Would LPELL/L4C be an efficient LL method?

[rubikmaster]

If you're not familiar with the tems from the title, go check them out on the wiki:
LPELL
L4C


Hey everyone, so I've been working on a new-ish LL method. It's not really anything new or inventive, since both LPELL and L4C have been around for some time but they've never been used together as an LL method (as far as I know). At first I was convinced I had invented LPELL myself (lol) but later found it on the Wiki. Surprisingly, I found only the 6 algs (+ mirrors) that insert the last pair and permute the edges (LPEPLL). In order to both permute and orient the edges while inserting the last pair you would need 48 algorithms (+ 48 mirrors). But, the full list of LPELL algs doesn't even exist yet, so that's where I come in. For the last few days I've been running some of the cases through Cube Explorer and trying to find some good algs (i.e. a good balance between short move count and fingertricky-ness). It's a lot of work, so first I wanted to ask you guys if you think LPELL/L4C could be a useful method for speedsolving? Also, I'm quite positive full LPELL could have useful applications for FMC (and of course I'm not the first person to notice that), but I'm mainly looking at it's application to speedsolving.

Pros:
- On average LPELL+L4C would be around 4 moves shorter than "insert last pair+OLL+PLL". Those are very rough estimates, so don't take my word for it just yet.
- In each solve there is a 1/3 chance you will run into a L3C case, which can be solved pretty fast by 3-cycle commutators used in BLD.
- After LPELL is done you have a 1/324 chance of getting an LL skip (compared to a 1/15,552 chance in CFOP).

Cons
- Recognition of the LPELL and L4C cases would be a bit slow but could be greatly improved with practice.
- This method would require learning 84 L4C algorithms and 48 LPELL algorithms (not including mirrors).

anyway guys, I want to hear your thoughts on this.

 

[supercavitation]

If you're not familiar with the tems from the title, go check them out on the wiki:
LPELL
L4C


Hey everyone, so I've been working on a new-ish LL method. It's not really anything new or inventive, since both LPELL and L4C have been around for some time but they've never been used together as an LL method (as far as I know). At first I was convinced I had invented LPELL myself (lol) but later found it on the Wiki. Surprisingly, I found only the 6 algs (+ mirrors) that insert the last pair and permute the edges (LPEPLL). In order to both permute and orient the edges while inserting the last pair you would need 48 algorithms (+ 48 mirrors). But, the full list of LPELL algs doesn't even exist yet, so that's where I come in. For the last few days I've been running some of the cases through Cube Explorer and trying to find some good algs (i.e. a good balance between short move count and fingertricky-ness). It's a lot of work, so first I wanted to ask you guys if you think LPELL/L4C could be a useful method for speedsolving? Also, I'm quite positive full LPELL could have useful applications for FMC (and of course I'm not the first person to notice that), but I'm mainly looking at it's application to speedsolving.

Pros:
- On average LPELL+L4C would be around 4 moves shorter than "insert last pair+OLL+PLL". Those are very rough estimates, so don't take my word for it just yet.
- In each solve there is a 1/3 chance you will run into a L3C case, which can be solved pretty fast by 3-cycle commutators used in BLD.
- After LPELL is done you have a 1/324 chance of getting an LL skip (compared to a 1/15,552 chance in CFOP).

Cons
- Recognition of the LPELL and L4C cases would be a bit slow but could be greatly improved with practice.
- This method would require learning 84 L4C algorithms and 48 LPELL algorithms (not including mirrors).

anyway guys, I want to hear your thoughts on this.

This gets proposed every so often. The problem is that it's significantly more algs than OLL-PLL, and L4C algs have a tendency to be horrifying.

 

[rubikmaster]

This gets proposed every so often. The problem is that it's significantly more algs than OLL-PLL, and L4C algs have a tendency to be horrifying.

I'm aware of that, that's why I'm doubtful of the efficiency of this method.

 

[Lyn Simm]

right after the beginners method, i was taught the Heise method by a friend, and that is what i currently use. i do intuitive LPELL and then 2 commutators (etc) to solve the LL corners. i dont think L4C is a good algorithm set, even though my friend thinks its not so bad

im trying to learn simplified "speed-heise" which is like advanced LPELL which forces a L3C case instead of a L4C case. its really fast, but i dont like remembering algorithms, so its taking me a while...

there is also a more advanced version, but that one is 72 algs so i hate it

the cool thing is that if you use L3C instead of L4C, you can always use a single insertion for the last 3 corners, which really improves the efficiency of this method in FMC.

