This seems somewhat similar to what I had in mind when doing B2 though your idea to use BLD memo is something new and could well be a better way to do it than the "triplet of pairs" method I currently use. I also would like to commend you as you explain it much better than I do and in much more detail so very well done!
I came up with two 2x2 methods and I will try to help you understand them.
Number one: Fortega
Is like ortega, but you can have the opposite side's color for part of the first side. (Note: this is not a good method to use by itself, but you can use it with ortega if you have a good fortega side.)
Example solve with fortega: R U2 R F2 U2 F R2 F U'
Fortega side: Z U R U R'
OLL: U F' R U R' U' R' F R
Solidsides (SS): Y R2 U' R2 U2 R2 U' R2
and do PBL
This method is ment for those people who are lazy and use ortega.
The next method, is not developed yet.
The use two algs to solve the whole cube (without bulding a layer/side)
First you use one to orient the corners, then solve the rest.
But I still need to come out with the algs for method no. two, if you could help that would be great!
I'm no expert, but I believe that, like Pyraminx (which I also don't know much about), it's probably best to be method neutral. Imo it could be good to use a combination of EG, TCLL, RoFL, non-matching layers/faces etc. The more you know, the more likely you'll have a first step skip and will be able to solve the cube in one alg with maybe a one or two move setup.
I do say that the beginning of ZZ is a little hard. But I still like the ergonomics of COLL-EPLL over OLL/PLL. You know how hard it is to do G perms OH? In fact, I specifically don't use CFOP for OH because of how much I hate OH-ing the last layer.
Every so often, one might get a solve that looks like this, where the third slot has a mismatched pair and the last pair is also formed. (And also edges are all oriented, because no method proposal is complete without assuming that you already use ZZ.)
You could fix the edges during insertion (example), during COLL (example), or during EPLL (example).
Fixing during insertion is the standard way of doing it and since it's the standard way, it's probably also the fastest and you should ignore the rest of this post. As for fixing during COLL, unfortunately it turns out that most of the algs are terrible; even the 2-gen ones are long or awkward (except maybe the pi case). And who's going to bother learning 42 bad algs for something that comes up only once in a few hundred solves?
I shelved the idea a long time ago, but then decided to generate the EPLL+fix algs on a whim and it looks like they're not too bad. There're also only five cases, which can all be done 2-gen, and 2-gen is awesome, right?
opposite:
R2 U2 R2 U2 R2 (5f)
R2 U2 R' U' R U R U2 R U R2 U2 R U' R U R U2 R (19f) lol
adjacent:
R2 D' M' U2 M D R2 U2 R2 (9s, 11f)
R U2 R U R U R2 U' R' U R2 U2 R2 (13f)
R' U R U' R2 U2 R2 U R' U' R U2 R2 (13f)
O, clockwise:
(R r) U2 r2 U2 (R r) U' M2 U' M2 (9a, 13f)
R2 U R2 U' R' U2 R' U' R' U2 R2 U R2 U R (15f)
O, anticlockwise:
M2 U M2 U (R r) U2 r2 U2 (R r) (9a, 13f)
R2 U' R2 U R U2 R U R U2 R2 U' R2 U' R' (15f)
W:
r2 U M2 U R2 U' M2 U' r2 (9s, 11f)
R2 U2 R2 U R' U' R U R U R U' R (13f)
R2 U2 R2 U' R U R' U' R' U' R' U R' (13f)
R2 U2 (R U R U R) U2 (R' U' R' U' R') U2 R2 (15f)
Every so often, one might get a solve that looks like this, where the third slot has a mismatched pair and the last pair is also formed. (And also edges are all oriented, because no method proposal is complete without assuming that you already use ZZ.)
You could fix the edges during insertion (example), during COLL (example), or during EPLL (example).
Fixing during insertion is the standard way of doing it and since it's the standard way, it's probably also the fastest and you should ignore the rest of this post. As for fixing during COLL, unfortunately it turns out that most of the algs are terrible; even the 2-gen ones are long or awkward (except maybe the pi case). And who's going to bother learning 42 bad algs for something that comes up only once in a few hundred solves?
I shelved the idea a long time ago, but then decided to generate the EPLL+fix algs on a whim and it looks like they're not too bad. There're also only five cases, which can all be done 2-gen, and 2-gen is awesome, right?
opposite:
R2 U2 R2 U2 R2 (5f)
R2 U2 R' U' R U R U2 R U R2 U2 R U' R U R U2 R (19f) lol
adjacent:
R2 D' M' U2 M D R2 U2 R2 (9s, 11f)
R U2 R U R U R2 U' R' U R2 U2 R2 (13f)
R' U R U' R2 U2 R2 U R' U' R U2 R2 (13f)
O, clockwise:
(R r) U2 r2 U2 (R r) U' M2 U' M2 (9a, 13f)
R2 U R2 U' R' U2 R' U' R' U2 R2 U R2 U R (15f)
O, anticlockwise:
M2 U M2 U (R r) U2 r2 U2 (R r) (9a, 13f)
R2 U' R2 U R U2 R U R U2 R2 U' R2 U' R' (15f)
W:
r2 U M2 U R2 U' M2 U' r2 (9s, 11f)
R2 U2 R2 U R' U' R U R U R U' R (13f)
R2 U2 R2 U' R U R' U' R' U' R' U R' (13f)
R2 U2 (R U R U R) U2 (R' U' R' U' R') U2 R2 (15f)
Interesting and clever idea.
