?New? Method - Swing Pair F2L (SPF2L)

[cubefactorx]

Hi all -

I had this idea many years ago and never took it very far. I've been out of the game for a while so apologies in advance if it has been hashed out previously.

The idea is to solve your F2L in traditional fashion, but along the way intentionally misplacing 2x F2L pairs diagonally from each other (i.e. FR&BL pairs or FL&BR pairs).

To visualize: apply R L U2 R' L' on solved F2L. Ref: FR&BL pairs are swapped. This would be a "finished" F2L with the swing pair method.

The idea here is that your final step in PLL will involve permutation of all the usual pieces + swapping F2L pairs back to their "true" home. The outcome is an algorithm subset for PLL that is very unique from the base PLL alg set. I have a very unrefined list of these cases that I will list below. Not all the cases are greatly optimized, but it should give a good feel for how things are different.

The great thing here is that the correction of pairs doesn't necessarily have to happen during a typical PLL. The OLL+SPF2L subset is very unique on it's own (in the limited number of cases I have checked anyway). It is possible one could arrive at an OLL case that is in the slower range during normal solving, but the OLL+SPF2L algorithm is faster by comparison. Then you would be left with a 'normal' PLL case to finish.

This should provide unique subsets for all manners of LL solving, and it is possible those subsets are more favorable overall compared to the normal approach.

SPF2L(PLL) cases:
You'll notice some normally fast cases are much worse, typically slower cases much better, and a small +/- on others. With probability of case occurence considered, this subset is 0.25HTM better and 0.68QTM worse compared to my personal base PLL set.
PLL HTM/QTM Algorithm
A1 15,16 U2 R' U [x] R U R U R U' [x'] U' R2 U R U F'
A2 15,16 U2 R U' [x'] R' U' R' U' R' U [x] U R2 U' R' U' B
U1 16,17 R U' L U' L' D' R U R' U2 R U R' D R' U'
U2 16,17 R D' R U' R' U2 R U' R' D L U L' U R' U
H 14,23 R2 F' U2 F2 R2 F' R2 U2 F2 R2 U2 F' U2 F2
Z 15,19 [x] L' u2 R' U2 L2 U R B' R' U R r2' U' R U'
E 10,15 [x] R2 u2 R L U2 M' U M2 U M2
T 9,9 r2 R U L' u2 R U' r' R2
J1 8,10 R U' L U2 R' U L' U2
J2 8,10 L' U R' U2 L U' R U2
N1 5,6 L' R' U2 R L
N2 5,6 L R U2 R' L'
Y 7,12 M2 U R2 B2 R2 U' M2
R1 14,18 R' U2 R L' U L U2 R' U' R L' U2 L U2
R2 14,18 L U2 L' R U' R' U2 L U L' R U2 R' U2
V 9,10 [x'] r U' R' u' R2 u R U r'
F 10,12 [z] U' D' M2 U R U' r2 D R' U
G1 13,18 R L U2 L2 R2 U2 L U L' U2 R U' L
G2 13,18 L' U R' U2 L U' L' U2 R2 L2 U2 L' R'
G3 13,18 L U' R U2 L' U L U2 R2 L2 U2 L R
G4 13,18 R' L' U2 L2 R2 U2 L' U' L U2 R' U L'
SS 15,19 z' U' r2 R' U L' U2'R U' R' U2 R L U'r2' U

 

[Waffle Cuber]

This is a really cool idea! As far as I know, it hasn’t been done, but I’m not fully sure. This idea is similar to EG-2 on 2x2. The last layer algs change due to the arrangement of the pairs. This could make F2L a lot more flexible. A subset for when two pairs have been ajacently swapped could also be cool!

 

[cubefactorx]

Thanks for the reply! For a long time I meant to take a closer look and develop things, but ideas get shelved when you stop competing. In the beginning I looked at the idea of adjacent pairs as well - thinking "well if I can play games with diagonal pairs then adjacent ones might be fun too". I've misplaced the subset I started on adjacent pair swapping years ago, but if I remember correctly it wasn't looking very hopeful. Somehow the symmetry between diagonal pairs is more workable.

For a while I practiced solving my F2L with pairs swapped and after making it habit my F2L average was slightly less. It is much easier to pick your first pair when you can start normally or with a swap placement (extended cross gives more options too). I never had the gumption to start learning cases before optimizing the algs which clearly never happened :/

 

[xyzzy]

It's not a new idea for sure, but I think you might be the first one to have generated and published good(-ish?) algs for the cases. Here's a thread from a few months ago where I mention what I think is a weakness of the method: either you have to learn algs for both ways to get a diagonal pair swap or you learn only one set and have to rotate half of the time.

(Maybe one use is as an alternative to 2-look PLL: the adjacent-diag and diag-diag cases are both very short, at 7 and 5 moves respectively. And after that it's just U/H/Z perms. In fact, you can even decompose some normal PLL algs into a combination of adj-diag and diag-diag, e.g. the RUL J perms and N perms.)