-Lyn

 

[rubikmaster]

right after the beginners method, i was taught the Heise method by a friend, and that is what i currently use. i do intuitive LPELL and then 2 commutators (etc) to solve the LL corners. i dont think L4C is a good algorithm set, even though my friend thinks its not so bad

im trying to learn simplified "speed-heise" which is like advanced LPELL which forces a L3C case instead of a L4C case. its really fast, but i dont like remembering algorithms, so its taking me a while...

there is also a more advanced version, but that one is 72 algs so i hate it

the cool thing is that if you use L3C instead of L4C, you can always use a single insertion for the last 3 corners, which really improves the efficiency of this method in FMC.

-Lyn

That's actually Advanced LPEPLL (notice the second P), you're permuting edges while solving 1 corner as well. The problem with this is that it requires the edges of the last layer to be oriented already meaning it wouldn't be applicable to standard CFOP solves (chances are your edges are not going to end up oriented in most solves so you'd have to orient the edges while solving your first 3 pairs).

Also, L4C is a just a bit slower than PLL, while full LPELL is much faster than "Insert last pair + OLL".

Anyway, please give me some feedback guys. Would you like to see the full LPELL algs sometime in the future?

 

[SenorJuan]

I too came up with what is called LPELL (about 6 months before Kenneth's claim, funnily enough), I called it PEST (pair-edge solving technique). I didn't work out algs for every case, but I have found a large number of them, I suppose I should publish them somehow, especially seeing as the wiki page doesn't list many. [ I need to find my notes first, that would help]
But as everyone agrees, the last 4 corners are tricky for recognition, the quantity of them isn't the main problem.

Here's Ken demonstrating the technique......he's not happy, because the cube is already solved for him....

 

[rubikmaster]

I too came up with what is called LPELL (about 6 months before Kenneth's claim, funnily enough), I called it PEST (pair-edge solving technique). I didn't work out algs for every case, but I have found a large number of them, I suppose I should publish them somehow, especially seeing as the wiki page doesn't list many. [ I need to find my notes first, that would help]
But as everyone agrees, the last 4 corners are tricky for recognition, the quantity of them isn't the main problem.

Here's Ken demonstrating the technique......he's not happy, because the cube is already solved for him....
https://www.speedsolving.com/wiki/images/thumb/8/88/Kubbuth.jpg/100px-Kubbuth.jpg

Feel free to post the algs.

 

[SenorJuan]

I'll try and find them tomorrow evening, but I haven't seen them for 5 yrs, so it could be tricky.

 

[molarmanful]

Efficiency, meaning speed or move count? Because LPELL + L4C is great for FMC (I personally use this), but it's horrible in terms of speed. The worst part about LPELL for speed is recognition, and for L4C, it's execution.

I do these steps intuitively (no algorithms), basically the last steps of Heise with last slot pairing.

 

[rubikmaster]

Efficiency, meaning speed or move count? Because LPELL + L4C is great for FMC (I personally use this), but it's horrible in terms of speed. The worst part about LPELL for speed is recognition, and for L4C, it's execution.

I do these steps intuitively (no algorithms), basically the last steps of Heise with last slot pairing.

Thanks for the input.

Ok, I'm guite sure now that not many people would want to apply LPELL to speedsolving. But, I know it could be very useful for FMC for the people who would be willing to actually learn all the algs. I'm going post my full list of LPELL algorithms later this week, once I'm finished.

 

[SenorJuan]

Here's some I came up with. These ones are for when the pair is made up as a 2x1x1 block. I've not posted the 'all edges oriented' algs, they were basically the same as those already on the wiki page.

2x1x1 pair, two oriented edges LL
U'R'FRF', F'UFRU'R'
F'U'FURU2R'

F'U2FRU'R', F'L'U'LF
F'U2FURU2R'
R'FRF'UFR'F'R
UF'UFU'RU2R'

F'UFRUR', [ U ]FRU'R'F'
F'UFURU2R'
R'FRF2UF
UR'FRF'RU2R'
UR'FRF'U'RU'R'

one oriented edge
S'RU'R'S
U'R'FR2UR'U'F'
URU'R'U'R'FRF'
RUR'U2R'FR'F'
UFR'F'RU'RU'R'
UFR'F'R2U2R'

No edges oriented
UR'FRF'U2R'FRF'

I'll see if there's more in my scrappy notes. And there's some opposite-pair algs, too.

