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Here is G2L an F2L method that I made that is supposed to be easy. It avoids making a cross and instead, it starts intuitively. I have to give credit to QiYI as the beginner's method it has contains algorithms (that I did not make) in my method. Here is the link (With Pictures :3) https://docs.google.com/document/d/1sC535JmRwaJNbM-cUUY3kuvOdyGguQGdEiET2VZ4aRM/edit?usp=sharing
Be sure to use proper nomenclature. Cross is already an intuitive step, even for beginners (unless you use daisy)

Don't get me wrong, I actually like this. Inserting 2 edges will be much easier for a beginner to grasp than all 4 cross edges at once.

Although I'd suggest doing the mirror of the second case for the 1st one, makes it easier to learn.

Edge to FR= (U) R U' R' U' F' U F
(U) R U' R' F R' F' R
Edge to FL= (U') L' U L U F U' F'
(U') L' U L F' L F L'

For the entire method you should only need
R U R' U'
Edge->FR
Edge->FL
F (R U R' U') F'= EO for LL
JPerm or any adjacent corner swap PLL
One of the U perms (I like Ua viewed from the back and MU)

Example
 
1LLSLL with only 821 algs!

Here's how it'd work: You'd do one of 328 algs that solves the last F2L pair while solving EO but without disturbing corners or EP (41 F2L cases times 8 EO cases). So the alg would just swap the unsolved F2L pieces with the pieces in the LS and solve EO at the same time. Then ZBLL, which has 493 algs.
Because nothing on the LL is affected, you could recognize what ZBLL case you'll get before doing the alg. The recognition would be different, but learnable. Here's an example:

setup: B U2 B' U2 R2 F' U2 F2 R F' U2 R2 U2 R U R' U'
Recognition: I'm going to imagine that the RFU and FDR corners are swapped, and also that FR and UL are swapped. Also that UF and UB are oriented correctly. I'd also have to (in my mind) adjust the corner orientation since the F2L corner will be solved.
Based on this, I would get an Antisune #64
So, first I'd do the alg that switches the F2L pieces while flipping each edge to solve EO:
R2 L' B' R B' U B2 U' B2 R2 U' L F R' F' (I didn't try finding a good alg right now)
Then the ZBLL: U2 R2 U' R' U R U R' U2 R' U R2 U R2
And an AUF: U (this would make it 2-look technically but I don't count it.)
 
1LLSLL with only 821 algs!

Here's how it'd work: You'd do one of 328 algs that solves the last F2L pair while solving EO but without disturbing corners or EP (41 F2L cases times 8 EO cases). So the alg would just swap the unsolved F2L pieces with the pieces in the LS and solve EO at the same time. Then ZBLL, which has 493 algs.
Because nothing on the LL is affected, you could recognize what ZBLL case you'll get before doing the alg. The recognition would be different, but learnable. Here's an example:

setup: B U2 B' U2 R2 F' U2 F2 R F' U2 R2 U2 R U R' U'
Recognition: I'm going to imagine that the RFU and FDR corners are swapped, and also that FR and UL are swapped. Also that UF and UB are oriented correctly. I'd also have to (in my mind) adjust the corner orientation since the F2L corner will be solved.
Based on this, I would get an Antisune #64
So, first I'd do the alg that switches the F2L pieces while flipping each edge to solve EO:
R2 L' B' R B' U B2 U' B2 R2 U' L F R' F' (I didn't try finding a good alg right now)
Then the ZBLL: U2 R2 U' R' U R U R' U2 R' U R2 U R2
And an AUF: U (this would make it 2-look technically but I don't count it.)
Really cool idea! I do feel like you'd run into problems with ergomony. Using it with ZZ would be even better; only about 20 F2L algs, if I'm not wrong, and better recognition, since you don't have to mentally flip edges.
 
Really cool idea! I do feel like you'd run into problems with ergomony. Using it with ZZ would be even better; only about 20 F2L algs, if I'm not wrong, and better recognition, since you don't have to mentally flip edges.
Good point, I haven't thought of that! So that brings down the total alg count from 800+ to just ~534 including ZBLL!
ZBLS has 302 algorithms, where do your 26 extra ones come?
I didn't take symmetry into account or anything like that, my 328 was more of a rough estimate.

