Best approach to true LL on 4x4?

[LBr]

I’ve been bored recently and trying to experiment on 4x4, since the yau method is boring af and I really want to switch to K4 since it has the same first half but it pivots to F3L, CLL and ELL (I do only cross then insert corners during F3L). I just think that reducing a big cube to 3x3 is disrespectful to the puzzle

I’ve been averaging comfortably sub 1 with this alternative method and can occasionally get singles around the 40 mark, but I’m definitely about 5-10 seconds faster with yau unfortunately.

So I’m wondering what the best approach to LL is (unpaired edges ofc) and there’s a few options:

Option 1: tedious edge pairing then 3x3 stage. In 2020 shortcat made a video on his second channel about layer by layer 4x4 and this was how he did last layer. This is bad for a few reasons, the main one being that when you have parity it’s super inefficient. K4 ELL incorporates parity much better than reduction based methods making move count more consistent.

Option 2: CLL/ELL. This is the K4 last layer general idea, but ELL has many different approaches which I want to go over.

2a. Opposite colours then finish. One commutator is used to solve the first colour and then its opposite block, before a single stage is used to finish the rest of the cube (can be either a commutator, a 2-2 cycle or a parity 2 or 4 cycle). I think this was what the creator was going for on his website but I don’t know honestly.

2b. 2 colours indiscriminately then finish. So basically like above but your second colour can be adjacent. Flexibility is better but I’m wondering if the algs are less good for the parity cases since the 3 cycles are really nice and intuitive as well.

2c. ‘OLL/PLL’ one alg to orient the remaining edges then another alg, often a commutator to finish. @Christopher Mowla proposed this I think, and the main advantage seems to be recognition, since I doubt the alg number is lower, and move count is probably similar. I’m not as enthused by this method but it’s definitely worth discussing as it could be very fast.

Option 3(edit). You can also use comms to solve 2 edges at a time regardless of colour, but recognition is awful and mitigation of parity is bad so I don’t think this is viable to be honest

If anyone wants to contribute to this discussion then this would help. I’d love it if more people got interested in the method and made strides to develop it for the first time in over a decade. It would be amazing if someone generated ergonomic fast and up to date algs for some of these cases, since then there’s a real alternative method for speedcubers that don’t want to cosplay as 3x3 solvers.

 

[Christopher Mowla]

I just think that reducing a big cube to 3x3 is disrespectful to the puzzle

I think @UnknownCorrespondent would agree with you. (Although I think he, like me, isn't a speedcuber.)

K4 ELL incorporates parity much better than reduction based methods making move count more consistent.

Well, you can see from this table that the move optimal algs (BHTM is half turns) that most last layer 2-cycle and 4-cycle wing permutation cases require a similar quantity of moves.

I recently shared this edge-pairing approach (for @6 by 6 on rCubers) for the last layer edges + 1 keyhole F(n-1) slot. Not sure how that particular solution compares with typical speedcuber's move counts for the last 5 edges of the 7x7x7 or how fast/practical it is.

(Also, 4x4x4 last 4 dedge pairing example.)

2a. Opposite colours then finish. One commutator is used to solve the first colour and then its opposite block, before a single stage is used to finish the rest of the cube (can be either a commutator, a 2-2 cycle or a parity 2 or 4 cycle). I think this was what the creator was going for on his website but I don’t know honestly.

I guess you are aware (you mentioned me) that I made this PDF. The first step is to complete 1 dedge with one algorithm. (I provided sample algorithms there. Maybe I should update that document and link the algs through cubedb, since that supports old WCA notation.)

Dan Cohen made this video doing something like this well before I made that PDF. (FYI)

Flexibility is better but I’m wondering if the algs are less good for the parity cases since the 3 cycles are really nice and intuitive as well.

All I can offer to this conversation are my alg sets. (Some of those algs are in my 3 alg method PDF.)

• A complete set of brief last layer 4-cycle algorithms
• A complete set of brief last layer 2 2-cycle algorithms
• Short and/or fast algorithms for "oriented" 1 3-cycle and 1 2-cycle cases (which, again, you can input them here. Example).
• The 4x4x4 parity alg wik page, starting here. (More 2-cycle and 4-cycle algs.)

2c. ‘OLL/PLL’ one alg to orient the remaining edges then another alg, often a commutator to finish. @Christopher Mowla proposed this I think, and the main advantage seems to be recognition, since I doubt the alg number is lower, and move count is probably similar. I’m not as enthused by this method but it’s definitely worth discussing as it could be very fast.

Well, I proposed just OLL/PLL for 3 of the dedges (because there are significantly fewer OLL/PLL cases for 3 than 4).

But if someone can solve the first dedge with 1 alg and manage to solve the remaining 3 with 2 algs, it doesn't matter if they use "OLL" and "PLL" or simply directly solve in 2 steps.

@Ben Whitmore made this alg set for full 4x4x4 OLL (includes the corners). Clearly not practical to use (477 cases for n=4 versus 57 for n = 3), but there could be some good algs for speedsolving there.

I'm not aware that he (or anyone else) made an alg set for full PLL though. But some of the 9 move algs I found for 2 2-cycles are definitely better than commutators. (They are simply an extrapolation of @Stefan 's PLL parity algorithm for the nxnxn.)
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Sorry to throw all of this at you at once, but that's really all I can say about this. (So take your time to digest/view everything that interests you.)