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1. 2x2x3 (12/12)
2. F2L Pairs (10/22)
3. Corners (10/32)
4. L5E (12/44)

Plain and simple lol.

Example:

U2 B' R2 B U2 F' R2 B' R2 B2 U F2 U' R' B2 D2 U' L F' D2

z2 y F2 L2 U' F' R2 (D U) r2 U2 r2 // FB (9/9)
y R U' R' U' F' y' U' R' U R' F R F' // Pairs + easy CP case (12/21)
R' U' R U' R' U2 R // Corners (7/28)
d M U' M U' M2 U' M' U2 M2 U2 M' U2 // L5E (13/41)

Sorta lucky but even so, this could definitely be sub-45 STM.
I actually used this method for a little while, it's pretty great for having 50 algs but I never found myself doing 12 move 2×2×3 blocks :p pretty fun method but not really more efficient than Roux in any way.
 
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1. 2x2x3 (12/12)
2. F2L Pairs (10/22)
3. Corners (10/32)
4. L5E (12/44)

Plain and simple lol.

Example:

U2 B' R2 B U2 F' R2 B' R2 B2 U F2 U' R' B2 D2 U' L F' D2

z2 y F2 L2 U' F' R2 (D U) r2 U2 r2 // FB (9/9)
y R U' R' U' F' y' U' R' U R' F R F' // Pairs + easy CP case (12/21)
R' U' R U' R' U2 R // Corners (7/28)
d M U' M U' M2 U' M' U2 M2 U2 M' U2 // L5E (13/41)

Sorta lucky but even so, this could definitely be sub-45 STM.
If you're doing l5e the same as one would do l6e, then what's the point? It's also pretty similar to a trick in roux where you do 1 square of each block, and then go fill in the pairs. I only do that if it's a good case though.

Also here are the algorithms I mentioned. To use them you orient the FR edge and pair it up with any corner, and then execute the algorithm.
https://docs.google.com/document/d/1QfN473PAZPdsukiR3H-MAFIEx2nI0r910mBpIFWWxKo/edit?usp=sharing
 
@Spencer131 you just gave me a great idea! This is kinda like WaterRoux in its format but more ergonomic and with less algs. This has an LMCF-like movecount with a fourth of the algs:

1. Two 1×2×2 blocks on the left side of the cube (basically a 2×2×3-the DR edge, ~10 moves)
2. Solve the last 6 corners (~11 moves) by
a. Orienting them (42 algs)
b. Permuting them (~50 algs?)
3. Do a y rotation and solve the FR and and FL edge (no sure how this would be done, ~7 moves?)
4. LSE (~12 with EORL)

I feel like this has potential (around 40 moves with <200 algs). Opinions?
 
@Spencer131 you just gave me a great idea! This is kinda like WaterRoux in its format but more ergonomic and with less algs. This has an LMCF-like movecount with a fourth of the algs:

1. Two 1×2×2 blocks on the left side of the cube (basically a 2×2×3-the DR edge, ~10 moves)
2. Solve the last 6 corners (~11 moves) by
a. Orienting them (42 algs)
b. Permuting them (~50 algs?)
3. Do a y rotation and solve the FR and and FL edge (no sure how this would be done, ~7 moves?)
4. LSE (~12 with EORL)

I feel like this has potential (around 40 moves with <200 algs). Opinions?
Most of your estimates looks pretty good except there is NO way you're solving 6 cornerrs in 11 moves. I would love to be proven wrong though XD. The FR and FL edge step would probably be like one of those edge pair thingies that efettah does in lmcf
 
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A couple things I just figured out.
1 - The last 6 corners thing might actually average close to 11 moves like you thought, which is amazing news
2 - The FRFL step could also be ULUR instead because it's basically the same thing
 
I know it's been a little since it was proposed initially, but I like the idea of SB-1 and inserting LE while doing orientation, EODBDF and TTLL: seems more efficient than LLOB with Ribbon Alpha. once I'm done running tests with proposed LLOB variants I may look into this further.

Making 2 1x2x2 blocks in that style would be very difficult to plan in inspection and corner permutation would likely be difficult to recognize. Not sure on FLFR, could be decent.

Have a few projects I'm looking at doing and I would like to know what you guys would like to see.

