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Idk if this belongs here, but here's a method that averages 34 moves-

Spoiler

Scramble: B2 L2 B2 R' U2 R' F2 U2 R F2 D' U' F' R' U2 B L2 B
U D2 L' U B2 D // Dual Squares (6)
U' F2 U' F' M' U2 F // Dual Pairs (7)
R' y' R U R2 U R2 U2 R' U y r // CMLL (10)
u2 M u2 U M U' M2 // LSE (7)
30 moves

Scramble: R D U F2 U B2 F2 U F2 R2 F2 U2 F R' U F' L D2 B F
D2 R' B U' R B L2 B // Dual Squares (8)
U' F U2 R' F R U F2 // Dual Pairs (8)
y R U2 R D R' U2 R D' R2 y' // CMLL (9)
M U M2 U' M U' M' U2 M U' // LSE (10)
35 moves

Scramble: R D' F2 L' F2 L D2 R F2 D2 L R2 F U' F2 D' F D2 B'
U L2 D2 F2 L D F D // Dual Squares (8)
L' U' R L2 D' R2 F L' // Dual Pairs (8)
F U' R' F' L F2 D' R F2 L' // CMLL (10)
F2 M2 U M U2 M2 U' M' U2 F2 // LSE (10)
36 moves

Scramble: F' B2 L D B2 R2 B U F U2 R2 U2 R' F2 R' D2 R2 F2 L B2 R2
y2 F D2 R' F' R' U L2 B // Dual Squares (8)
U2 M' F2 U' F' M U2 F2 // Dual Pairs (8)
F' L F L' U2 L' U2 L // CMLL (8)
U2 F2 U M' U' F2 U M2 U' M' U' // LSE (11)
35 moves

Scramble: F2 R2 B2 D' U F2 D' L2 R2 D L B' D F' U2 R D2 B' R F'
L2 B' D2 B2 L D2 // Dual Squares (6)
U F2 U' x U2 M U' M2 U x' // Dual Pairs (8)
R2 F2 R' U' R F2 R' U R' // CMLL (9)
U2 M U' F2 U' M' U' M U2 F2 U' // LSE (11)
34 moves

Since I don't care much for this method, I won't write a long post with lots of info or anything.

Basically.
Movecount is likely much lower, but less ergonomic because you have to use F moves.
Dual Squares is also harder to predict in inspection than FB (debatable)
Btw, the best way to think about Dual Pairs is NOT left pair + right pair, but kinda more like corners -> edges.

You can do some testing if you want to see which is better, you're probably more experienced with Roux.

Actually, using this, it would be difficult to get <45 moves for FMC...
The 34 movecount figure is misleading because I used Cube Explorer to solve steps (because I’m iffy at blockbuilding and I don’t know all cmll’s), and each slice turn is 2 moves for FMC.
Speedsolving movecount is probably ~42 using this, nowhere near 34.
FMC is about the same maybe less because the moves you save in efficient blocks is negated by slice moves.
If you want to get decent FMC results without working hard, Kociemba / Kociemba-based ideas might be the way to go! I’ve gotten any PB, 24 moves, by doing it, and I don’t know any advanced FMC techniques like NISS or insertions or whatever people use. Link to 24 single

Actually, using this, it would be difficult to get <45 moves for FMC...
The 34 movecount figure is misleading because I used Cube Explorer to solve steps (because I’m iffy at blockbuilding and I don’t know all cmll’s), and each slice turn is 2 moves for FMC.
Speedsolving movecount is probably ~42 using this, nowhere near 34.
FMC is about the same maybe less because the moves you save in efficient blocks is negated by sliding moves.
If you want to get decent FMC results without working hard, Kociemba / Kociemba-based ideas might be the way to go! I’ve gotten any PB, 24 moves, by doing it, and I don’t know any advanced FMC techniques like NISS or insertions or whatever people use. Link to 24 single

Yeah, I noticed that the LSE was really weird. I guess that makes sense. I am somewhat interested in FMC and will probably learn some techniques, but thanks for providing all of that info!

