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Not too long ago I bought a Mastermorphix and a Fisher Cube, and it didn't take long for me to realize I'm not very good at dealing with rotated centers. I figured out a few algorithms I can use, but they're not very efficient and I was wondering if anyone knows of any better ones

For rotating one center 180 degrees, I do R U R' U 5 times
For rotating two centers 90 degrees each, I do 3 U perms

Not too long ago I bought a Mastermorphix and a Fisher Cube, and it didn't take long for me to realize I'm not very good at dealing with rotated centers. I figured out a few algorithms I can use, but they're not very efficient and I was wondering if anyone knows of any better ones

For rotating one center 180 degrees, I do R U R' U 5 times
For rotating two centers 90 degrees each, I do 3 U perms

Move-optimal for rotating one centre 180 degrees is (R U2 R' L' U L)2 (and related versions like (L R U2 L' R' U)2), but (R U R' U)5 might be faster if you can fingertrick it.

For rotating two centres by 90 degrees, use a commutator: M' U M E/E2/E' M' U' M E'/E2/E.

For rotating two adjacent centres by 180 degrees, (M' U2 M U2)3. Or use a commutator like the above.

However, you should generally try solving the puzzle so that the centres that need orienting are handled first (and don't break them up later). For example, the Fisher Cube has two centres where the orientation doesn't matter; if you use one of those as your last layer, then you don't have to worry about centre orientation once you have F2L solved, provided that you don't use last layer algs that destroy F2L centre orientation (e.g. most U perm algs, the RUD G perms, most V perm algs).

Not too long ago I bought a Mastermorphix and a Fisher Cube, and it didn't take long for me to realize I'm not very good at dealing with rotated centers. I figured out a few algorithms I can use, but they're not very efficient and I was wondering if anyone knows of any better ones

For rotating one center 180 degrees, I do R U R' U 5 times
For rotating two centers 90 degrees each, I do 3 U perms

I want to find a short and good algorithm for the no-swap L COLL, but all the algs there are very long. Is there a BLD alg/thing that I can do to solve this case more efficient?

I want to find a short and good algorithm for the no-swap L COLL, but all the algs there are very long. Is there a BLD alg/thing that I can do to solve this case more efficient?

The shortest alg listed on algdb is HTM move optimal, and is also a BLD commutator:
[F' R D2 R' F, U2]
=
F' R D2 R' F U2 F' R D2 R' F (U2)

For the <RU> algs, does it help to know that they are triple Sune?
(R U R' U R U2 R') (R U R' U R U2 R') (R U R' U R U2 R')
=
R U R' U R U' R' U R U' R' U R U2 R'

The shortest alg listed on algdb is HTM move optimal, and is also a BLD commutator:
[F' R D2 R' F, U2]
=
F' R D2 R' F U2 F' R D2 R' F (U2)

For the <RU> algs, does it help to know that they are triple Sune?
(R U R' U R U2 R') (R U R' U R U2 R') (R U R' U R U2 R')
=
R U R' U R U' R' U R U' R' U R U2 R'

Fun pseudo-2-gen version of that alg: [r u' R2 u r' : U2]. (Not that it's really possible to execute this wide move version quickly because of the weird grip.)

Fun pseudo-2-gen version of that alg: [r u' R2 u r' : U2]. (Not that it's really possible to execute this wide move version quickly because of the weird grip.)

Weird grip, not regrip; I meant that you have to hold the 1×1×3 block on the bottom-left which makes it hard to execute it quickly. Maybe I'm just bad at executing it that way though!

The actual alg I use for this ZBLL/2GLL case is R U' R' L' U2 L U L' U L R U2 R'.