A: Optimized OH/2H EOLS
B: 1LLL, subset pseudo 2gen
C: Righty OH ZBLL
D: Full OLS for CFOP (all 42 CFOP LS cases solving F2L alongside)
E: TCMLL for Roux, both front and back slot algs
 
Have anyone thought of forcing every LL cases into T-ZBLL or U-ZBLL after F2L is done by using a fast alg like F R U R U' F' or r U R' U R U2 r'?
I know Feliks uses the first alg but I want to expand it into something more?
 
@Thermex Oh really? Well if you can solve FB in around 7-8 moves, it shouldn't take more than 4 or 5 more moves to add in the last two pieces. Also, what you proposed could be done much more easily like this:

1. Squares (10/10)
2. Last two corners (5/15)
3. CMLL (10/25)
4. FRFL (7/32)
5. L6E (12/44)

Only 42 algs, except you might as well just use Roux at this point.

Edit: This might actually be good. FRFL is probably closer to 6 moves, according to the few test solves I've done, so if corners can be solved in 11, that leaves us with:

1. Squares (10/10)
2. Corners (11/21)
4. FRFL (6/27)
5. L6E (12/39)

Sub-40 moves...
 
Just did a little test solve with the method using a hand scramble and got these numbers:

Square in 11 moves
Corners in 12 moves using CubeExplorer to generate the orientation and permutation algs
FRFL in 4 moves
L6E in 12 moves

So the total was 39 moves, exactly as I predicted :p. Jk, I know this probably doesn't reflect the real move count, but I'll do some more tests to get a better idea of what we're working with here.
 
I know it's been a little since it was proposed initially, but I like the idea of SB-1 and inserting LE while doing orientation, EODBDF and TTLL: seems more efficient than LLOB with Ribbon Alpha. once I'm done running tests with proposed LLOB variants I may look into this further.

Making 2 1x2x2 blocks in that style would be very difficult to plan in inspection and corner permutation would likely be difficult to recognize. Not sure on FLFR, could be decent.

Have a few projects I'm looking at doing and I would like to know what you guys would like to see.

A: Optimized OH/2H EOLS
B: 1LLL, subset pseudo 2gen
C: Righty OH ZBLL
D: Full OLS for CFOP (all 42 CFOP LS cases solving F2L alongside)
E: TCMLL for Roux, both front and back slot algs
Glad you think this Roux variant has potenetial, I feel like with the set @Spencer131 came up with it's much better; it has far less algs and is more ergonomic than TSLE. I still am a bit skeptical about the method, like @Teoidus said, it's still pretty close in MC to Roux and with 50 more algs, but I still prefer it over Roux since I find learning algs so fun.

As for this new method I proposed yesterday, I've been thinking about it for a little. I believe there are people (?) who can one-look 2×2×3 blocks, and the two blocks made in this method are literally the same thing-1 edge, so although they're more difficult to one-look than, say, a 1×2×3 in Roux, it could definitely be done with some practice. As for the OC+PC steps, I'm not too worried about PL6C recog, as long as you understand the way OL6C moves the pieces around you could look ahead to see your P6C case. I also proposed this exact method a while ago for 2×2, so I think it could definitely be transfered to 3×3 pretty smoothly. You could also use the Twisty-EG algs I'm making here if you already knew them.
For L8E, I'm really not sure what to do. The obvious approach would be to do what @Spencer131 said and solve ULUR and then do an x rotation into LSE, but I feel like there's a more efficient strategy that could be used here.

@Thermex Oh really? Well if you can solve FB in around 7-8 moves, it shouldn't take more than 4 or 5 more moves to add in the last two pieces. Also, what you proposed could be done much more easily like this:

1. Squares (10/10)
2. Last two corners (5/15)
3. CMLL (10/25)
4. FRFL (7/32)
5. L6E (14/46)

Only 42 algs, except you might as well just use Roux at this point.
I'm glad FBs can be done in 10 moves, that makes this even lower in terms of movecount. My main goal for a while now has been to create a method compareable to Roux in movecount and algs but that utilizes L6C (it's almost as easy to solve 6 corners as it is 4 corners). I feel like this method is it, and it would be kinda pointless to use CMLL during the third step as you proposed. After a bit more feedback here are my estimates (for the method in it's current state):
1. First Blocks (10/10
2. L6C (11/21)
3. URUL (6/27)
4. L6E (13/40)
(This is including AUFs)

Have anyone thought of forcing every LL cases into T-ZBLL or U-ZBLL after F2L is done by using a fast alg like F R U R U' F' or r U R' U R U2 r'?
I know Feliks uses the first alg but I want to expand it into something more?
If I understand what your saying correctly, basically you form your LS pair, insert it with VHLS, and then use an alg to force a certain type of ZBLL case? I don't really think it's worth it for an average cuber, but maybe a good strategy if you know like half of ZBLL and you're still learning the rest.
 