Basically.
Movecount is likely much lower, but less ergonomic because you have to use F moves.
Dual Squares is also harder to predict in inspection than FB (debatable)
Btw, the best way to think about Dual Pairs is NOT left pair + right pair, but kinda more like corners -> edges.

You can do some testing if you want to see which is better, you're probably more experienced with Roux.

I usually do dual squares on the 4x4 instead of first block/second block, since I like the extra freedom of the F face, and I find that it helps with recognition. You don't really need to do F turns, since there are always alternative pairings and insertions that use the U layer. It depends on how badly you want a low move count.

I always thought it was strange that Roux did the entire first block before the second block, because it seemed very restrictive. But I think the main reason is that it's easy to plan the first block in inspection. I'm getting more into Roux lately and having a blast.

Here I present a method way better than what is currently done....... for the Tower Cube 2x2x3 lol.

Seriously though, most people do Seperate -> PBL -> E-layer which is not as good as this method I made-

Steps:
Left Block- A 1x2x2 block, 2 corners 2 edges, on the down-left. Looks sort of like Roux FB. This is pretty easy to see in inspection, average ~3 moves. You can even predict the next step, which is: R Pair- Simply a pair. Usually RB. Can be RF pair as well, but you would have to rotate before final step. After this step it should look like F2L-1. This step is actually really easy to recognize, averages ~3 moves, and is entirely 2-gen
-Combining these steps in one makes this a two step method PL5C- Permute Last Five(5) Pieces. This step only has 8 total algorithms, which means its very realistic to learn, even for puzzle that's not official. Most of these are somewhat short. I should note that this step has WAY easier recognition than E-layer, the last step of the method most people use. PL5C Algs:
Diag Top- R2 U' R2' U' R2 U R2' D' R2 U R2' U' R2 D R2'
Adj. Top- R2 U R2' U' R2 U' D R2' U' R2 U R2' D'
Opp. Front- R2 U2 R2' U' R2 U' R2'
Opp. Right- y' R2' U2 R2 U R2' U R2
Bar Front- D' R2 U R2’ U' R2 D R2’
Bar Right- (U) R2' D' R2 U R2' U' R2 D
Diagonal- R2 U R2' F2 U' R2 U R2' U F2
Basically Solved- R2 U R2' U' R2 D R2' u' R2 U R2'
Average movecount: 9.033

Pros:
- movecount <16
- algcount <10
- Fast recognition
- Fairly easy to predict R Pair in inpection
- Great ergonmics, R Pair is 2-gen and PL5C has fast algs.
- PL5C is objectively better than PBL (don't argue this)
- Cool blocks (subjective)
- Rotationless solve

EXAMPLE SOLVES:
Scrambles from cstimer, under LxMxN

Scr: D2 F2 D' F2 U R2 U' F2 D F2 U'
z2
u2 R2 D' // Left Block + R Pair (3)
U2 R2 D' R2 U R2 U' R2 D // PL5C (9)

Scr: R2 U2 R2 U R2 D F2 U' R2 D F2
y’
u’ R2 u R2 u’ // Left Block + R Pair (5)
R2 U R2 U R2 U2 R2 U // PL5C (7)

Scr: R2 U R2 U F2 U2 R2 D' R2
z2
u R2 u2 // Left Block (3)
R2 U R2 // R Pair (3)
U’ R2 U R2 U' R2 U' D R2 U' R2 U R2 D’ U’ // PL5C (15)

Scr: U' R2 U D2 R2 U' F2
y’
E2 R2 D’ // Left Block (3)
R2 U2 R2 U R2 U2 R2 U’ // Pair + PL5C (8)
(1-looked solve!)

I am aware this isn't an official event, but it can still be fun to be fast. Have fun with this method!

Here I present a method way better than what is currently done....... for the Tower Cube 2x2x3 lol.

PL5C- Permute Last Five(5) Pieces. This step only has 8 total algorithms, which means its very realistic to learn, even for puzzle that's not official. Most of these are somewhat short. I should note that this step has WAY easier recognition than E-layer, the last step of the method most people use.

