2x2x2 move count

[Pedro]

Does anyone have the numbers for Guimond and Ortega methods?
like, how many moves in average should the 1st face take, considering color neutrality?
what about the Guimond 1st step?

thanks in advance

 

[Gparker]

im not color neutral and i use ortega, well i am part if you count yellow or white. it takes me about 5 moves to get one face, and im not sure about guimond id say almost the same

 

[James Kobel]

For a face, it takes 2 moves usually and for the guimod first step takes about 1.

 

[Lt-UnReaL]

Some numbers I found a while ago:

OFOTA 1st step ~ 1
SS 1st step ~ 1
CLL 1st step ~ 5.5
Ortega 1st step(also Full EG 1st step) ~ 3.5


Ortega ~ 18.5
OFOTA ~ 14
SS ~ 14
CLL ~ 14
CLL + adjacent EG case ~ 12.5
Full EG(CLL + adjacent & diagonal EG) ~ 12

Sorry, don't know about Guimond...and G-FASSST, who knows? (Okay, 1st step of G-FASSST ~ 1)

 

[cuBerBruce]

For a face, it takes 2 moves usually

I doubt it's that low. May a face containing opposite colors, but not a single-color face (Ortega method).

and for the guimod first step takes about 1.

You must be thinking of what I call "step 0" and step 0 takes close to zero moves on average. What I think of as step 1 certainly takes over 3 moves on average.

EDIT:
I once wrote a program to calculate the number of moves needed for Guimond "step 0" for all 2x2x2 positions (color neutral). 3097152 positions required no moves. 569088 positions required 1 move. 7776 positions required 2 moves. 144 positions required 3 moves. This works out to an average of approximately 0.159 moves.

I note that this analysis makes the assumption of always performing step 0, even if the corners are already all oriented. In reality, if you had all corners oriented, you would just skip step 0 & 1, rather than making make 3 moves to complete step 0 (and then another 3 moves to complete step 1).

 

[Lucas Garron]

I'm pretty sure I haven't seen the suggestion before, but I don't wanna make a new thread.

Has anyone considered the following variation/simplification of EG before?

solved case bottom layer: CLL
adj case bottom layer: adj alg
opp case bottom layer: R2 F2 R2 + CLL

 

[TMOY]

You must be thinking of what I call "step 0" and step 0 takes close to zero moves on average. What I think of as step 1 certainly takes over 3 moves on average.

I tried something like 20-30 step 1 solves of (my own slightly modified version of) Guimond.
Got one 2-moves solve, two 3s, two 5s, two 6s and all the rest were 4s, which makes an average slightly above 4 moves.

 

[Swordsman Kirby]

Ortega ~ 18.5
OFOTA ~ 14
SS ~ 14
CLL ~ 14
CLL + adjacent EG case ~ 12.5
Full EG(CLL + adjacent & diagonal EG) ~ 12

What really.

 

[Lt-UnReaL]

Ortega ~ 18.5
OFOTA ~ 14
SS ~ 14
CLL ~ 14
CLL + adjacent EG case ~ 12.5
Full EG(CLL + adjacent & diagonal EG) ~ 12

What really.

Yes, really.

I'm just going to assume that you meant to say, "Not really", because that's what it sounds like. If you think the move count I provided for step 1 for all of those methods is accurate, then the move count I provided for all steps for all of those methods must be accurate. All I did was take the first step and add the average move count it takes for each algorithm needed afterward, and added 0.75 to the total for AUF (added 1.00 to Ortega because it needs 2 separate algorithms after step 1, but lots of them have easy mirrors).

 

[James Kobel]

For a face, it takes 2 moves usually

I doubt it's that low. May a face containing opposite colors, but not a single-color face (Ortega method).

and for the guimod first step takes about 1.

You must be thinking of what I call "step 0" and step 0 takes close to zero moves on average. What I think of as step 1 certainly takes over 3 moves on average.

Yes, I was talking about a face of opposite colors. And is your step zero where you get 3 corners oriented?

 

[cuBerBruce]

For a face, it takes 2 moves usually

I doubt it's that low. May a face containing opposite colors, but not a single-color face (Ortega method).

and for the guimod first step takes about 1.

You must be thinking of what I call "step 0" and step 0 takes close to zero moves on average. What I think of as step 1 certainly takes over 3 moves on average.

Yes, I was talking about a face of opposite colors. And is your step zero where you get 3 corners oriented?

Ok, but one face of opposite colors isn't applicable for either Guimond or Ortega methods.

More precisely, step 0 gets 3 oriented corners and 1 mis-oriented corner in one layer.

 

[DavidWoner]

I'm pretty sure I haven't seen the suggestion before, but I don't wanna make a new thread.

Has anyone considered the following variation/simplification of EG before?

solved case bottom layer: CLL
adj case bottom layer: adj alg
opp case bottom layer: R2 F2 R2 + CLL

yes, people who are too lazy to learn the rest of EG are doing this right now.