 

[Waffle Cuber]

Thanks for the reply! For a long time I meant to take a closer look and develop things, but ideas get shelved when you stop competing. In the beginning I looked at the idea of adjacent pairs as well - thinking "well if I can play games with diagonal pairs then adjacent ones might be fun too". I've misplaced the subset I started on adjacent pair swapping years ago, but if I remember correctly it wasn't looking very hopeful. Somehow the symmetry between diagonal pairs is more workable.

For a while I practiced solving my F2L with pairs swapped and after making it habit my F2L average was slightly less. It is much easier to pick your first pair when you can start normally or with a swap placement (extended cross gives more options too). I never had the gumption to start learning cases before optimizing the algs which clearly never happened :/

I would assume it makes you faster, but xyzzy is right. There are some weaknesses I didn’t notice when I wrote that reply. But, it I still a good idea and I think there is a lot that could be done with it.

 

[cubefactorx]

I first posted publicly on this idea in April 2007. I had a feeling it would not remain a novel idea for over a decade.

The cube rotation thing could be a problem. Ideally there are no rotations and you learn one strict set (either FR/BL or FL/BR) for recognition purposes. Being aware of this restriction from the beginning of a solve is a minor problem since cube rotations are being eliminated more and more; just know which foot to step forward with

It may be difficult to measure the outcome before more cases are generated. It is by chance that the average turn count is similar (PLL+Swap vs. regular PLL). Other subsets could be considerably better by sheer luck. Let's not forget that my PLL swap subset was generated solo without much optimization - there may still be a lot of room for improvement just in there.

 

[Thom S.]

As I have generated algorithms for exactly this set myself months ago I think I am qualified to speak here
Some cases like Diagonal CP swaps have really nice algorithms but it's either too restrictive to be viable or too many algorithms to be attractive.
If one learns this set, F2L will only improve if there is a good Diagonally swapped case and these are very rare to actually be better. If you want to have the freedom of Adjacent there are at least 2 Sets to learn(if @xyzzy could calculate the amount of algorithms, I would be very grateful, I think the number is 17x22 -1 = 373) and to make your F2L flexible you would need even more sets (at least Opp+2Adj+2A Perm cycles+2 O Perm cycles+ 2 W Perm Cycles to only rarely rotate twice) which makes this a big set. Big set's aren't bad, I just think the freedom you get at F2L isn't worth it enough. That's at least for me, I am open to get proven wrong, please prove me wrong if you can and show that this is viable. If I can't, you maybe can

 

[cubefactorx]

The selling point is definitely not to improve upon F2L execution times. With some imagination I think there is room for some nominal improvement on F2L times, but I'd rather ignore that notion completely if it will distract from the main concept. At worst, SPF2L and F2L execution times should be identical.

I don't have the time or resources on my own to prove it is viable, but I haven't seen any proof so far that it isn't. I can definitively say that the average turn count for SPF2L-PLL cases is virtually identical to traditional PLL cases when probability is weighted. This is leaving a window open...this indicates potential.

It is difficult to directly compare new subsets to any established LL methods - many of which have been refined over and over again by thousands of eager speedcubers over a 20 year span.

 

[Solvador Cubi]

I think others have made good observations and comments about the viability of this variant.

Learning Roux is what made me think of doing this type of pair placement.
For my beginner-level Roux implementation, I always place pairs in opposite corners to set up an easier 2 look CLL.

Perhaps an SPF2L would be useful for a Corners/Columns first solve.


-= Solvador Cubi

 

[DGCubes]

It'd be interesting if this could be incorporated into a ZZ method followed by anti-COLL so you force a diag-swap. I would also like to see the OLL+SPF2L algs to see if they're viable.

One problem I always have with methods like these is there's no chance of a skip in the end. Because of that, I think any method like this needs to be powerful enough that it's worth sacrificing lucky singles to get better (but more consistent) averages. I think EO, SPF2L, anti-COLL, diag-SPPLL could be really powerful. Diag-SPPLL has an average movecount of 7.2 HTM, which is quite good.

 

[WombatWarrior17]

It'd be interesting if this could be incorporated into a ZZ method followed by anti-COLL so you force a diag-swap. I would also like to see the OLL+SPF2L algs to see if they're viable.

One problem I always have with methods like these is there's no chance of a skip in the end. Because of that, I think any method like this needs to be powerful enough that it's worth sacrificing lucky singles to get better (but more consistent) averages. I think EO, SPF2L, anti-COLL, diag-SPPLL could be really powerful. Diag-SPPLL has an average movecount of 7.2 HTM, which is quite good.

This is interesting, but it would hinder the use of ZBLL. I'm going to try this out for fun. @PapaSmurf, thoughts?