# HD vs EG: 2x2 method showdown



## Sue Doenim (Dec 3, 2017)

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


Spoiler: NLL movecount distribution



Moves: number of cases, chance, cumulative chance
0: 1, 0.56%, 0.56%
1: 0, 0%, 0.56%
2: 0, 0%, 0.56%
3: 3, 5%, 5.56%
4: 2, 4.44%, 10%
5: 3, 6.67%, 16.67%
6: 3, 6.67%, 23.33%
7: 7, 24.44%, 47.78%
8: 5, 11.11%, 58.89%
9: 15, 33.33%, 92.22%
10: 1, 2.22%, 94.44%
12: 1, 1.11%, 95.56%
13: 1, 4.44%, 100%



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.


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## Reed Merrill (Dec 3, 2017)

Sounds sweet! Next time I feel super motivated to learn CLL I might go for the way lower alg count and do HD instead. I'm not anything close to a good 2x2 solver, and too many algs is mainly what keeps me away from trying get a lot better.


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## efattah (Dec 3, 2017)

I was pretty excited about HD and even considered learning it (despite already known EG1 & CLL), but at the present moment I find the HD algorithms slow and non-fingertricky. I believe they need to be expanded and improved, possibly choosing longer algorithms that are faster and being less obsessed with movecount. Look at some of the CFOP PLL's that are 19-21 moves that some people can execute in sub-1. HD is a great method, it just needs more community participation to develop the algorithms. The HD algorithms (currently) have a lot of half turns (too many F2's in particular). I am losing faith in STM as a means of measuring the length of an algorithm. Personally I have been switching to QSTM (M = 1 turn, M2 = 2 turns, F2 = 2 turns, etc.) although I think something like 1.5-STM is better (M2 = 1.5 turns, F2 = 1.5 turns). Counting an F2 or B2 as 1 turn I think is quite deceptive when you end up comparing something like R U R' U' with R' F2 R2 F2 and calling them the same length.


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## Thermex (Dec 4, 2017)

Sue Doenim said:


> 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)
> ...


It sounds like HD-G (I think we should come up with a better name for it) could really change the viability of the method; though I wish you could go a little more in depth on how you're doing the first two steps for your statistics. Otherwise I really like how this is shaking out, I think times very comparable to EG are possible with more developed algs. (I'll try to add some of this stuff to the wiki page I created).


efattah said:


> I was pretty excited about HD and even considered learning it (despite already known EG1 & CLL), but at the present moment I find the HD algorithms slow and non-fingertricky. I believe they need to be expanded and improved, possibly choosing longer algorithms that are faster and being less obsessed with movecount. Look at some of the CFOP PLL's that are 19-21 moves that some people can execute in sub-1. HD is a great method, it just needs more community participation to develop the algorithms. The HD algorithms (currently) have a lot of half turns (too many F2's in particular). I am losing faith in STM as a means of measuring the length of an algorithm. Personally I have been switching to QSTM (M = 1 turn, M2 = 2 turns, F2 = 2 turns, etc.) although I think something like 1.5-STM is better (M2 = 1.5 turns, F2 = 1.5 turns). Counting an F2 or B2 as 1 turn I think is quite deceptive when you end up comparing something like R U R' U' with R' F2 R2 F2 and calling them the same length.


I agree with this; I feel like it's one of the main flaws of the method. I wish there was some sort of movecount-system that could measure the ergonomy and speed of an algorithm. Something that counts certain strings of moves with certain values (ex: F, U = 3 moves, R, U = 1.5 moves) that could be used to measure the true potential of a method. I plan on maybe going back and editing some of the NLL's this winter break.


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## Duncan Bannon (Dec 4, 2017)

Where are the algs? I want to see how hard and fingertricky they are. Thanks


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## Sue Doenim (Dec 4, 2017)

The first step is like Guimond, but you cancel into or out of them to force Vs. Check the 2x2 example solve thread for examples. You can get to the algs from the link in here. https://www.speedsolving.com/forum/threads/hd-method-2x2-alternative-to-cll.65442/
Note that this document does not include HD-G at the current time.


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## shadowslice e (Dec 4, 2017)

Duncan Bannon said:


> Where are the algs? I want to see how hard and fingertricky they are. Thanks


For the first step you could conceivably use a slightly altered version of the OL5C algs from SSC (though you can probably get better algs from regent ing the cases for 2x2). For the second set look up VOP.