I forgot to mention this, but you don't actually have to picture the F2L pieces being swapped with the ones in their slot to recognize the case, you can figure out the ZBLL case by just looking at the LL and ignoring the F2L pieces. It would just require a different recognition system.

EDIT: One of the last slot algs would literally just be z' y' (Jb perm including the U' post AUF) y z
 
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I started a spreadsheet for my 1LLSLL step 1 algs here.
I'll work on finishing it up tomorrow if not today. If anyone has a better alg than one I have up then feel free to suggest it!
 
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1LLSLL with only 821 algs!

Here's how it'd work: You'd do one of 328 algs that solves the last F2L pair while solving EO but without disturbing corners or EP (41 F2L cases times 8 EO cases). So the alg would just swap the unsolved F2L pieces with the pieces in the LS and solve EO at the same time. Then ZBLL, which has 493 algs.
Because nothing on the LL is affected, you could recognize what ZBLL case you'll get before doing the alg. The recognition would be different, but learnable. Here's an example:

setup: B U2 B' U2 R2 F' U2 F2 R F' U2 R2 U2 R U R' U'
Recognition: I'm going to imagine that the RFU and FDR corners are swapped, and also that FR and UL are swapped. Also that UF and UB are oriented correctly. I'd also have to (in my mind) adjust the corner orientation since the F2L corner will be solved.
Based on this, I would get an Antisune #64
So, first I'd do the alg that switches the F2L pieces while flipping each edge to solve EO:
R2 L' B' R B' U B2 U' B2 R2 U' L F R' F' (I didn't try finding a good alg right now)
Then the ZBLL: U2 R2 U' R' U R U R' U2 R' U R2 U R2
And an AUF: U (this would make it 2-look technically but I don't count it.)

I use stuff like this every now and then for ZBLS. It's usually good when you can solve ZBLS with a 3-style alg because 3-style algs are very optimized.

For example, I use these in solves, and it helps me a bit with the ZBLL recognition.

R' D' R U R' D R

M' U R U' M U R' U'

L E' L' U' L E L'

r U' r' R U R' U r U' r' R U R'

D' R' D R U' R' D' R D

Unfortunately I don't think this would be great to use this all the time. I think it would only be worth using this if the alg is really good - at least comparably fast to the normal ZBLS alg. If you have to use an awkward alg for the last slot, I think that would negate the benefits of having a 1LLSLL.

I wouldn't mind having a list of cases for which good algs exist for this, but I imagine it'd be a pretty niche algset.

As well as that, your method could potentially add a lot of moves to ZB (since the speed optimized algs will most likely be longer), bringing the movecount closer to that of normal CFOP - where people already have such fast recognition and prediction skills that your method might not bring much of an advantage.
 
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I use stuff like this every now and then for ZBLS. It's usually good when you can solve ZBLS with a 3-style alg because 3-style algs are very optimized.

For example, I use these in solves, and it helps me a bit with the ZBLL recognition.

R' D' R U R' D R

M' U R U' M U R' U'

L E' L' U' L E L'

r U' r' R U R' U r U' r' R U R'

D' R' D R U' R' D' R D

Unfortunately I don't think this would be great to use this all the time. I think it would only be worth using this if the alg is really good - at least comparably fast to the normal ZBLS alg. If you have to use an awkward alg for the last slot, I think that would negate the benefits of having a 1LLSLL.

I wouldn't mind having a list of cases for which good algs exist for this, but I imagine it'd be a pretty niche algset.

As well as that, your method could potentially add a lot of moves to ZB (since the speed optimized algs will most likely be longer), bringing the movecount closer to that of normal CFOP - where people already have such fast recognition and prediction skills that your method might not bring much of an advantage.
My method would be better as a ZZ variant, because then you wouldn't have to worry about EO so there would only be 20 algs, and I've generated them already and only 2 of them are really bad algs (as of now, I'm going to try and find better ones).
 
I think I have a 4x4 variant of the reduction method, which can make beginner cubers who are not ready for an advanced method get better times. The problem is, I don't know if this exists already and/or if it effects ones times. Is anybody willing to help? It is a more effective method of creating centers and, if in the wrong orientation, can fix that issue. I'm sorry if I'm to vague.
 
