: 44 moves STM
Theoretical execution time: 8-12 seconds

Pros:
- ELL is more effecient than an EO + EPLL strategy
- ELL uses faster algorithms than EZD's final step algorithms
- This variant is more effecient than every other variant apart from the EZD variant

Cons:
- ELL recognition may be even worse than that of EZD's last step strategy

Which variant is the best?

According to the statistics, the EZD, NoEO or L6E variants should be the best with theoretical optimal execution times of 8 seconds and an average movecount of around 44. I do believe these are the best variants for me, specifically the EZD variant. I have achieved a sub-15 average of 12 with the EZD variant and am sub-18 with ALL variants. I think you should choose the method that suits you best. ZZ solvers will prefer the Broken Variant, Roux solvers will lean towards the L6E variant and CFOP solvers will go for the Permute-Last variant. Despite all this, the Original method is the simplest and can be very fast, considering I have gotten a 15.91 average of 12 using it.
 
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Shadowslice
#3
I'm still dubious about your movecount for step 3. Seems more like 9 moves for CP and 5 moves for corners to layers.

So, basic variation of the SSC method I'm going to call SSC-M (SSC-Misoriented- the original will be refered to as SSC-Oriented). It will use a different, slightly less restricted subset of SLS which does not have to preserve edge orientation (although it will have the same required number of algs) which I will henceforth refer to as SLS-M.

NOTE: bear in mind that this is still just an idea and has not been fully fleshed out yet.

1) Form 3/4 of the e-slice (as in SSC-O but it does not have to orient edges)
2) Orient 3 d-corners.
3) set up to SLS-M
4) SLS-M
5) Permute corners

From here there are two options:

First option: orient all edges and proceed with LEE as in SSC-O

Second option: Solve the DR and DL edges and proceed as per LSE.


This variant might be useful as it would provide a better lookahead for the first few steps (in fact the first two steps could even be done simultaneously- this could make it essentially a less strict PCMS that uses SLS as opposed to CMLL or WV etc) and SLS-M would have a lower move count than SLS-O (although it would likely not be a significant reduction but the setup would be shorter as well in SQTM)

However, orienting all the edges later in the solve may be less move count efficient than the EoEdge at the start of SSC-O and SLS-M would have more memorising as the additional orientation that the edge could be placed in could slow down recognition time.

So, all in all, this variation would improve the start of the solve by way of improved lookahead and slightly lower move count at the cost of some efficiency and recognition at the end of the solve
I realize it may not be as efficient, but what about finishing F2L and performing EPLL? More algs, but faster ( I think anyway)
It's a nice idea that I looked at one point (when I was transitioning from Beginners to Roux) but I eventually came to the conclusion that it would take more moves to place all the D-edges than to place RU/LU and RD/LD. In addition, the EPLL takes more moves than the L4E used in roux

So I would conclude that while less efficient it could be a good alternative for a CFCE, CFOP or ZZ/ZB user who is a much faster turner when doing an alg and ends up faster with the higher move count than the lower move count intuitive LSE/LEE approach.
So i would say that the method is more of a variant of SSC (specifically SSC-M)
 
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Thread starter #7
I'm still dubious about your movecount for step 3. Seems more like 9 moves for CP and 5 moves for corners to layers.

So i would say that the method is more of a variant of SSC (specifically SSC-M)
Separating corners is occasionally 1-2 moves, so when you account for that the average moves drops drastically.

Referring to your SSC-M, now that I read it over I'm amazed I just worked about an hour on a method that has already been invented... Oh well, at least I've... Developed it a little
 
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#10
Separating corners is occasionally 1-2 moves, so when you account for that the average moves drops drastically.

Referring to your SSC-M, now that I read it over I'm amazed I just worked about an hour on a method that has already been invented... Oh well, at least I've... Developed it a little
No, don't worry I'm sure that every method developer has done that at some point- I once spent a while developing a megaminx method which just turned out to be Yu Da Hyun's S2L style and developed what eventually turned out to be Roux.

Considering your times I would definitely encourage you to go with this method further as I am not yet fast enough to prove it's worth yet.
 
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Thread starter #11
No, don't worry I'm sure that every method developer has done that at some point- I once spent a while developing a megaminx method which just turned out to be Yu Da Hyun's S2L style and developed what eventually turned out to be Roux.

Considering your times I would definitely encourage you to go with this method further as I am not yet fast enough to prove it's worth yet.
Yeah. As I mentioned in the intitial post, I have achieved sub-15 with the EZD variant and am extremely close with the L6E, NoEO and Original variants. I am currently working on a better system for this method that resembles the EZD variant/Broken variant and uses a special set of algorithms I will have to generate.
 
