2x2 method ideas:

2x2 CT: 3 solved pieces in a layer (V), orientation, permutation
Have a look at VOP
2x2 Crazy CT (terrible name, I know): Bar, orientation, permutation
Why not orient, permute? Just as easy really.
2x2 WV: V, WV, PLL
Interesting but again largely superceded by VOP
1LLSLL: V, solve everything else
I know of at least one person who is actually learning this already and you may also want to look up 42/22.
 
How many different/useful 2x2 sets are there to learn?

What I have as a list rn are

CLL
EG-1
EG-2
LEG-1
NLL
LOLS (useful in this scenario or no?)
L5C (how many sets are actually useful/decent to recognize? is BTR better?)
TEG (how many sets are there? just TEG-2+/- ?)
PBL
TCLL+/-

Let me know if I forgot anything
 
How many different/useful 2x2 sets are there to learn?

What I have as a list rn are

CLL
EG-1
EG-2
LEG-1
NLL
LOLS (useful in this scenario or no?)
L5C (how many sets are actually useful/decent to recognize? is BTR better?)
TEG (how many sets are there? just TEG-2+/- ?)
PBL
TCLL+/-

Let me know if I forgot anything
Depending on your definition if useful, OL5C, OLS, PLS and other RoTFL subsets may or may not be useful.
 
A ZZ variant that someone probably experimented with: ZZ-42
Step 1: EO
Step 2: F2L-1 + 1 oriented top layer corner
Step 3: Conjugated COLL
Step 4: L5E
The most practical way to do L5E is using conjugated EPLLs for 3 cycles and 2-2 swaps, while using optimised algs for 5 cycle cases.

There aren’t many advantages of using this over 42 as far as I know. The only one I can think of is low alg count for L5E since EO is solved.
I’ll do example solves when I have time.
 
Frisk Method (Skewb)

Beginner Frisk Method:
1. 1st layer but 1 is unoriented (rotated) [3/4 solved layer or EG layer]
2. VHLS (10 easy algs)
3. OLL/EG-OLL (6 easy algs)
4. L4C (3 easy algs)

Intermediate Frisk Method:
1. 1st Layer but 1 is unoriented [EG or solved layer]
2. VHLS + Winter Variation(optional) [18 algs]
3. Advanced Sarah's Case (23 algs or less) + EG-L4C(OLL is solved but EG layer isn't, and optional)[4 algs]
4. L4C (sometimes)

Advanced Frisk Method:

Variant (1):
1. 3/4 Layer [solved or EG]
2. VLS [90 algs]
3. L4C & EG-L4C

Variant (2):
1. 3/4 Layer [solved or EG]
2. VHLS+WV
3. NS Last Layer (23 algs) & NS-EG Last Layer (28 algs)
 
Frisk Method (Skewb)

Beginner Frisk Method:
1. 1st layer but 1 is unoriented (rotated) [3/4 solved layer or EG layer]
2. VHLS (10 easy algs)
3. OLL/EG-OLL (6 easy algs)
4. L4C (3 easy algs)

Intermediate Frisk Method:
1. 1st Layer but 1 is unoriented [EG or solved layer]
2. VHLS + Winter Variation(optional) [18 algs]
3. Advanced Sarah's Case (23 algs or less) + EG-L4C(OLL is solved but EG layer isn't, and optional)[4 algs]
4. L4C (sometimes)

Advanced Frisk Method:

Variant (1):
1. 3/4 Layer [solved or EG]
2. VLS [90 algs]
3. L4C & EG-L4C

Variant (2):
1. 3/4 Layer [solved or EG]
2. VHLS+WV
3. NS Last Layer (23 algs) & NS-EG Last Layer (28 algs)
I really like the sound of this method. Do you have any links for the algorithms yet?
 
Different way to do EOCross:

Since z rotations don't change EO, you can build the cross on the right face (or the left side if you are left-handed) and do a z rotation afterwards. The steps are:

0. Rotate the cube such that the cross center faces to the right, and recognize EO just like you would if cross were on bottom.
1. Solve EO while making sure that oriented cross pieces don't end up in the FL or BL positions. In particular, don't have two unoriented cross edges in FU and FD at the same time (also not BU and BD at the same time).
2. Solve cross on right using only <R, U, D> moves.
3. z rotation

Pros:
  • <R,U,D> is a nice and ergonomic move set
  • having more structure to the solve (i.e. restricting to <R,U,D>) makes it easier, because there are less cases to consider
Cons:
  • Worse look-ahead into your first F2L pair because of the z rotation. If you build your first F2L pair before the z rotation, look-ahead still suffers, because you have to do the z rotation eventually.
Example solve:

[R U L' R2 B R' U R' U z

Edit March 7:
after experimenting with it, I think doing EO while separating cross pieces to the L and D layers, then doing cross on D with <L,D> moves is better than the above. It eliminates the rotation, is very ergonomic, and the number of possible cases where the cross pieces are oriented and on the L, D layers is tiny.
 
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5x5x5 method idea: Yau4 optimized for EOCross 3x3 stage. Maybe Zao? As in ZZ + Yau.

1a) Solve 2 opposite centers
1b) Pair and insert 3 cross edges like in 4x4 Yau
1c) Line up the last 3 tredge pieces in the M slice and pair them up, then insert into cross without messing up centers
2) Solve 4 edges and insert them into the U layer as you solve them. Make sure they're oriented correctly in regards to your ZZ orientation as you insert them! If you have to use the edge flip algorithm make sure that an unsolved edge is in the UL position (in Speffz it's 'B') so that you don't misorient any edges.
2b) Last 4 Edges like in redux. If you have to use the edge flip algorithm, always use the same edge in UL twice in a row so you end up with a maximum of 1 misoriented edge in the U layer.
3a) 3x3 stage! Start by orienting the edges, there will be a maximum or 4 bad edges and they will always all be in the E layer, so turning them into good edges should be easy. Make sure you don't mess up the cross!
3b) Continue with 3-gen F2L (U L and R), then COLL/EPLL or ZBLL.