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## Sue Doenim (Dec 11, 2017)

I'm working on algs, so I'll post alternatives here for you guys to judge. Tell me what needs work, what's good, and what's best. If you have a better alg, please share!
V permuted set:
F opp.
(U2) R2 U R2 U' R2 (original)
R opp.
y' (U2) R2 U' R2 U R2 (original)
F bar
(U') F2 U R2 U' B2 D R2 (original)
y' (U') R U' R' U2 R U R' D R2
y (U') R2 U R2 U' R2 D R2 
(U') R' U' L U2 R' U R U2
x' F' R' F' R U2 R' U R U2
(U') x' R' F' R U2 R' U R U2
(U') x' L' U' L U2 R' U R U2 
x' F' L' U' L U2 R' U R U2
R bar
(U) R2 U' F2 U R2 U' B2 (original)
(U) R2 D' R2 U R2 U' R2 
x' U2 R' U' R U2 L' U R
x' U2 R' U' R U2 R' F R
x' U2 R' U' R U2 L' U L
Solved (This one's really difficult, I'd appreciate some help with it.)
R U R' F2 R F' R U R2 F2 (original)
y' L U' L D R U' R2 D L U2 L 
R2 U R2 U' R2 D R2 U' R2 U R2
R U R' F2 R U R2 F R U' F
Diagonal
R2 U' B2 U2 R2 U' F2 U' R2 (original)
R2 U' F2 D' R2 D R2 D R2 
R2 D' R2 D' R2 U R2 U R2
y2 R' U' R D' R2 D R' U R 
F R F' U R2 U' F R' F'
y R U R' D R2 D' R U' R'


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## efattah (Dec 11, 2017)

For the solved case you can use some set up moves then an Ortega permute
U' R2 U' F2 R2 U2 + (Ortega PBL=) R2 U' B2 U2 R2 U' R2 [13]
It looks slow but if you finger trick it properly it has no regrips and is really fast, the F2 is done with the right ring finger. However the one given, R U R' F2 R U R2 F R U' F [11], if finger tricked properly is also pretty good. Does require regrip though.


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## Neuro (Dec 11, 2017)

Neuro said:


> Sure! I'm using CN HD-Guimond
> 
> 1: 13
> x' y2 R U R' U' R U2 R'
> ...


 Not very indicative of "true" average movecount, but I just got a 12.8 mean of 5 with HD-Guimond. Used standard algs to do this and didn't remove cancellations (past V+CO.) The 8 move solve is pretty cool, shows what can happen if you're lucky. Scrambles and OG post on The 2x2 Example Solve Thread here on the forums


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## Duncan Bannon (Dec 11, 2017)

I did a little average game against him and with Pure CLL no EG got 14 mean and 14.33 Ao5. Ill do a quick Ao5 here with full EG and see what I can get. @Neuro Let do it again right here. Ill use EG. I know the alg count is very different but lets go.

Straight from CS timer.

1. R2 U2 R' F2 R' U' F U R'
2.R' U' F2 R F' U R2 U R2
3.F' U R' F2 R2 U R' F2 U'
4.F R U' R F' U2 F R U2
5.U2 R' U2 R U R2 U F2 R2 U2


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## Duncan Bannon (Dec 11, 2017)

1.
Z’, X’
U’,F’, U2, F’
U2, R’, U’,R, U’, R’, U2, R, U - 13

2.
Z
U, R’, U, R, U’, R’
R' F' U R' F R2 U2’ R' U R U2 - 17

3.
X, Y2
R,U,R’
U F' R U R' U' R U R2' F' R, U’ -15

4.
X, Y’
U’,R’
F' L F L' U2 L' U2 L U’ - 11

5.
X2, Y’
R2, U’, R’
U2 R U' R' F U2 R2 F' R F' R - 14 

Didn’t want to keep you waiting, so I did this pretty quick. Me and Neuro are going to do some in a PM, May tell you guys how it goes.

Ao5- 14
Mean of 5- 14


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## genericcuber666 (Dec 12, 2017)

*


Sue Doenim said:



V+CO: 3.90 moves (from 100 solves by myself)

Click to expand...

 how do you do that? I thought that co was done with an alg?*


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## Sue Doenim (Dec 12, 2017)

It is sort of, it's done semi intuitively, but you use modified versions of Guimond algs.