 

[SenorJuan]

More 2x1x1 pair algs I missed:

Where 3 edges are flipped:
[ U ]U'R'F'RU2M'U'M

One edge oriented
URUR'U'R'FRF'
RUR'U2R'FRF'
U'R'FR2UR'U'F'

Two edges oriented
UF'UFU2RU'R'

And a few for the 'opposite pair' situation:
RUR'
RUR'U'RU'R'
RU2RURU2R'
RU'R'U2R'FRF'
UFR'F'RUF'U'F
RU2R'F'U2FRU'R'
RU2R'F'UFRU'R'
U2M'F'U2FM
U'SF'UFU'S'

 

[rubikmaster]

Here's some I came up with. These ones are for when the pair is made up as a 2x1x1 block. I've not posted the 'all edges oriented' algs, they were basically the same as those already on the wiki page.

2x1x1 pair, two oriented edges LL
U'R'FRF', F'UFRU'R'
F'U'FURU2R'

F'U2FRU'R', F'L'U'LF
F'U2FURU2R'
R'FRF'UFR'F'R
UF'UFU'RU2R'

F'UFRUR', FRU'R'F'
F'UFURU2R'
R'FRF2UF
UR'FRF'RU2R'
UR'FRF'U'RU'R'

one oriented edge
S'RU'R'S
U'R'FR2UR'U'F'
URU'R'U'R'FRF'
RUR'U2R'FR'F'
UFR'F'RU'RU'R'
UFR'F'R2U2R'

No edges oriented
UR'FRF'U2R'FRF'

I'll see if there's more in my scrappy notes. And there's some opposite-pair algs, too.

More 2x1x1 pair algs I missed:

Where 3 edges are flipped:
U'R'F'RU2M'U'M

One edge oriented
URUR'U'R'FRF'
RUR'U2R'FRF'
U'R'FR2UR'U'F'

Two edges oriented
UF'UFU2RU'R'

And a few for the 'opposite pair' situation:
RUR'
RUR'U'RU'R'
RU2RURU2R'
RU'R'U2R'FRF'
UFR'F'RUF'U'F
RU2R'F'U2FRU'R'
RU2R'F'UFRU'R'
U2M'F'U2FM
U'SF'UFU'S'

Looks good. I'll be posting my full list of LPELL algs later today.

 

[SenorJuan]

I was a bit disappointed by how few 'distant pair' algs I had, there were several duplicates and suchlike. I've posted a duplicate or two in those two lists, I think, doh.
I remember I got a bit bored with working out algs, and started back on one-handed practice, then I was really busy at work and didn't do any cubing, then other things came up, and 5 years on it took quite a rummage to find the notebook.
It will be interesting to see what you come up with, and how you identified the cases, as my notes have drawings with arrows all over the place on them, that don't help much...

 

[rubikmaster]

I was a bit disappointed by how few 'distant pair' algs I had, there were several duplicates and suchlike. I've posted a duplicate or two in those two lists, I think, doh.
I remember I got a bit bored with working out algs, and started back on one-handed practice, then I was really busy at work and didn't do any cubing, then other things came up, and 5 years on it took quite a rummage to find the notebook.
It will be interesting to see what you come up with, and how you identified the cases, as my notes have drawings with arrows all over the place on them, that don't help much...

I'll only be posting the 48 1x1x2 pair cases, but I'm planning on doing the "opposite pair" cases too. They're all move optimal algs since I've concluded LPELL would be much more useful for FMC, but quite a few of them could be executed quickly. Although I don't believe anyone would use them for speedcubing since recognition would be awful, as well as the L4C cases after LPELL.

The algs are divided into 8 orientation categories which are identified by the top face: All Oriented, Line, L-Shape, Upside-down L-Shape, F-line (i.e. yellow sticker of UF edge on top face), L-line, B-line, Dot
And each category contains these permutation cases: 0, FR, FL, BR, BL, FB.

The letters denote which two edges need to be swapped. Not to be confused with FR edge, BR edge, BL edge, etc.
0 - all edges permuted
F - UF edge
R - FR edge
B - UB edge
L - UL edge

FB stands for both FB swap and LR swap since they're both opposite swaps and their algs are the same, while only the AUFs are different.

 

[SenorJuan]

Another look in the notebook and I've found a few more 'opposite pair'algs, I knew there wuz more.

RU2R'U'R'FRF'
S'RUR'S
U'F'U2FURU'R'
U'F'U2FU2RU2R'
U'F'U2FR'FRF'