I think I have a 4x4 variant of the reduction method, which can make beginner cubers who are not ready for an advanced method get better times. The problem is, I don't know if this exists already and/or if it effects ones times. Is anybody willing to help? It is a more effective method of creating centers and, if in the wrong orientation, can fix that issue. I'm sorry if I'm to vague.
I’m interested can you pm me
 
I'm not sure if this has been done, but I've come up with a 2-Look OLL variant that might be good for beginners.

The steps are:
1) Insert last F2L pair (this will be important later)
2) Orient corners of the last layer
3) Do OLL 28 or 57

I think that it is more efficient than the regular method because it's easier to look ahead into steps 2 and 3, as the orientation of the corners or edges does not change. It also requires fewer algorithms, because part of the method is looking ahead into your OLL while inserting the last F2L pair, to avoid getting the case where all of the corners are oriented, but none of the edges are.

In closing, I think it's better because there are fewer algorithms to learn, teaches you how recognise OLL cases and forces you to look ahead in solves. Let me know what you think!
 
This has been thought of before, but the main issue I see with it is that if the person wants to continue with CFOP and learn 1-look OLL, they will be more unfamiliar with the cases. With the system of EO -> CO, the learner encounters a subset of 1-look OLL (all edges oriented). It further assists recognition of cases in the long run. Your idea can be executed faster, but it has a tradeoff.
 
This has been thought of before, but the main issue I see with it is that if the person wants to continue with CFOP and learn 1-look OLL, they will be more unfamiliar with the cases. With the system of EO -> CO, the learner encounters a subset of 1-look OLL (all edges oriented). It further assists recognition of cases in the long run. Your idea can be executed faster, but it has a tradeoff.
As I had said in my original post, I had quickly mentioned that I think that it might improve recognition of OLL cases as you have to look at the orientation of the corners, and then look ahead into the edge orientation.

I know the standard 2-Look OLL, and now use both methods as an intermediate solver. However, thank you for showing me that it might not be the best for beginners
 
I have a cfop substep:
1. 3/4 cross (finish 3 pieces of cross, the empty one must be a yellow piece)
2. F2L
3. LEOC (last edge of cross (put the last edge back))
4. OLL and PLL
Pros: Makes annoying cross combination easier
Cons: has to put the last piece back
 
I have a cfop substep:
1. 3/4 cross (finish 3 pieces of cross, the empty one must be a yellow piece)
2. F2L
3. LEOC (last edge of cross (put the last edge back))
4. OLL and PLL
Pros: Makes annoying cross combination easier
Cons: has to put the last piece back

I think the cons heavily outweigh the pros here - I think you'll be much better off just solving cross correctly every time, and just embracing the 'annoying' cases as good practice for optimising your cross solutions.
 
I have a cfop substep:
1. 3/4 cross (finish 3 pieces of cross, the empty one must be a yellow piece)
2. F2L
3. LEOC (last edge of cross (put the last edge back))
4. OLL and PLL
Pros: Makes annoying cross combination easier
Cons: has to put the last piece back
Check out 3CFCE.
 
I have a cfop substep:
1. 3/4 cross (finish 3 pieces of cross, the empty one must be a yellow piece)
2. F2L
3. LEOC (last edge of cross (put the last edge back))
4. OLL and PLL
Pros: Makes annoying cross combination easier
Cons: has to put the last piece back
What's generally thought of as a better way of solving F2L-1 Cross is CLL->L5E. However, this is the same method as CFCE as Sue pointed out. Another potential way of doing it is using Hawaiian Kociemba. With this approach, you orient the remaining 10 pieces and then permute them (similar to ZZ-CT but using a cross edge. Other than these two approaches I don't think there's really better ways of solving this set.
 
This is a concept I am positive already exists, but what if you optimised the first layer of 2x2 so you can also permute one or two LL corners, so you could reduce the amout of CLLs to speed recognititon?

Since I have stubby fingers which make it hard for me to turn with a high tps, I might start learning more efficient intuitive methods to accomodate.
 
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