Optimal TCLL face

[Erglug]

I am currently finishing all alg of EG, and while playing with the face solver of cstimer to improve my face efficiency, i was wondering if a tcll face should’nt be slightly shorter in average.

I have search a lot but i havent’ found any informations about the average optimal number of moves to have a TCLL state.

I strongly think it should be shorter because you have 6 possible ways to create a EG face (diag swap, solved, back swap, face swap, left swap, right swap), and 8 or 9 (idk if CLL is a TCLL) when looking to do a TCLL face (4 corners who can be twisted in two ways). This would mean for me that tcll is a method as good or even a bit better than EG, maybe with the restriction of being in the good orientation after doing the tcll face, restriction that doesn’t exist with EG0 and EG2.

Do anyone knows how to find this ? I have tried to find a solution with batch solver, but i can have an optimal solution only for one face and one twisted corner at a time, and cube explorer is not good to find 2x2 solutions.

Thanks !
(sorry for my bad english haha)

 

[Erglug]

Hello everyone, i think because my post went some time before being public, not many people saw it so if you have an answer to the average 2x2x2 optimal tcll face, or an idee to solve this problem, feel free to let us know !

 

[Silky]

A TCLL face should be the same move-count as a CLL layer. Here's the breakdown.

Ortega/EG (a face)
distance	positions	Cumulative total
0	22654	0.62%
1	132828	4.23%
2	626354	21.28%
3	2057908	77.29%
4	832588	99.95%
5	1828	100%
Average distance = 2.97

LBL/CLL (a layer)
distance	positions	Cumulative total
0	3814	0.10%
1	22530	0.72%
2	130105	4.26%
3	651371	21.99%
4	1787884	70.65%
5	1061152	99.53%
6	17296	99.99%
7	8	100%
Average distance = 4.03

I could be wrong (probably am) but I thought this would at least help.

 

[WACWCA]

A TCLL face should be the same move-count as a CLL layer. Here's the breakdown.

Ortega/EG (a face)
distance	positions	Cumulative total
0	22654	0.62%
1	132828	4.23%
2	626354	21.28%
3	2057908	77.29%
4	832588	99.95%
5	1828	100%
Average distance = 2.97

LBL/CLL (a layer)
distance	positions	Cumulative total
0	3814	0.10%
1	22530	0.72%
2	130105	4.26%
3	651371	21.99%
4	1787884	70.65%
5	1061152	99.53%
6	17296	99.99%
7	8	100%
Average distance = 4.03

I could be wrong (probably am) but I thought this would at least help.

TCLL actually has lower move count on average than CLL because there are more ways to construct a valid TCLL layer than a CLL layer (Any corner can be twisted, and in either direction)

 

[Erglug]

A TCLL face should be the same move-count as a CLL layer. Here's the breakdown.

Ortega/EG (a face)
distance	positions	Cumulative total
0	22654	0.62%
1	132828	4.23%
2	626354	21.28%
3	2057908	77.29%
4	832588	99.95%
5	1828	100%
Average distance = 2.97

LBL/CLL (a layer)
distance	positions	Cumulative total
0	3814	0.10%
1	22530	0.72%
2	130105	4.26%
3	651371	21.99%
4	1787884	70.65%
5	1061152	99.53%
6	17296	99.99%
7	8	100%
Average distance = 4.03

I could be wrong (probably am) but I thought this would at least help.

I think this is wrong, because you have 8 different ways to do a tcll face, so it's absolutely not the same as a cll face.
But where do you find these stats? If the same thing is existing for tcll it would be perfect

 

[Silky]

TCLL actually has lower move count on average than CLL because there are more ways to construct a valid TCLL layer than a CLL layer (Any corner can be twisted, and in either direction)

I think this is wrong, because you have 8 different ways to do a tcll face, so it's absolutely not the same as a cll face.
But where do you find these stats? If the same thing is existing for tcll it would be perfect

You're both absolutely correct. I realized my mistake right after posting. I was thinking of a EG-2 Face which is the same as a cll face (at least from what I remember). I pulled the stats from here. Really loved this site and am sad it's no longer around

 

[Erglug]

Wow, thank you, in tho sources of the site i have partly found my answer:

http://2x2.great-site.net/index.html

This is a really old site but in it i have find this:
Aby ułożyć bloczek 3x1x1 i mieć czwarty róg dobrze spermutowany potrzeba średnio 2,736 ruchu. Pełny rozkład znajduje się w tabeli poniżej:
(It takes an average of 2.736 moves to complete a 3x1x1 block and have the fourth corner well spermmutated. The full schedule is in the table below

Liczba ruchów	Liczba przypadków	Prawdopodobieństwo	Scramble
0	32974	0,898%
1	187866	5,113%
2	938217	25,536%
3	2073175	56,426%
4	440864	11,999%
5	1064	0,029%	Link

So TCLL state is theoritically 2.73 away in average of a scramble, so a bit shorter than EG face who is 2.97 ( 0.14 is small but still)

My quest is half way done ! Now i just wanna know if a tcll solver is already existing, or if not, how to do one. As i already said, I have tried with batch solver but it was finding the optimal solution for a corner of a face at a time...

 

[Jorian Meeuse]

'Prawdopodobieństwo'
Polish scares me.

 

[Deleted member 36445]

'Prawdopodobieństwo'
Polish scares me.

I didn't know scramble was a polish word

 

[Silky]

Wow, thank you, in tho sources of the site i have partly found my answer:

http://2x2.great-site.net/index.html

This is a really old site but in it i have find this:
Aby ułożyć bloczek 3x1x1 i mieć czwarty róg dobrze spermutowany potrzeba średnio 2,736 ruchu. Pełny rozkład znajduje się w tabeli poniżej:
(It takes an average of 2.736 moves to complete a 3x1x1 block and have the fourth corner well spermmutated. The full schedule is in the table below

​

Liczba ruchów	Liczba przypadków	Prawdopodobieństwo	Scramble
0	32974	0,898%
1	187866	5,113%
2	938217	25,536%
3	2073175	56,426%
4	440864	11,999%
5	1064	0,029%	Link

So TCLL state is theoritically 2.73 away in average of a scramble, so a bit shorter than EG face who is 2.97 ( 0.14 is small but still)

My quest is half way done ! Now i just wanna know if a tcll solver is already existing, or if not, how to do one. As i already said, I have tried with batch solver but it was finding the optimal solution for a corner of a face at a time...

Don't know if there is a solver (are you asking for a TCLL face solver?) Here are algs

 

[Deleted member 36445]

Don't know if there is a solver (are you asking for a TCLL face solver?) Here are algs

man, that is cursed.

 

[Silky]

man, that is cursed.

There are a few more links on the wiki, I'm sure there is a better sheet but I'm lazy

 

[Jorian Meeuse]

man, that is cursed.

you've clearly never seen this:

Best 2x2 Algs

docs.google.com

 

[Deleted member 36445]

There are a few more links on the wiki, I'm sure there is a better sheet but I'm lazy

yeah, I'm not talking about the algs, they look fine, I'm talking about the weird ocll cases with unoriented corner
I'll try to learn them eventually but I never had seen what they looked like lol

you've clearly never seen this:

Best 2x2 Algs

docs.google.com

thanks!