(New?) 'commutator-cancelling' idea for 3BLD

[Jorian Meeuse]

So recently I thought of a pretty cool way to cancel commutators in 3BLD, and I have never seen anyone discussing this, despite it being able to save you a whole alg on some scrambles. The idea is that commutators don't only work for individual pieces, but also for a bar (attached corner and edge). For example: [U, Rw' D Rw] cycles UFR-LDF-UBR, and also UF-LD-UR. This is much faster than doing [U : [U, L' E' L]] during edge exec, and [U, R' D R] during corner exec, because it saves you an alg.
The most basic way you can encounter this, is in a scramble like this:
F2 L2 B2 U F2 R2 D' R2 D2 L' D F' L' F2 L B2 L B' U L'
Corner memo (UFR buffer, Speffz) starts with RO, so we will see if edge memo also includes RO
Edge memo (UF buffer, Speffz) starts with AJ WK RO, so edge memo includes RO
This means we can start executing like this:
[R' U' : [S, R2]]
[D: [S', R F R']]
Instead of the regular commutator for RO, we will now do [L D2 : [Rw' D Rw, U']] to cancel the edge RO commutator with the corner RO commutator.
You can also cancel an edge commutator with a corner commutator that is not the first corner commutator. Take this scramble for example:
U' B2 U F2 D' R2 D' R2 B2 L2 B' U B' D2 R' B' L' D2 B U2 R'
Corner memo: KA LB OB + 2 twists (which I would memorize visually)
Edge memo: AX LB DO JR TS UE
Notice how both corner and edge memo include the pair LB. This means we can solve like this:
[U : [S', L2]]
Now we have LB on edges, but we can't cancel with the corner alg yet. First we have to do KA corners:
[U D : [R D R', U2]]
Now we can cancel LB on edges with LB on corners, which we can nicely do with a J Perm here:
L' U2 R U R' F' R U R' U' R' F R2 U' R' U2 L
An even faster alg would be this: R U2 L' U' L U2 R' U
(Notice how this case is best done algorithmically. I have not yet tried to come up with good commutators for all cases, but the ones I tried worked out pretty nicely. It shouldn't hurt to learn a few algs for some cases where that is objectively better though)
From here it is just normal 3-style.

I am aware that noticing the potential of this technique in a scramble can be extremely difficult. It requires a lot of concentration to notice that corner memo partially matches with edge memo. I am also not even close to being able to implement this in my solves, but I definitely think this is possible for some people, and also for me in the future. I might make a sheet with algs sometime in the coming months, but I'll prioritize practicing 3BLD a lot and implementing full floating.

 

[Mike Hughey]

I know that Daniel Beyer (the "B" in the BH method of blindsolving) has told me he has done solves with this approach in competition officially. And I believe Chris Hardwick (the "H" in the BH method) has also talked about doing it sometimes. But I played with it a little and decided it was much too hard for me to process, so I have never really tried it. I suspect that for most solvers at the fastest speeds today, the distraction of trying to figure this out and get comfortable with it might be too much to justify the small gain that comes from it. But perhaps if it's the only thing left to try to gain an extra second or two, it will become necessary to learn to do this in order to be the best someday. I wish you luck in trying it.

 

[abunickabhi]

Practically, the cases where you can cancel a corresponding edge comm and corner comm is rare. It hinders your thinkahead and slows down your memo as you have to think a bit.

On the other hand, I have been trying to cancel two consecutive edge 3-style algs for the past 7 years and made a lot of progress. We save about 4 moves per commutator on average.

Average UF3 alg count - 8.5
Average UF5 alg count - 10.5

The only constraint is good recall and fingertrickability.

Good TPS and good thinkahead is a derivative of the factor I mentioned above.

I appreciate your idea and would like more such wacky ideas being discussed. But as Mike said, block commutators is nothing new and has been explored by the OGs, Beyer and Chris.

 

[asierrayk]

Do you have a list of these algs? I think it is very interesting technique. Using advanced weak swap should be possible to force some cases

 

[Jorian Meeuse]

Do you have a list of these algs? I think it is very interesting technique. Using advanced weak swap should be possible to force some cases

I started making a list but I kinda forgot about it. I think I'll continue soon.

 

[Jorian Meeuse]

Haha I just did a 5BLD solve and I got 5:21.48 while using this technique, not with edge-corner cancelling but midge-wing cancelling, which is a lot easier to notice but I still like it

 

[ZBRoux]

These are called block commutators, if I'm remembering/understanding correctly. I've only ever heard of this concept being utilised in FMC. 3BLD is now at speeds where everything should be as autonomic as possible, and (from my limited perspective) this feels as if it would intrude on that. Perhaps 4BLD+ could benefit? I can envison relatively regular instances where this idea could be extrapolated to centers in some manner, especially for cycle breaks. Are people already doing something like that? It's been a while since I practiced any sort of BLD.

 

[Tao Yu]

Tommy Cherry already uses this stuff sometimes. I watched a livestream where he got an ~18 (I think) with a block comm (not sure where to find it though). There's a few places it has been discussed. Andy Wong has this sheet of block comms for 3BLD and I think Elliott discusses them in this video: