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So I finished LOLS but then gave up with this method. The NLLS have some nasty cases and I need to start practicing events I want to improve in. I might try it out again once I finish full 3style.

Well, mostly, I just haven't been generating them, I guess I'll get back on that. Help would definitely be appreciated, and I think that basically this thread is going to be the place for sharing new algs.

That can happen in lucky cases. Basically, V+CO is done like Guimond, but you often change the last move of the alg. Check some of my example solves for examples.

LOLS is super easy to learn, I would reccoment learnings LOLS then inserting the corner if needs be then using PBL to solve it until you finish full HD

If you do it that way, how do you end up learning the fancy HD-G where V+CO takes like 3.x moves on average? Cause that lowers the movecount by quite a lot.

HD or Higgs-Demars, is a method for 2x2 speedsolving, comparable to EG. It breaks the solve into two steps: orient all corners and force a V separation case, and solve the rest with one of 36 algs. Here are movecount comparisons for EG and HD.

HD:
V+CO: 3.90 moves (from 100 solves by myself)
NLL: 8.13 moves (from current algs, factoring in probability)
Total (AUFs included): 13.53 moves

EG:
Face (optimal): 3.80 (unsure)
EG case: 9.54 (factoring in probability, using algs from Chris Olsen's website)
Total (AUFs included): 14.84 moves

Other arguments:

Alg count:
HD: 41
EG: 128

One looking:
HD: Track permutation of 8 pieces
EG: Track permutation of 8 pieces, orientation of 4

Ergonomics:
HD: First step decent, second step good, rather undeveloped algs
EG: First step decent, second step great, developed algs

Add ons:
HD: possibly more NLLs but for non V separation cases
EG: TCLL, LEG, possibly TEG if you are crazy

Sorry for not making this way earlier. Credit to myself, @Thermex, @Shiv3r, and @Neuro for the method, also thanks a little bit to @efattah for helping with movecount. HD is way cool, I really hope some people prove its viability with fast times. Note that these statistics are not guaranteed to be perfectly accurate, but they should be. Also note that the method called HD here is known more specifically as HD-G, or HD-Guimond, as the first step is similar to that of Guimond. Please post any more arguments or aspects I missed, and feel free to debate against what I have here.

I know it's been like 9 months, but it should be noted that optimal face does not require 3.8 moves. I did 50 scrambles with an optimal face solver and it was 2.940 moves. (And it you're wondering, I did it with layers too and optimal layers require just 3.920)
I also did V's. They were a mere 0.920 moves on average. Average LOLS is 5.52. 0.92+5.52=6.44. It amazes me how you got 3.90 avg for V + CO, even if you cancelled 2 moves on average, its would still be 4.44. You must figure out which face you can cancel the most moves by doing, right?3.90 seems pretty low, but I definetely believe it.
Also just saying your calc for AUF was correct at 1.5. Good job.
I checked the EG alg avg movecount, and I got 9.11 moves. EG algs vary, so there can't be an exact number put down, but the average even for different algs seems to be always is between 9 and 10 moves.

HD:
V and CO without cancelling moves: 6.44
NLL: 8.13
All AUF: 1.50
Total: 16.07
If you are good at cancelling moves then
Total: 13.53

EG:
Face: 2.94 (computer optimal)
EG alg: 9.11
All AUF: 1.50
Total: 13.55
If your EG algs average 9.54 then
Total: 13.98

So HD and EG are about the same, but it can vary by one or two moves depending on how good you are at cancelling moves and the algorithms you use. I do support HD method and I will develop NLL algs for it!
Edit: These are some new NLL algs made by me-

I know it's been like 9 months, but it should be noted that optimal face does not require 3.8 moves. I did 50 scrambles with an optimal face solver and it was 2.940 moves. (And it you're wondering, I did it with layers too and optimal layers require just 3.920)
I also did V's. They were a mere 0.920 moves on average. Average LOLS is 5.52. 0.92+5.52=6.44. It amazes me how you got 3.90 avg for V + CO, even if you cancelled 2 moves on average, its would still be 4.44. You must figure out which face you can cancel the most moves by doing, right?3.90 seems pretty low, but I definetely believe it.
Also just saying your calc for AUF was correct at 1.5. Good job.
I checked the EG alg avg movecount, and I got 9.11 moves. EG algs vary, so there can't be an exact number put down, but the average even for different algs seems to be always is between 9 and 10 moves.

HD:
V and CO without cancelling moves: 6.44
NLL: 8.13
All AUF: 1.50
Total: 16.07
If you are good at cancelling moves then
Total: 13.53

EG:
Face: 2.94 (computer optimal)
EG alg: 9.11
All AUF: 1.50
Total: 13.55
If your EG algs average 9.54 then
Total: 13.98

So HD and EG are about the same, but it can vary by one or two moves depending on how good you are at cancelling moves and the algorithms you use. I do support HD method and I will develop some NLL algs and I will learn this and use it!

Thanks for the support! The biggest thing about HD now is that LOLS is obsolete now, and instead V+CO is done by doing CO, a lot like in the Guimond method, and forcing a V or adding moves to make it happen. The 3.90 was from me doing an average of 100 of doing a scramble, spending a minute or two to find the shortest solution I could, and writing the movecount down. I don't have any experience with HARCS or anything, so that was the best I could do to estimate optimal movecount. Face movecount was based on an estimate from @efattah, who has a lot of experience with EG and low movecount (definitely check out his LMCF [Low Movecount Corners First] method for 3x3). I took the algs from CYOtheKing's website, and actually factored in case probability, so that might have changed the average. The biggest thing about HD is the NLL algs. The current algs are mostly trash, so once those get redone the movecount might be a bit higher. Also, I introduced a new variant where instead of always having your U layer corner in DRF, it can be in any position. This is very similar to the concept of LEG. It gets rid of a lot of awkward rotations and D moves for the cost of 108 more algs. If anyone decides to get really serious with the method, I think that that especially has huge potential. I've done about 1/6 of the algs. I'll send you a link to the tutorial/algsheet that is very much a work in progress in a PM if you want. Thanks a lot for the true optimal movecounts, and thanks for the support!

It's done very similar to the first step of Guimond. Guimond algs can be really helpful, especially when starting out. Basically, you look at different cases you would do for Guimond, and find one that goes into a V or can be easily added on to to get a V.

Examples:
F R' U2 F' R U2 R U' F U'
This one is really nice and has 3 nice 4 move cases. The L, F, and D faces all have a 3/4 face of opposite colors, which is what you usually look for. You could solve this as any of these:
x' U' R U R'
z' y2 U' R U R'
y U' R U R'

F2 U2 F' R' U' F' R' U F' U'
On this one, the best option seems to be the L face.
z' y2 U2 R U2 R'

F U' R U R2 F' R U2 R
The U face looks okay, but the case isn't very nice, so I'd go with the R face.
z y2 U2 R U' R

R' F R2 F R U2 R F2 R2
The R face here is nice.
z y2 U R2 U R'

R' U' R U2 F2 R' U' F2 R2
The L face here has the only premade "opposite V", and it's okay. It also goes directly into a PBL.
z' y U' R' U2 F R

So, as you can tell, it's really not very hard to do. Here are some algs for less easy cases:

Spoiler: Helpful algs

I took those from this site, which has a bunch of other helpful stuff on Guimond.

Alright, so I’ve made a sheet linked here that I had put HD algs on. I’ve spent two days on it and I will keep working until all the HD algs are perfect. I don’t want HD to be a method where people are interested but then taken away because of bad NLLs. I’m currently using mostly CLL and LBL and some Ortega for my solves. I don’t know if I should learn full CLL and use it in all solves or maybe learn HD.
If HD algs can be as fast as CLL algs then I would probably choose HD.
The algs on the sheet are a WIP but will be finished soon and hopefully draw more people to HD.

Alright, so I’ve made a sheet linked here that I had put HD algs on. I’ve spent two days on it and I will keep working until all the HD algs are perfect. I don’t want HD to be a method where people are interested but then taken away because of bad NLLs. I’m currently using mostly CLL and LBL and some Ortega for my solves. I don’t know if I should learn full CLL and use it in all solves or maybe learn HD.
If HD algs can be as fast as CLL algs then I would probably choose HD.
The algs on the sheet are a WIP but will be finished soon and hopefully draw more people to HD.

I use Cube Explorer, and instead of going for low movecount I just find the best algs. I might change a move or something. I avoid having preAUF so none of the algs have it except obvious ones like U R2 U' R2.

I believe everyone with the link can view and comment on it, but request access or tell me your email and I'll let you edit it.
Thanks for helping!

I use Cube Explorer, and instead of going for low movecount I just find the best algs. I might change a move or something. I avoid having preAUF so none of the algs have it except obvious ones like U R2 U' R2.

I believe everyone with the link can view and comment on it, but request access or tell me your email and I'll let you edit it.
Thanks for helping!

So, I've been developing the algs this past week and the Solved V algs are basically perfect. I have algs written down for all the other cases but they need to be refined until they are perfect. I am making these algs so good that people won't withdrawl because of bad NLL's.
I really am making HD a viable method.
You can check them out: My HD Algorithms