I think you could force this case when blocks are stupid bad, but shouldn't be used much otherwise.
I like: Rw2 U2 R2 U2 Rw2 U2 (6f) [E: actually more like x Rw U2 R2 U2' Rw2' U2' Rw]
For opposite because it feels more tactile than (R2 U2)x3, if that makes sense.
I already do this technique quite often during roux. It makes planning FB much easier. I usually do like D2 L2 D2 for first block and then R2 U2 R2 U2 R2 for SB. If you could find some algs to fix those sometime later in a roux solve, I would love it(maybe some, like, last SB pair thing)
I decided to get my 4x4 method and optimize it into a 3x3 method, and actually, it seems quite good, so i'll place the format here. I found it to be a hybrid of Petrus and PCMS, which are two methods highly acclaimed for their low movecount and ergonomics. Since none of the steps are really unique to this method, I'm inclined to call it LMBC, or Low Movecount Block Conglomerate.
- Make a 2x2x3 block at the back of the cube. The sky is the limit. I usually do A 2x2x2 block and add a 1x2x2 extension. However, you could also make a 1x2x3 and extend that into a 2x2x3, or make a 3cross and add the two f2l pairs.
- Make two columns on the F face. you could also do a psuedo WV here if you wanted to.
I've done this before, usually as a 3cfce variant, and its okay. I can't get super good times on it, but I do know full CLL so I use that.
EDIT: I have tried using it as a method, I just recorded an Ao5 for this method.
Time List(Cstimer copypaste):
1. (23.34) U' R' B Fw2 R2 Uw' D U2 Fw' R Fw R2 Uw F' R' B Rw' F2 Rw' Uw U' L' F Rw Uw2 L' Fw2 B2 U' L2 D Uw2 B2 U2 R' Fw2 D R Fw2 L'
2. 20.48 L' U' F L2 D' F' B2 U B R' U2 L' D2 L D2 R B2 U2
3. 23.23 L2 F2 R2 F L2 F D2 F2 R2 D2 F L F' D' R2 D2 U' R' B2 D2
4. (18.38) D2 U2 F2 L2 R B2 F2 U2 R' F2 D2 F' R' D U' R2 U L' B2 U R2
5. 19.72 F B2 R D' L F2 B D2 L' F' U2 L2 F' B L2 F U2 F2 U2 R2
I've done this before, usually as a 3cfce variant, and its okay. I can't get super good times on it, but I do know full CLL so I use that.
EDIT: I have tried using it as a method, I just recorded an Ao5 for this method.
Time List(Cstimer copypaste):
1. (23.34) U' R' B Fw2 R2 Uw' D U2 Fw' R Fw R2 Uw F' R' B Rw' F2 Rw' Uw U' L' F Rw Uw2 L' Fw2 B2 U' L2 D Uw2 B2 U2 R' Fw2 D R Fw2 L'
2. 20.48 L' U' F L2 D' F' B2 U B R' U2 L' D2 L D2 R B2 U2
3. 23.23 L2 F2 R2 F L2 F D2 F2 R2 D2 F L F' D' R2 D2 U' R' B2 D2
4. (18.38) D2 U2 F2 L2 R B2 F2 U2 R' F2 D2 F' R' D U' R2 U L' B2 U R2
5. 19.72 F B2 R D' L F2 B D2 L' F' U2 L2 F' B L2 F U2 F2 U2 R2
Hey, so with all The CP+Roux talk, it got me thinking about maybe you could use ZZ-d-style (porky2 style)CP with roux. So the steps would be something like this(may be a really nice OH method, IDK)
1.first square + place DFR/DBR on D in inspection
2.setup DFL corner+ ZZ-d alg(pretty much porky2, which has relatively good recognition)
3.Finish F2B-1, and do something like BLS or some other subset to cancel as much of CMLL/LSE as possible
4.rest of LSE
pros:
-ZZ-porky2 recog simpler than most CP recognition subsets
-easier in inspection - all youre doing is solving first square and permuting the DR corners
-no EOline like the original ZZ variant
-Corner permutation allows for a massive amount of 2-gen solving(I call it 2.5 Gen - <R M U>) -- may be good for OH?
cons:
-Still not any nice algsets for canceling a lot after F2B besides BLS(maybe a pinkie-pie type thing would work -- how many algs would 2.5-gen OLLCP be?)
-Not as nice as CMLL
-the current ZZ-D missing link is not terribly efficient
EDIT: figured out how many algs 2-gen OLLCP would be. 7 CLL's * 8 EO cases = 56 algs. Not too much, given OLLCP usually is a ton of algs. Not sure about alg count with mirrors/inverses, but Definitely less than 2GLL still...