PL5C Algs:
Diag Top- R2 U' R2' U' R2 U R2' D' R2 U R2' U' R2 D R2'
Adj. Top- R2 U R2' U' R2 U' D R2' U' R2 U R2' D'
Opp. Front- R2 U2 R2' U' R2 U' R2'
Opp. Right- y' R2' U2 R2 U R2' U R2
Bar Front- D' R2 U R2’ U' R2 D R2’
Bar Right- (U) R2' D' R2 U R2' U' R2 D
Diagonal- R2 U R2' F2 U' R2 U R2' U F2
Basically Solved- R2 U R2' U' R2 D R2' u' R2 U R2'

I use this trick often- whenever you see an alg and not sure exactly what it does (what case, which angle, what auf, etc.), apply the inverse and you will see.
Diag Top and Adj. Top do exactly what you think, its PLL just like 2x2.
For the other 6 cases, for recognition, you ignore the D color piece, which should be in BLU, so all you look at is 4 stickers- 2 in front, 2 on right. If the 2 stickers in front are opposite colors, you do Opp. Front.

Hope that cleared up your question!
Just in case you cared, using this method I've gotten 2.5 Ao5 and my global average is sub-6 on Tower Cube.

Here I present a method way better than what is currently done....... for the Tower Cube 2x2x3 lol.

Seriously though, most people do Seperate -> PBL -> E-layer which is not as good as this method I made-

Steps:
Left Block- A 1x2x2 block, 2 corners 2 edges, on the down-left. Looks sort of like Roux FB. This is pretty easy to see in inspection, average ~3 moves. You can even predict the next step, which is: R Pair- Simply a pair. Usually RB. Can be RF pair as well, but you would have to rotate before final step. After this step it should look like F2L-1. This step is actually really easy to recognize, averages ~3 moves, and is entirely 2-gen
-Combining these steps in one makes this a two step method PL5C- Permute Last Five(5) Pieces. This step only has 8 total algorithms, which means its very realistic to learn, even for puzzle that's not official. Most of these are somewhat short. I should note that this step has WAY easier recognition than E-layer, the last step of the method most people use. PL5C Algs:
Diag Top- R2 U' R2' U' R2 U R2' D' R2 U R2' U' R2 D R2'
Adj. Top- R2 U R2' U' R2 U' D R2' U' R2 U R2' D'
Opp. Front- R2 U2 R2' U' R2 U' R2'
Opp. Right- y' R2' U2 R2 U R2' U R2
Bar Front- D' R2 U R2’ U' R2 D R2’
Bar Right- (U) R2' D' R2 U R2' U' R2 D
Diagonal- R2 U R2' F2 U' R2 U R2' U F2
Basically Solved- R2 U R2' U' R2 D R2' u' R2 U R2'
Average movecount: 9.033

Pros:
- movecount <16
- algcount <10
- Fast recognition
- Fairly easy to predict R Pair in inpection
- Great ergonmics, R Pair is 2-gen and PL5C has fast algs.
- PL5C is objectively better than PBL (don't argue this)
- Cool blocks (subjective)
- Rotationless solve

EXAMPLE SOLVES:
Scrambles from cstimer, under LxMxN

Scr: D2 F2 D' F2 U R2 U' F2 D F2 U'
z2
u2 R2 D' // Left Block + R Pair (3)
U2 R2 D' R2 U R2 U' R2 D // PL5C (9)

Scr: R2 U2 R2 U R2 D F2 U' R2 D F2
y’
u’ R2 u R2 u’ // Left Block + R Pair (5)
R2 U R2 U R2 U2 R2 U // PL5C (7)

Scr: R2 U R2 U F2 U2 R2 D' R2
z2
u R2 u2 // Left Block (3)
R2 U R2 // R Pair (3)
U’ R2 U R2 U' R2 U' D R2 U' R2 U R2 D’ U’ // PL5C (15)

Scr: U' R2 U D2 R2 U' F2
y’
E2 R2 D’ // Left Block (3)
R2 U2 R2 U R2 U2 R2 U’ // Pair + PL5C (8)
(1-looked solve!)

I am aware this isn't an official event, but it can still be fun to be fast. Have fun with this method!