 

[Edmund]

im color nuetral and ortega is fast. but guimond is a bit faster. it shouldn't take more than 4 moves 4 an ortega side and for guimond idk

 

[cuBerBruce]

I realize I have previously analyzed the case of making a face of opposite colors. The worst case positions required 3 moves, and the average was approximately 1.0294 moves.

I have modified my code to also do the analysis for one face of one color, and for two faces of two opposite colors. The worst case for Ortega step 1 is 5 moves, not 4. However, over 99.95% of cases do not require more than 4 moves.

Results of my analyses are below:

Goal: one face of opposite colors

distance  positions
    0      699984
    1     2189088
    2      762048
    3       23040

Average distance = 1.0294


Goal: one face of a single color

distance  positions
    0        22654
    1       132828
    2       626354
    3      2057908
    4       832588
    5         1828

Average distance = 2.966


Goal: two opposite faces of two opposite colors

distance  positions
    0        14832
    1        29376
    2       175392
    3       851040
    4      2066688
    5       535680
    6         1152

Average distance = 3.779

Note, that if you strictly follow Guimond step 0 + step 1, the average move count will be higher than 3.779, since the above table is for the optimal number of moves to reach the goal of step 1 from the initial state.

 

[Swordsman Kirby]

Can you do an average step 1 for SS? (the 3/4 of a single-color face step) I'm wondering if there are any length 3 positions.

 

[cuBerBruce]

Can you do an average step 1 for SS? (the 3/4 of a single-color face step) I'm wondering if there are any length 3 positions.

OK, here are the results I get.

Goal: 3 or more stickers of the same color on at least one face.

distance  positions
    0      1075254
    1      2149200
    2       447630
    3         2076

Average distance = 0.830

Goal: Exactly 3 stickers of the same color on at least one face.

distance  positions
    0      1060856
    1      2140980
    2       470142
    3         2182

Average distance = 0.840

An example of a position that requires three moves to get at least three stickers of the same color on a face is given by the following scramble:

R' F' U F' U F2 U R' F U'

 

[Swordsman Kirby]

Can you do an average step 1 for SS? (the 3/4 of a single-color face step) I'm wondering if there are any length 3 positions.

OK, here are the results I get.

Goal: 3 or more stickers of the same color on at least one face.

distance  positions
    0      1075254
    1      2149200
    2       447630
    3         2076

Average distance = 0.830

Goal: Exactly 3 stickers of the same color on at least one face.

distance  positions
    0      1060856
    1      2140980
    2       470142
    3         2182

Average distance = 0.840

An example of a position that requires three moves to get at least three stickers of the same color on a face is given by the following scramble:

R' F' U F' U F2 U R' F U'

Interestingly enough, one of the positions that go from distance 0 to 3 between the two sets is the solved position.

 

[Michal Robaczyk]

I want to share some stats I've calculated for first step in different 2x2 methods. The values already calculated in this topic are correct according to my independent tests. Here I want to paste the first step for CLL stats. Full report on other methods is on my website here:
http://2x2.great-site.net/stats.html.

CLL first step - average distance 4.028

Distance	Positions	Probability
0	3814	0.104%
1	22530	0.613%
2	130105	3.541%
3	651371	17.728%
4	1787884	48.661%
5	1061152	28.882%
6	17296	0.471%
7	8	0.0002%

On http://2x2.great-site.net/stats.html there are also all scrambles to longest cases for first steps. For example:

• CLL/LBL first step (first layer)
  • 7 moves: http://2x2.great-site.net/scramble/warstwa_4x1_7r.txt
  • 6 moves: http://2x2.great-site.net/scramble/warstwa_4x1_6r.txt
• VOP first step (3/4 first layer)
  • 5 moves: http://2x2.great-site.net/scramble/warstwa_3x1_5r.txt
  • 4 moves: http://2x2.great-site.net/scramble/warstwa_3x1_4r.txt
• TCLL first step (3/4 layer + 4th corner permuted)
  • 5 moves: http://2x2.great-site.net/scramble/warstwa_separacja_3x1_5r.txt
• Ortega/EG first step (first face)
  • 5 moves: http://2x2.great-site.net/scramble/scianka_4x1_5r.txt
• SS/HD first step (3/4 face)
  • 3 moves: http://2x2.great-site.net/scramble/scianka_3x1_3r.txt
• SOAP first step (2/4 face + separation)
  • 4 moves: http://2x2.great-site.net/scramble/separacja_2x1_4r.txt
• OFOTA first step (first face but can be with opposing corners)
  • 3 moves: http://2x2.great-site.net/scramble/scianka_z_naprzeciwleglymi_4x1_3r.txt
• Guimond first step (3/4 face but can be with opposing corners)
  • 2 moves http://2x2.great-site.net/scramble/scianka_z_naprzeciwleglymi_3x1_2r.txt