The New Method / Substep / Concept Idea Thread

[wir3sandfir3s]

That is pretty much true as I think about it.
Petrus is already very efficient, but the first two steps don't necessarily have the 'Best' fingertricks.
ZZF2L Statistics show that it takes more average moves than CFOP-F2L.
EO can be done in an average of 3-4 moves.
A 2x2x2 block can be done in around 5-7 moves on average.

I am also trying to figure out a way to influence the last layer during F2L to the point where I can skip the whole LL.

Skipping the whole LL is already invented, L2S.
For you method though, I would solve a 2x2x3 in the back and do L2S in the front.
For the beginning block building, the best thing to do is restrict it and it'll be more finger trick friendly.

 

[JTWong71]

Skipping the whole LL is already invented, L2S.
For you method though, I would solve a 2x2x3 in the back and do L2S in the front.
For the beginning block building, the best thing to do is restrict it and it'll be more finger trick friendly.

I mean taking use of more than just two slots, only influencing on two slots will likely take more moves than influencing on three or four slots.

Example:
30 STM
x' //Inspection
U2 F2 U D L D R' U R' B //XXCross + EO
z R D R U' R' U R2 D' //F2L-3 + Last Layer Setup
R' D U' R D' R U R U' R U R //F2L-4 + LL

 

[wir3sandfir3s]

I mean taking use of more than just two slots, only influencing on two slots will likely take more moves than influencing on three or four slots.

Example:
30 STM
x' //Inspection
U2 F2 U D L D R' U R' B //XXCross + EO
z R D R U' R' U R2 D' //F2L-3 + Last Layer Setup
R' D U' R D' R U R U' R U R //F2L-4 + LL

Did you phase or correct EO in this? Was hard to tell. It could work out. Also, as far as I can tell, you only took advantage of the 2 slots. It probably wouldn't be a good idea to take advantage of all 4 slots because you would need algs to make the pairs, most likely, but 3 could be possible. First is EO, then CO, then PLL?

 

[crafto22]

Speed-heise/ZBLL

1. Heise blocks --> F2L-1 (no EO)
2. ZBLS
3. ZBLL

x2 L' F // First square
D' // Second square
L2 U' R2 F' R U2 R // Third square
F2 U2 F2 // Fourth square
L' B' // F2L-1
y2 F R2 U2 F R F' U2 R2 F' // ZBLS
U R L B2 L D' R2 U R2 L' B2 L D R' L2 // ZBLL

 

[JTWong71]

Speed-heise/ZBLL

1. Heise blocks --> F2L-1 (no EO)
2. ZBLS
3. ZBLL

x2 L' F // First square
D' // Second square
L2 U' R2 F' R U2 R // Third square
F2 U2 F2 // Fourth square
L' B' // F2L-1
y2 F R2 U2 F R F' U2 R2 F' // ZBLS
U R L B2 L D' R2 U R2 L' B2 L D R' L2 // ZBLL

Nice Solve.
Then, when you see how few moves F2L-1 is, you see how many moves are used for ZBLS+ZBLL.
ZB took over 50% of your solve...

 

[JTWong71]

Doing it in a more standard Heise, I got:

34 STM
x2 L' F // First square
D' // Second square
L2 U' R2 F' R U2 R // Third square
F2 U2 F' // Fourth square
U F' U L' y U R' //EO + F2L-1
U R' F R U R U' R2 //AB3C (Lucky, got to cancel a couple moves)
B2 R F' R' B2 R U' //L3C

 

[wir3sandfir3s]

Doing it in a more standard Heise, I got:

34 STM
x2 L' F // First square
D' // Second square
L2 U' R2 F' R U2 R // Third square
F2 U2 F' // Fourth square
U F' U L' y U R' //EO + F2L-1
U R' F R U R U' R2 //AB3C (Lucky, got to cancel a couple moves)
B2 R F' R' B2 R U' //L3C

Do you know how the one-pair approach works? I am trying to learn it but the best I can do is two-pairs...

 

[JTWong71]

Do you know how the one-pair approach works? I am trying to learn it but the best I can do is two-pairs...

I kind of know how to do the one pair, but sometimes I make both pairs and then two of my edges are misplaced.
I will usually try different moves to get different results.

