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If you solve the OLL-Parity on a 4x4 (or 6x6,...) and only use wide turns (Rw and Lw), then you also swap two corners. You could use this in some cases two skip OLL:
I've made some thoughts about this:
The OLL-Parity I use is: Rw2 B2 Rw' U2 Rw' U2 B2 Rw' B2 Rw B2 Rw' B2 Rw2 B2 (U2).
(It does not swap two edges, so it also does PLL-Parity. If you use an only-OLL-parity, you have to be careful, because it switches two edges (top-right and top-left), too.)
Because of only two included corners, you can only skip OLL on all cases where at least two corners are solved already (Bowtie, Headlights, Chameleon and solved).
I made up a few setup moves to skip OLL on all 13 possible cases, the only misoriented edge is in front:
Solved:
setup: L or R'
Headlights:
solved corners in front: R' L
solved corners on the left: B L
solved corners on the right: B' R'
solved corners on the back: no setup
Chameleon:
solved corners in front: L B' R2 or R' B L2
solved corners on the left: B2 L2
solved corners on the right: B2 R2
solved corners on the back: R2 B R' or L2 B' L
Bowtie (the color stickers that have to go on the top are on the following sides):
back and right: B L2
back and left: B' R2
front and right: R B R'
front and left: L' B' L
If you have one of the cases above, instead of doing [OLL-Parity], I now do [setup] [OLL-Parity] [setup]' to get an OLL-Skip, e.g.:
For the 2. chameleon case, I do B2 L2 [OLL-Parity] L2 B2.
It does only work on paritys like the above, that only swap two corners and no edges.
If you use another one you have two change the setups (e.g. do R2 B2 R2 instead of B2 R2) to save the edges. Or you can use it to orient the edges during Parity (e.g. if the one oriented edge is on the left and you do B L [OLL-Parity that also changes the Up-Left and the Up-Right edge] L' B').
Does this 'algset' (better setupset) already have a name? If not, I'd suggest 'CKCO(LL)' (Christian König Corner Orientation (of the Last Layer)).
I've made some thoughts about this:
The OLL-Parity I use is: Rw2 B2 Rw' U2 Rw' U2 B2 Rw' B2 Rw B2 Rw' B2 Rw2 B2 (U2).
(It does not swap two edges, so it also does PLL-Parity. If you use an only-OLL-parity, you have to be careful, because it switches two edges (top-right and top-left), too.)
Because of only two included corners, you can only skip OLL on all cases where at least two corners are solved already (Bowtie, Headlights, Chameleon and solved).
I made up a few setup moves to skip OLL on all 13 possible cases, the only misoriented edge is in front:
Solved:
setup: L or R'
Headlights:
solved corners in front: R' L
solved corners on the left: B L
solved corners on the right: B' R'
solved corners on the back: no setup
Chameleon:
solved corners in front: L B' R2 or R' B L2
solved corners on the left: B2 L2
solved corners on the right: B2 R2
solved corners on the back: R2 B R' or L2 B' L
Bowtie (the color stickers that have to go on the top are on the following sides):
back and right: B L2
back and left: B' R2
front and right: R B R'
front and left: L' B' L
If you have one of the cases above, instead of doing [OLL-Parity], I now do [setup] [OLL-Parity] [setup]' to get an OLL-Skip, e.g.:
For the 2. chameleon case, I do B2 L2 [OLL-Parity] L2 B2.
It does only work on paritys like the above, that only swap two corners and no edges.
If you use another one you have two change the setups (e.g. do R2 B2 R2 instead of B2 R2) to save the edges. Or you can use it to orient the edges during Parity (e.g. if the one oriented edge is on the left and you do B L [OLL-Parity that also changes the Up-Left and the Up-Right edge] L' B').
Does this 'algset' (better setupset) already have a name? If not, I'd suggest 'CKCO(LL)' (Christian König Corner Orientation (of the Last Layer)).