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Thread starter #12
Don't know if anyone will care, but I got my first sub-9 with ECE! I think this method actually has great potential! The solve's lookahead was easy, especially since the first step was three moves. My global average with ECE, specifically EZD is around mid-14 seconds. Hopefully someone else will see this solve as proof of this method's potential.

This solve was done with the EZD variant of this method. I know all WV, CO, CP and EPBL algs (56 algs) for anyone wondering. You can find CO and CP algs in any Square-1 tutorial.

Scramble: L' U B' D2 F' D' F2 R L2 D' F2 R2 D2 F2 L2 U' L2 D2 B2

Solution:

y' U2 D R' // 3 Edges + 3 oriented corners
y' D r U r' d' U2 // Setup for CO
R U' L' U R' U2 L // CO
U' R2 U' R2 U D R2 D' R2 // CP
U D' M' U2 M U D' M' U M // EO + Edge seperation
x M U' D L U2 D2 L' U' D M' x' U' D2 // Edge permutation of both layers

I'm counting this as 42 moves since U D or U D' gets executed as one move, since I execute both moves at the same time.
42 moves / 8.97 = 4.68 turns per second

I'm very pleased with this method's low movecount!
 
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#15
The algs are the same as in SSC (ie SLS with mirrors) it is almost the same as SSC-M. Still cool though.
and the corner perm algs are the same for square-one right? But i dont get the turns interpretations, i guess.
also, this method is different. for example, it has been proven to be a sub-15 or at least sub-20 method.
 
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#16
and the corner perm algs are the same for square-one right? But i dont get the turns interpretations, i guess.
also, this method is different. for example, it has been proven to be a sub-15 or at least sub-20 method.
No this method is the same as SSC-M (with a little bit of extra development). SSC-O has been proven to be sub-20 as well. The corner perms and stuff are also the same as SQ-1 though you can see better optimised 3x3 versions on the SSC thread.
 
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#17
ECE, or E-slice edges, Corners, Edges is a solving method that focuses on many things that make a method great:
- ergonomics
- low movecount
- good lookahead
- quick execution

There are many variants of the ECE solving style. I will go over these variants and give my thoughts on each one and which one is better suited for different solvers.

The Original Variant:

Steps:

1. Solve 3 E-slice edges whilst simultaneously placing 3 oriented corners in the D layer
Moves: 5-9
Execution time: 2-3 seconds

2. Pair up the last E-slice edge with a corner and insert the pair whilst orienting the remaining corners on the cube through a CO method (WV, MGLS, etc)
Moves: 9-11
Execution time: 1-2 seconds

3. Separate corners into their layers and then permute them using 5 square-1 algorithms
Moves: 11
Execution time: 2-3 seconds

4. Solve the D layer edges whilst orienting the remaining edges
Moves: 12-15
Execution time: 3-4 seconds

5. Permute the remaining edges trough EPLL
Moves: 7
Execution time: 1 second

Total moves: ~47 STM
Theoretical execution time: 9-15 seconds

Pros:
- Easy to learn
- Low movecount
- Mostly ergonomic movesets
- Low algorithm count
- Effecient use of inspection time
- Placing D layer edge placement is tedious
- Lookahead from one step to the next is good

Cons:
- Bad recognition for second step
- Semi-difficult first step
- D layer edge placement is tedious

The L6E Variant:
This variant is simple and only slightly changes the last steps. This variant is better suited for Roux solvers.

Steps:

Steps 1 through 3 are identical to the Original Variant
Moves: 25-27
Execution time: 5-8 seconds

4. Place two opposite D layer edges whilst optimizing edge orientation for the following step (L6E)
Moves: 8
Execution time: 1-2 seconds

5. L6E with optimized edge orientation
Moves: 10-12
Execution time: 2-4 seconds

Total moves: ~45 STM
Theoretical execution time: 8-14 seconds

Pros:
- Mostly ergonomic movesets
- L6E finish is more effecient than the Original Variant's EPLL finish
- Lower movecount than the Original Variant
- Good lookahead
- L6E is very fast when edges are pre-oriented/easily orientable

Cons:
- L6E is occasionally slow despite being effecient
- This strategy requires more "looks" than the Original Variant

Broken Variant

The Broken Variant solves the first two layers quite differently and results in a PLL finish. This variant is better suited for ZZ solvers.