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## Neuro (Dec 13, 2017)

Gonna try and really abuse the efficiency in these solves while still using the normal algs

1: 9
z y U R' U' R
U R2 U R2 y U2

2: 12
z U R U2 R y
U R2 U R2 U' F2 R2 U2

3: 10
z U2 R' U R'
y2 U R2 U' F2 R2 U

4: 11
x y' U' R U' R2' F R F'
R2 U R2 U2

5: 13
U' R U2 R'
x' U L U' R2 U L' U F' U2 x

Mean of 3: 11 moves
Mean of 5: 11 moves

This is indicative of what the method is capable of; although it may not be truly realistic by a human in 15 secs. It's fun in context of trying to get the most efficient solves though  When I do the Ao50 I'll provide solutions most indicative of a speedsolve


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## genericcuber666 (Dec 14, 2017)

so in its current state where do you think the speed limit lies?


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## Thermex (Dec 14, 2017)

genericcuber666 said:


> so in ts current state where do you think the speed limit lies?


Hard to say, though considering it has a lower average movecount than EG (with slightly worse ergonomics) I'd say like 2 seconds is probably around the limit.


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## WACWCA (Dec 14, 2017)

With Full Eg, leg, and tcll my move count is in the 13s I believe, I've checked before doing ao100


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## Duncan Bannon (Dec 14, 2017)

Thats in 15 seconds right? You can probably do slighly better.


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## The Pocket Cuber (Jan 8, 2018)

I will definitely learn this method!


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## Underwatercuber (Jan 8, 2018)

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.


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## Duncan Bannon (Jan 24, 2018)

How are generating these algs doing? Need help?


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## Sue Doenim (Jan 24, 2018)

Duncan Bannon said:


> How are generating these algs doing? Need help?


 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.


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## Duncan Bannon (Jan 24, 2018)

Okay PM me the details and how you are doing it.


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## The Pocket Cuber (Jan 26, 2018)

The algs don’t seem to have pictures. Is there any alg sets with pictures?


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## Sue Doenim (Jan 26, 2018)

The algs in the link in this sheet do have pictures, but are not updated yet. So far, we're 1/3 of the way through redoing the algs.


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## Roussell (Jan 27, 2018)

How do yo do v and co in 3 moves?


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## Sue Doenim (Jan 27, 2018)

Roussell said:


> How do yo do v and co in 3 moves?


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.


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## bren077s (Feb 16, 2018)

How would one go about learning HD-G. Would they start with Guimond? Start with beginner's HD and then learn full HD with LOLS? other?


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## Underwatercuber (Feb 16, 2018)

bren077s said:


> How would one go about learning HD-G. Would they start with Guimond? Start with beginner's HD and then learn full HD with LOLS? other?


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


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## bren077s (Feb 16, 2018)

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.


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## WoowyBaby (Aug 25, 2018)

Sue Doenim said:


> 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)
> ...


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-


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## Sue Doenim (Aug 25, 2018)

WoowyBaby said:


> 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.
> ...


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!


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## Underwatercuber (Aug 27, 2018)

How do you do the V + CO intuitively?


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## Sue Doenim (Aug 28, 2018)

Underwatercuber said:


> How do you do the V + CO intuitively?


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.


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## WoowyBaby (Sep 25, 2018)

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.


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## Underwatercuber (Sep 26, 2018)

WoowyBaby said:


> 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.


How do generate better algs? I would love to help add to the list


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## WoowyBaby (Sep 26, 2018)

Underwatercuber said:


> How do generate better algs? I would love to help add to the list


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!


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## Underwatercuber (Sep 26, 2018)

WoowyBaby said:


> 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 will just comment the algs


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## WoowyBaby (Sep 29, 2018)

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


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## Underwatercuber (Oct 5, 2018)

Could someone do an average movecount with @WoowyBaby ’s algs?


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## WoowyBaby (Oct 5, 2018)

Underwatercuber said:


> Could someone do an average movecount with @WoowyBaby ’s algs?


What exactly do you mean? Like the average movecount of my NLLs? If so, then it’s pretty easy to do, just add up all the moves and divide by 36 (or 42 if PBL is inc)


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## Hazel (May 6, 2019)

I'm interested in getting back into 2x2, is HD worth learning now that @WoowyBaby has reworked the algs?


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## WoowyBaby (May 6, 2019)

@Aerma Try it out! Here's my algorithm sheet


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## ImmolatedMarmoset (May 7, 2019)

WoowyBaby said:


> @Aerma Try it out! Here's my algorithm sheet


Lol. I have a comp with 2x2 on June 1st. I’m seriously thinking about learning full HD for it, just to see if I could. Any reccomendations?

EDIT: I have cube explorer too, so I’ll gen algs for the cases I don’t like of the NLLs. I wouldn’t replace them with the ones already on your sheet, just add them on so we can have multiple options.


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