# HD vs EG: 2x2 method showdown

#### Sue Doenim

##### Member
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
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

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.

#### Reed Merrill

##### Member
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.

#### efattah

##### Member
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.

#### Thermex

##### Member
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
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

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.
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).
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.

#### Duncan Bannon

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

#### Sue Doenim

##### Member
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.

#### Sue Doenim

##### Member
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'

#### efattah

##### Member
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.

#### Neuro

##### Member
Sure! I'm using CN HD-Guimond

1: 13
x' y2 R U R' U' R U2 R'
y2 U R2 F2 U' R2 U2

2: 14
x' y U2 R' U R'
x2 R' U R' F2 R F' R' F2 R2 U'

3: 14
x' U R' U2 R U2 R
F' U R' U2 R U' F U2

4: Scrambles for 3/4 are the same, using this instead: U F' U F' U2 R' U F U'. 15
z' y2 D F R2 U' F
y2 R2 U' B2 U R2 U' R2 D' B2 U2

5: 8
z' F' U2 F'
U2 R2 U' R2 U

MEAN: (13+14+14+15+8)/5= 12.8 avg movecount
Disregarding highest/lowest: 13.66 avg movecount
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

#### Duncan Bannon

##### Member
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

#### Duncan Bannon

##### Member
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

#### genericcuber666

##### Member
V+CO: 3.90 moves (from 100 solves by myself)
how do you do that? I thought that co was done with an alg?

#### Sue Doenim

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

#### Neuro

##### Member
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

#### genericcuber666

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

Last edited:

#### Thermex

##### Member
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.

#### WACWCA

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

#### Duncan Bannon

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

#### The Pocket Cuber

##### Member
I will definitely learn this method!