Steps:

1. The first step resembles EOLine, but the line is built on the left of the cube using the appropriate E-slice edges
Moves: 6-7
Execution time: 1-2 seconds

2. This step is identical to the first and second step of the Original Variant, but it will be significantly easier due to their being half of the E-slice pre-built
Moves: 12-15
Execution time: 2-3 seconds

3. Place the FD and BD edges
Moves: 3-4 moves
Execution time: 1 second

4. Finish the first two layers using R2, L2 or U moves.
Moves: 15-18
Execution time: 4-6 seconds

5. Permute the last layer
Moves: 11
Execution time: 1-2 seconds

Total moves: ~50 moves STM
Theoretical execution time: 9-14 seconds

Pros:
- Orienting edges at the beginning premotes effeciency
- Individual steps are faster than in the Original Variant
- Pre-oriented edges creates a faster first two layers

Cons:
- Higher movecount than the Original Variant
- First two layer strategy lacks freedom
- PLL is substantially slower than EPLL

The Permute-Last Variant

The Permute-Last Variant focuses on rapid turning that makes up for a higher movecount. CFOP users will enjoy this variant most.

Steps:

Steps 1 and 2 are identical to those of the Original Variant
Moves: 14-16
Execution time: 3-5 seconds

2. Build the first two layers without caring for corner permutation or D layer edge permutation. Do note that corner orientation does matter. Do note that it may be necessary to use slice moves to orient some D-layer edges, although this only occurs on certain occasions.
Moves: 12-15
Execution time: 2-4 seconds

3. Orient the remaining edges and separate them into their respective layers.
Moves: 6-9 moves
Execution time: 2-4 seconds

4. Permute the remaining layers in a two step system (Recognize both PLL cases, execute PLL, rotate, execute PLL)
Moves: 20-22
Execution time: 2-4 seconds

Total moves: ~55 STM
Theoretical execution time: 9-17 seconds

Pros:
- Ignoring initial permutation promotes fast turning and fluid execution
- The permutation step can be done in one look allowing for continuous movement

Cons:
- Reliance on fast turning ruins effeciency
- Permuting both layers requires a rotation unless one learns a new set of PLLs

EZD (Easy D-layer) Variant

This variant brings a slight change to the last steps that improves execution time for the lengthiest step of the Original Variant.

Steps:

Steps 1 through 3 are identical to the Original Variant
Moves: 25-27
Execution time: 5-8 seconds

4. Place the D-layer edges whilst orienting all edges without caring for edge permutation.
Moves: 8-12
Execution time: 2-3 seconds

5. Permute edges from both layers through a special set of algorithms I will generate.
Moves: 7-9
Execution time: 1-2 seconds

Total moves: ~43 moves STM
Theoretical execution time: 8-13 seconds

Pros:
- This variation is the most effecient
- Permuting multiple pieces at once can be done far more quickly
- Mostly ergonomic movesets
- Quicker D layer edges allows for better lookahead
- Permuting the edges of layers i surprisingly fast and using nice <UMD> algorithms

Cons:
- Admittingly EPLL is definetely faster than this variant's multi-edge permutation

The NoEO Variant

The NoEO Variant is once again a slight modification on the Original Variant's last two steps.

Steps:

Steps 1 through 3 are identical to the Original Variant
Moves: 25-27
Execution time: 5-8 seconds

4. Place the D layer edges.
Moves: 8-12
Execution time: 2-3 seconds

5. Solve the 4 remaining edges.
Moves: 10-11
Execution time: 1 second

Total moves: 44 moves STM
Theoretical execution time: 8-12 seconds

Pros:
- ELL is more effecient than an EO + EPLL strategy
- ELL uses faster algorithms than EZD's final step algorithms
- This variant is more effecient than every other variant apart from the EZD variant

Cons:
- ELL recognition may be even worse than that of EZD's last step strategy

Which variant is the best?

According to the statistics, the EZD, NoEO or L6E variants should be the best with theoretical optimal execution times of 8 seconds and an average movecount of around 44. I do believe these are the best variants for me, specifically the EZD variant. I have achieved a sub-15 average of 12 with the EZD variant and am sub-18 with ALL variants. I think you should choose the method that suits you best. ZZ solvers will prefer the Broken Variant, Roux solvers will lean towards the L6E variant and CFOP solvers will go for the Permute-Last variant. Despite all this, the Original method is the simplest and can be very fast, considering I have gotten a 15.91 average of 12 using it.
what are the EZD algorithms? youve said that you got pretty low with it, so what is that algset?
 
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Thread starter #18
what are the EZD algorithms? youve said that you got pretty low with it, so what is that algset?
I just have them all memorized, so I would have to re-generate all the algs. There are only 16, so I'm sure it wouldn't be too much trouble to find some good algs with Cube Explored.
 
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