This is actually awesome! If I had a 2x2x3 I would so learn this! I think it's cool when cubers take on a challenge like this, especially when it isn't for an official WCA event. I like how interesting this method is, and how it uses some cool algs. Bravo.

I made this kind of 3x3 method (don’t know if it exists probably does) but here are the steps: solve 3 cross edges then solve all f2l pairs don’t insert the last cross edge then solve all top corners then permute them with a j or y perm then using the empty cross edge slot do cmll on top layer so all edges top and bottom are yellow and white then insert last edge if not already solved then u perm ua perm z perm or h perm

I use this trick often- whenever you see an alg and not sure exactly what it does (what case, which angle, what auf, etc.), apply the inverse and you will see.

Yes, I realize I can reverse algs to see the cases, but at the time, I was just walking through a solve and following along
and when I got to the last step, I didn't know which case I had.

What do you think the average move count is for a standard method of: Sep -> PBL -> E-layer ?
Looking back at an info sheet I made using that: http://solvexio.cf/app/#/MiniTower_Page
(note that I prefer holding it "sideways", so the notations are relative to that orientation)

It appears that if the corners can be separated in 4 moves, the rest would average 13.. then totaling 17.
I don't know the probabilities, so perhaps my averages are off, though.

Yes, I realize I can reverse algs to see the cases, but at the time, I was just walking through a solve and following along
and when I got to the last step, I didn't know which case I had.

What do you think the average move count is for a standard method of: Sep -> PBL -> E-layer ?
Looking back at an info sheet I made using that: http://solvexio.cf/app/#/MiniTower_Page
(note that I prefer holding it "sideways", so the notations are relative to that orientation)

It appears that if the corners can be separated in 4 moves, the rest would average 13.. then totaling 17.
I don't know the probabilities, so perhaps my averages are off, though.

You’re just asking about movecounts, right?
I don’t know much more than you, sorry.
I personally believe movecount is not a big part of speed, example, compare CFOP vs. Roux, it’s like 60 moves vs. 48 moves yet both are similar speed.

If you don’t know the probabilities or can’t calculate the movecount, just do a bunch of solves and count the moves to get a good idea, it’s called movecount for a reason lol

Testing data (normal solves, NOT fmc)-
Left block: 3 / 2 / 4 / 3 / 3 / 3 / 5 / 1 / 4 / 3 / 3 = 3.4 moves
R Pair: 1 / 2 / 2 / 0 / 2 / 2 / 4 / 1 / 2 / 2 / 2 = 2.0 moves
PL5C: 8 / 1 / 9 / 8 / 7 / 9 / 9 / 8 / 11 / 13 / 8 = 9.1 moves
TOTAL- 14.5 MOVES
Sample size is fairly small so actual number could be different, I think it’s 15.0

For Sep->PBL->E-layer I don’t even know the pbl’s haha so these movecounts are just guesses-
Seperation ~3.5
PBL ~9.5
E-layer ~4
Total- 17 moves maybe??

Going outside of movecounts and comparing these methods directly, Seperation and Left block and very comparable, PBL and PL5C are very comparable, but then E-slice is way WAY worse than R pair.
Maybe take that with a grain of salt as my opinion is baised towards my method lol xd, (though perhaps I have good reason because I average 5 flat with it, so...)

That’s about it for today, I’m glad people are supportive of my ideas here!

yes, move counts. I'm preoccupied with them lately.
I would agree with your estimates of around 15 and 17, though.

Anecdotally, my Roux solves are about 10% faster than my CFOP solves, which for me is about about a 10-15 move difference.
But I agree that lower move counts don't always mean faster times.
Just like i'm trying to see if I can be faster at my ParKoci than my Roux.
i.e. lower move count vs fewer steps

Do you think this 2x2x3 method could be expanded for something like 2x2x4? Or maybe any 2x2xn?
It may be possible to reduce the E layers to one layer, and then do the R pair and PL5C. I think that might prove to be pretty interesting.

Also, you need a name for this method. Saying "WoowyBaby's 2x2x3 Method" is kind of a lot.