 

[2180161]

How is this for a method, Part ZZ and Part Petrus:

I. 2x2x2 Block (In BDL)
II. EO (Steps 1 and 2 can be combined with practice)
III. F2L (Blockbuilding)
IV. Last Layer (EO is done, Subsets such as ZBLL for 1LLL, OCLL/PLL...)

Example Solves:

36 STM
x2 //Inspection
R2 F' R' B' D' R2 L F' //2x2x2 + EO
U2 F2 //EOArrow + 1
R' L' U' R2 //Block
U' l F M' U' R2 //F2L (Cancel into ZZLL)
U2 R2 U' R U' R' U R' U' D R' U R U D' R //ZZLL

37 STM
z2 y //Inspection
D' L' F L B' R F L U' L //EOArrow + 1
U' R D R2 U D' //2x2x3
R U R U R' //F2L
y' R2 U' R2 U' R U2 D' R U' R' U' D R U R2 U2 //ZBLL

I came up with the exact same thing a while back. here

Petrus-a (A petrus variant)

Hello. Before I begin, I have found no such variant of Petrus, or any for that matter, so that is why this is Petrus-a. Anyway, now for the steps, with the approximated movecount following the step:
2x2x2 block:7?
EO:8?
2x2x3:7?
R,U F2L-1:10?
L5C:10?
L5E:13?

Pros:

Spoiler

Ergonomic
fairly low movecount
Easy look-ahead.
EO is done sightly earlier to allow for a more ergonomic solve
L5E can be 2-gen

Cons:

Spoiler

Large alg count
Not as efficient as regular Petrus
L5C recognition may not be very good.

Example Solve:

Spoiler

Scramble:L2 B R2 U2 B U2 R2 F2 L2 B L' R D B2 F' R2 U' B2 U' L
z2 L' F L U2 L' U2 F' U R U2 F'//2x2x2
y D' F D U' F R F//EO
U R' U R' U2 R U D R' D' U' L' U L// 2X2X3
U' R2 U R//F2L-1
U2 R L U2 R' U' R U2 R' L' U'//L5C
M2 U' M U2 M' U' M2//L5E
Terrible move-count, but that is on my end. I am not very effiecient at all

there it is, It is a different ll, but nothing major

 

[wir3sandfir3s]

I came up with the exact same thing a while back. here

there it is, It is a different ll, but nothing major

Maybe adding speed heise or something similar or LPELL would help? LPELL into L4C for FMC or even Speedsolving?
I feel like this would be great with some LL influence.

 

[2180161]

Maybe adding speed heise or something similar or LPELL would help? LPELL into L4C for FMC or even Speedsolving?
I feel like this would be great with some LL influence.

I thought about LPELL, but decided against it. can't remember why though. I did however think about CP and LPELL, 2-gen of course, which would provide a 14? alg LL, all 2-gen.

 

[wir3sandfir3s]

I thought about LPELL, but decided against it. can't remember why though. I did however think about CP and LPELL, 2-gen of course, which would provide a 14? alg LL, all 2-gen.

EO+Pseudo CP+EP can make for an awesome 1lll. I think it would be best for fmc no matter what you do...

 

[wir3sandfir3s]

Kind of a random idea I had when I was thinking about CP. As with most of my random ideas, it probably isn't very efficient but could be on to something.
1. 2x2x3 and EO. Pretty easy.
2. CP. Also pretty easy.
3. Finish F2L but the corner do not have to be oriented. I think this will help speed up F2L.
4. EPLL
5. O6C. Just orient the remaining corners using 1 alg. Recog shouldn't be too bad, just normal OCLL with an extra corner to look at.
I mostly focued on low alg count with this. I'm pretty sure it would be less than CFOP.
I think CP methods could be so much better and absolutely amazing with a good recog system, which we clearly don't have. I will try, and then post your idea.
Mine isn't that great, but it is an idea to get started.
1. In inspection, plan out how to solve the corners of the first layer. Two adjacent corners on one side don't have to be oriented. The solved ones will be part of a 2x2x3.
2. While doing this, look ahead and see which corner case you have. You should figure out the case by the time you finish the FL corners.
3. Perform CP.
4. Finish the 2x2x3 using pseudo 2-gen.

