# ECE - New 3x3 Solving Method

#### Shiv3r

##### Member
tfw guy who was making name dispute complains about name dispute

Also, I would start using this method because it seems pretty cool but there are no algerinos and I'm not good at generating them
me and Crafto are generating the algorithms. besides that you need to know some algorithms that are fairly easy to find and some adapted square-2 algorithms(look at lars vendenbergh's cubezone for that)
theres no algorithms you really need to gen unless ur looking at EZD

##### Member
EZD is the most efficient so people would want algs for those. Btw square one algs are good for corners but not the most efficient. After generating efficient algs for EPBL and CPBL, you guys should post a wiki article that holds these algs in a set called 3PBL(sounds cool?), as regular PBL is for 2x2. Also, why don't square on algs work for the edges?

#### crafto22

##### Member
Guys, I've had a pretty good idea recently and I think it is even better than ABC. It is a sort of combination of ABC and Roux and the result is pretty intriguing. I would appreciate it if you guys would go check out the thread and tell me what you think!

#### Shiv3r

##### Member
Guys, I've had a pretty good idea recently and I think it is even better than ABC. It is a sort of combination of ABC and Roux and the result is pretty intriguing. I would appreciate it if you guys would go check out the thread and tell me what you think!
where? I want to see.

I like all new methods, but for now I think the variants of Briggs-Adams will be big, so Im focusing on them now.

Also, crafto22, when are you going to post the EBPL algorithms?

#### crafto22

##### Member
where? I want to see.

I like all new methods, but for now I think the variants of Briggs-Adams will be big, so Im focusing on them now.

Also, crafto22, when are you going to post the EBPL algorithms?
It's like right under ECE, you'll spot it if you look. I am trying to finish the EPBL algs, they'll be up soon

#### Shiv3r

##### Member
How many Algorithms would you need to combine two of the steps with the corners? lemme think:
orientation+seperation: at least 7*5 algs=35 algs(this is if you insert the pair and then only use COLL cases). Thas isn't too bad really, but recognition might be hell
what about seperation+permutation: 5*3 cases(where both layers need perms)=15 cases(seperation and permutation may be better for just plain old single-layer perms)
say, that's not too bad! but recognition will probably be hell.

##### Member
If you separate and permute corners at the same time, you get around 8!/16/2/2=630 algs. A little bit more than 15...

Also, if you want CPETL, I'm currently generating those algs. There are something like 48 algs I'll look it back up in a bit. I've almost finished with them though.

There is also an improved CO step created by SqAree and myself over on the SSC thread if anyone is interested.

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#### JensRenders

##### Member
From the wiki

"This method has been independently invented by at least 3 people, but the person that has developed it the most, crafto22, is the official inventor of this method."

That seems like a ridiculous statement to make. What is an official inventor? Who wrote this? himself?

"The method is one of the most move-efficient method to ever have a sub-10 second solve"

How do you know that?

#### crafto22

##### Member
From the wiki

"This method has been independently invented by at least 3 people, but the person that has developed it the most, crafto22, is the official inventor of this method."

That seems like a ridiculous statement to make. What is an official inventor? Who wrote this? himself?

"The method is one of the most move-efficient method to ever have a sub-10 second solve"

How do you know that?
I have no connection whatsoever to the wiki, whoever wrote it is responsible for their words

#### JensRenders

##### Member
I have no connection whatsoever to the wiki, whoever wrote it is responsible for their words

I wonder who...

#### wir3sandfir3s

##### Member
I wonder who...
I believe it was Shiv3r. I only did the SSC page but that was a while ago so it's not quite up to date (though it did exist before the other page and I think is more balanced and detailed)- I need to add the bit about the new CO stuff though.

#### Shiv3r

##### Member
I wrote the wiki page in order to provide a basis of the method and to point people towards this thread. anyone who wants to fix it is welcome to.

##### Member
I'm a ZZ solver and I thought about giving this a shot, but I'm having trouble understanding the broken variant:

1. The first step resembles EOLine, but the line is built on the left of the cube using the appropriate E-slice edges
Ok

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
After steps 1 and 2 of the original variant are done the E slice is solved and all corners are oriented, so I guess that's what I'm meant to do in this step.

3. Place the FD and BD edges
Can do, but not in 3 moves.

4. Finish the first two layers using R2, L2 or U moves.
I can do this using domino cube algs, but not in 15 moves.

5. Permute the last layer
Ok.

So either I'm misunderstanding something or this variant is not very good. An example solve would be appreciated.

##### Member
So either I'm misunderstanding something or this variant is not very good. An example solve would be appreciated.

It's not really tbh (it's basically a very slightly better variant of pure belt though it's still not really very good for speedsolving due to the higher movecount, worse ergonomics and not quite as nice lookahead). there are much better variants out there such as LEE->LSE or EZD. You could also try some style a bit more like the last few phases of pure HTA

##### Member
Good to know. Thanks, I'll look into those.

#### Shiv3r

##### Member
ECE, or E-slice edges, Corners, Edges is a solving method that focuses on many things that make a method great:
- ergonomics
- low movecount
- 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
- 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.
crafto22, I would suggest sharing the EZD algorithms, please. None of us can gen good algs, and you supposedly have a god ergonomic algset. please? I will switch over to this method myself, I just need the EZD algs.

#### crafto22

##### Member
crafto22, I would suggest sharing the EZD algorithms, please. None of us can gen good algs, and you supposedly have a god ergonomic algset. please? I will switch over to this method myself, I just need the EZD algs.
I posted the algs I have in the SSC thread