If anyone likes, I can make an example solve sometime this afternoon.
 
So, I briefly thought about this, but from chris Olson’s yau5 Tutorial, I thought that you could make your line edges and two other edges (orientated), plus the centres like in normal yau5. Then you pair up any two edges (or the pairs) and put them on L. Then you rotate, do Petrus eo and zzf2l, although I do feel like normal yau5 with Petrus eo then <RU> f2l is better.
 
@Aerma and @PapaSmurf, I have 2 ways I'd suggest going about doing ZZ on 4x4/5x5

This one provides EO Cross which could have faster F2L

1) F2C
2) 3 Cross Edges (as in Yau)
3) Centers
4) Last Cross edge, rotate to preferred orientation (unless you're CN which in that case just do a z' everytime :))
5) Edge Pairing (6-2 or 3-2-3)
6-2
5a) Pair 6 edges while doing EO simultaneously
5b) Pair L2E with a specialized algset that solves EO for both edges
3-2-3
5a) Pair 3-2 edges while doing EO simultaneously
5b) Pair L3E with a specialized algset that solves EO for all 3 edges

I'd learn both the L3E and L2E sets to be safe and have more flexibility while pairing
(This isn't necessary on 5x5, all you need are standard L2E algs)

6) Standard ZZ solve (I'd suggest F2L, COLL, EPLL+Parity)

This one only provides you with EO Line but may be more efficient

1) F2C
2) EO Line edges + 1 random oriented edge (positions same as in Yau 3 cross edges) If CN this can be super efficient
3) Centers
4) 1 random edge, oriented and placed in UL. Perform z'.
5) Same as above
6) Same as above (with the exception of true blockbuilding F2L)

You could also combine the 2 and end with 3 cross edges already solved but it depends on what you like.

EDIT: You don't need the L2E/L3E subsets, you could pair all edges while doing EO until you have either 0 or 1 bad edge, in which case you can use an edge flipping alg. The subsets will probably make you faster though.

While we're on the topic of 5x5 methods, I've made a 1st draft that models itself off of both Yau-5 and Meyer on 4x4.

1) LR Centers
2) FB
3) Centers
4) 1 random edge in UL, rotate z' y' or use M slice pairing
5) Freeslice 4 edges (one must be an SB edge, place oriented in U/R depending on how you pair)
6) L4E
7) Solve as normal

FB's comparable to 3 cross edges, edge pairing's pretty good once you get used to 4r/4u moves, prepping an SB edge allows for better SB lookahead, and of course the rest of the solve is pretty good if you're good with M slices on big cubes (magnetic cube basically required)

Should be about the same efficiency as Yau 5/redux->CFOP. I suspect it's slightly slower than Yau5/redux->CFOP but it's still a really good method IMO.

I did a solve with it that's 192 STM. I'm awful at freeslice pairing but I did get pretty lucky on 3x3 stage. For reference, the WR 5x5 solve is 221 moves using redux-CFOP.

I didn't want to have any larger of a text wall than this post already is so here's a link to the solve :p
 
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My zz-4x4 method goes like this:
1. L/R centres.
2. 3 from: Random orientated edges
Random orientated edges
Line edge
L cross edge
Place them like a yau cross on L. If you have green on front, white on bottom red will be on the left.
3. L4C
4. Whatever you didn’t do for step 2. Solve the pseudo yau cross.
5. Do a z’ rotation then 3-2-3 edge pairing for the rest of the edges.
6. Solve the eoline while preserving the other three pseudo cross edges on L.

7. Do a y then Petrus style eo + parity.

8. y’ and ZZF2L

9. COLL/EPLL

I average slightly slower with this than yau after about a week, but theoretically it should have a very similar movecounts. The only drawback I see is the necessary y and y’ rotations for eo, although rotationless f2l and more efficient first three edges and 3x3 stage should help.

With yours, @Neuro, doing eo and edge pairing at the same time (to me) seems inefficient and annoying, but I haven’t done it a lot.
 
It is but I hadn't thought of anything better so it's what I used. Your 4x4 method looks pretty nice, haven't seen that approach before. I guess I didn't understand your earlier post because the methods actually look pretty nice now that I look at it again
 
Thanks. I think that the other posts that I’ve done on it/other ideas haven’t been that specific one, but it’s definitely the best idea I’ve come up with. And any critiques are welcome. Zz needs it’s own 4x4 method.
 
This is Just a whim thought, so just take this with a grain of salt, but wouldn't it be ultra efficient for ZBLL users to Miss one cross edge, Leaving one whole layer fully open, F2l, L5EOP, ZBLL, Or F2L- DF Edge, WV, L5EOP, EPLL? It would probably be a bit less efficient movecount wise, but I'm sure it's much more ergonomic since L5EOP is two gen for the most part.

Basically:

Cross - One edge
F2L+WV
L5EOP
PLL

Or for more experienced solvers:
Cross-One Edge
F2l
L5EOP
ZBLL

This was just a small thought I had, which happens to be a mashup of My Columns Method and CFOP.
 
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@Neuro You've clearly put a lot of thought into this :) The problem with that though is that you have to memorize extra algorithms that may not be that good just for the edge orientation, and I don't know if recognition would be all that great either. Maybe your ideas would just be an advanced variant? I personally like doing it my way and I'd rather not learn a bunch of extra algs and steps.
 
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