 

[JTWong71]

1. 2x2x3 and EO. Pretty easy.
2. CP. Also pretty easy.
3. Finish F2L but the corner do not have to be oriented. I think this will help speed up F2L.
4. EPLL
5. O6C. Just orient the remaining corners using 1 alg. Recog shouldn't be too bad, just normal OCLL with an extra corner to look at.

Would this leave pure corner flips?
How many moves do you think they would average?

 

[JTWong71]

I think CP methods could be so much better and absolutely amazing with a good recog system, which we clearly don't have. I will try, and then post your idea.
Mine isn't that great, but it is an idea to get started.
1. In inspection, plan out how to solve the corners of the first layer. Two adjacent corners on one side don't have to be oriented. The solved ones will be part of a 2x2x3.
2. While doing this, look ahead and see which corner case you have. You should figure out the case by the time you finish the FL corners.
3. Perform CP.
4. Finish the 2x2x3 using pseudo 2-gen.

I also think that CP Methods can work well, but yes, recognition is hard.
I've done it with Petrus and I got 2 solves that are 26 HTM/STM.

 

[wir3sandfir3s]

Would this leave pure corner flips?
How many moves do you think they would average?

Good question, I'm not too sure. It shouldn't be too many.

I also think that CP Methods can work well, but yes, recognition is hard.
I've done it with Petrus and I got 2 solves that are 26 HTM/STM.

Cool Any ideas for a good recog system?

 

[JTWong71]

Cool Any ideas for a good recog system?

Nope, nothing other than brute force for me.
If I do CP, I'll solve one corner.
I just remember that if BDR is solved, then CP is solved if FDR swaps with FUR, and UBL swaps with UBR, or unless of course all pieces are already correctly placed.

 

[xyzzy]

1. 2x2x3 and EO. Pretty easy.
2. CP. Also pretty easy.
3. Finish F2L but the corner do not have to be oriented. I think this will help speed up F2L.
4. EPLL
5. O6C. Just orient the remaining corners using 1 alg. Recog shouldn't be too bad, just normal OCLL with an extra corner to look at.
I mostly focued on low alg count with this. I'm pretty sure it would be less than CFOP.

I tried generating algs for this because I didn't believe it could be good, but this H perm R U' R U' R U2 R U' R U' R might be really nice for OH?

Too bad the corner twists are kind of awful, though. There are 8×7=56 cases if you don't allow rotations (one of which is a skip), and the average move count with optimal (6-gen) algs is about 13.55, not counting AUF. (The subset with two corners in the D layer twisted the same way is the worst, with average move count 14.63.) Restricting the algs to 2-gen will increase the move count even more.

As for alg count, this definitely doesn't compare favourably to OCLL/PLL (~30 algs) or even COLL/EPLL (~45 algs).

 

[JTWong71]

How is this for a 1LLL with less algorithms, with some F2L Influence of course...
Before approaching the Last Layer, EO is solved, and then after Last Slot, 2 Adjacent Corners and the In-Between Edge is solved. This will leave 17 1LLL Cases, 2 Pure Flips, 5 PLL's, 5 T-Set ZBLL's, and 5 U-Set ZBLL's.

L2S or something along those lines may help a lot to make the line before Last Layer.

 

[wir3sandfir3s]

How is this for a 1LLL with less algorithms, with some F2L Influence of course...
Before approaching the Last Layer, EO is solved, and then after Last Slot, 2 Adjacent Corners and the In-Between Edge is solved. This will leave 17 1LLL Cases, 2 Pure Flips, 5 PLL's, 5 T-Set ZBLL's, and 5 U-Set ZBLL's.

L2S or something along those lines may help a lot to make the line before Last Layer.

I had the EXACT same idea today, I kid you not.
This could work out awesome IMO, we just need an efficient way of solving the line.
EO is pretty easy, just solve in the beginning or after a 2x2x3 block.
Here is my idea for the line:
Solve EO and F2L-1.
Solve 2 pairs: the last F2L pair and a LL pair. Both pairs should be able to be aligned so that the R face is free (besides F2L).
Position the corner so that however you insert it, the corner connects with the LL pair forming a line.

However this is done, I think the best way to do this is to intuitively position the last corner of a LL pair so that it joins with the pair when the last F2L pair is inserted. It may take some time to get used to and fast at, but I think it will be much like F2L in the sense that it will just come naturally eventually. EO may also be able to be solved during the insertion.