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One more thing, if no one wants to work with me on this method, I'll probably just call it "Higgs" (my last name) but otherwise I think this name makes sense:

Blocks
Orient corners
Permute corners
Edges

"BOPE"
 
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When I said that you could do ULUR instead of UFUR, I meant that you could do either one and have 2 different options during the solve. I didn't mean to do ULUR every time instead of UFUR.
 
So you are orienting 6 corners in 5-6 moves, and then permuting 6 corners in 5-6 moves?

I am very skeptical that those movecounts are right... permuting 6 corners I could plausibly see with y <R2 U> y' stuff, but then that'd force 2 rotations.
 
Wow, 4-5 move orientation??
Can I see some of the cases + solutions?

EDIT: Oh wait, nevermind. I believe it.
 
I think that with the right ergonomics the method can be fast. You solve to L8E in ~20 moves which is pretty insane, you need good algs for the cases and a decent recog system for the second half of corners. And from there it's pretty solid IMO. Little hesitant on the squares, but I think that this has some pretty incredible potential so GG; you beat WaterRoux with under half the algs :) I'd like to help with this at some point

Decided that I'm probably just going to do a bit of all the things I said earlier, just one at a time. Won't be on the forums much as I'm heading off to University in a week or so but I'll try and update on the projects or if I have a good idea.
 
I think that with the right ergonomics the method can be fast. You solve to L8E in ~20 moves which is pretty insane, you need good algs for the cases and a decent recog system for the second half of corners. And from there it's pretty solid IMO. Little hesitant on the squares, but I think that this has some pretty incredible potential so GG; you beat WaterRoux with under half the algs :) I'd like to help with this at some point

Decided that I'm probably just going to do a bit of all the things I said earlier, just one at a time. Won't be on the forums much as I'm heading off to University in a week or so but I'll try and update on the projects or if I have a good idea.
I'm glad everyone thinks this method is a good idea! This is really what be been aiming for ever since I joined this thread, to create an improvement to WaterRoux with less algs.

Tbh there's still a lot of stuff to work out though; although it seems like a good idea and not too many algs need to be generated, I'm still a bit skeptical about some steps, namely the Permute 6 corners step and how easy it will be to one-look the blocks. There also still needs to be an efficient sub-20 move method to solve L8E.

For @Neuro and anybody else that wants to contribute to this method, just PM me if you give me your email and I'll invite you to the Google spreadsheet I made for the LSC (this is what I propose calling the step where you solve the 6 corners) algorithms.

One more thing: I'll probably call this "Higgs" since I proposed it, but if anybody objects or has another name in mind I'll change it (I still kinda like "BOPE")
 
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@Spencer131 you just gave me a great idea! This is kinda like WaterRoux in its format but more ergonomic and with less algs. This has an LMCF-like movecount with a fourth of the algs:

1. Two 1×2×2 blocks on the left side of the cube (basically a 2×2×3-the DR edge, ~10 moves)
2. Solve the last 6 corners (~11 moves) by
a. Orienting them (42 algs)
b. Permuting them (~50 algs?)
3. Do a y rotation and solve the FR and and FL edge (no sure how this would be done, ~7 moves?)
4. LSE (~12 with EORL)

I feel like this has potential (around 40 moves with <200 algs). Opinions?

I tried a variant of this a while back when tweaking LMCF. The method was 2x2x1 block on back left and back right, then solve the DFR and DFL corners randomly (they could be swapped), then use EG-1 or CLL (to solve the remaining corners), variants that don't damage the back blocks (turns out most of the existing algorithms don't damage them). Then finish with LMCF E2L/L6E and Waterman L6E. This was one of the several ways I tried to improve the ergonomics of LMCF. It has big potential, my problem is I'm not good at block building so I kind of abandoned it.
 
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