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So I want to learn COLL. When I am about to learn a new algorithm set, I just have to find the best algorithms, so I spent some time researching COLL algorithms. The most useful resources for finding LL algorithms I found are:

10 of the COLL algorithms that I chose had 0-2 users on algdb.net or weren't even listed there.

R U' R' U F' r U' L' U2 R' U R U' x' (first alg is always the underrated alg that deserves some spotlight)
R' F R U' R' U' R U R' F' R U R' U' R' F R F' R (second alg is always the most popular alg on algdb.net, for comparison

U R U2 r' F R' F' r U' R U' R'
U' R U' R' U2 R U' R' U2 R' D' R U R' D R

F U R' U' R2 U' R2 U2 R F' L' U L
R U D' R U R' D R2 U' R' U' R2' U2' R

U2 r' F R F' r U' R' U' R U' R'
R U' L' U R' U L U L' U L

r' F2 r F' r U' R' U' R U2 r' F
R' F2 R U2 R U2 R' F2 U' R U' R'

F U R' U' R F' U' R' U2 R
U L R' U' R U L' U2 R' U2 R

U' R' F U2 F' R F R' U2 R F'
U2 R' U' R U' R' U R' D' R U R' D R2

and the last three algorithms would be the inverses of the three Antisune cases above.

Let me know if you like one of the algorithms, or if you think they are horrible.

Using conjugated PLLs(like you do in the first case) is really helpful and fast when you go for full ZBLL as there are nice cases in which moves cancel out, but if you don't, consider the following
You do a PLL you want to avoid plus two more moves as your OLL in order to get another PLL = 2-Look PLL all over again.

I actually want to use the shorter alg R U' R' U F' r U' L' U2 R' U R U' and not the conjugated PLL, which I just listed for comparison. And I forgot to consider that you have to do a x' rotation at the end of the shorter alg, but the rotation won't matter much.

Edit: That absurdly long algorithm has more than 10 times more users than any other alg for that case (54 users vs 5 users). Maybe because it's easy to learn and the flow feels good, but I can't do it nearly as fast as the short alg.

R U R’ F’ R U2’ R’ U’ R U’ R’ F R U’ R’
y R U2 R’ U’ F’ R U2 R’ U’ R U’ R’ F R U’ R’
y F U R U’ R’ U R U’ R2’ F’ R U R U’ R’
y’ R2 D R’ U2 R D’ R2’ U’ R U’ R’
R U’ R2’ U’ R2 U R’ F’ R U R2’ U’ R’ F R2
Those algs are good. I like these also.

So I was messing around with my OLL algs and I figured out you can do a Z perm if you do it enough. You 2 of the egdes you need to swap on the left hand side. The alg is f (RUR'U') f' F (RUR'U') F' f (RUR'U') f' F (RUR'U') F' f (RUR'U') f' F (RUR'U') F'
Just wanted to share this completely random useless alg.

Messing around with trying to optimise 4×4×4 parity; found a bunch of 23-move U perm + flip algs. (These aren't on the parity wiki page and haven't been generated by anyone else, afaict. SiGN notation is used, so "r" means "Rw", not the inner slice.)

R2 r U2 R' r2 U' r' U2 r U2 r' U R' r2 U2 R' r2 U R' U R U2 r'
r U2 R2 r U R U R2 r2 U2 R2 r2 U R' U' r U2 r U2 R r' U2 r2
r U2 r U R2 U R2 r2 U2 R2 r2 U R2 U' R2 r U2 r U2 R r' U2 r2
r U2 r U R' U R2 r2 U2 R2 r2 U R U' R2 r U2 r U2 R r' U2 r2
r2 U2 R2 r2 U R2 U R' r U2 R' r U R2 U r2 U2 r' U2 R' r U2 r
r U2 R' U' R U' R r2 U2 R r2 U' r U2 r' U2 r U R r2 U2 R2 r'
r U2 R' r U2 r' U2 r2 U R2 U R' r U2 R' r U R2 U R2 r2 U2 r2 < This one is almost actually usable for speedsolving, methinks.
r2 U2 R r' U2 r U2 R2 r U' R U R2 r2 U2 R2 r2 U R' U r U2 r
r2 U2 R r' U2 r U2 r U' R' U R2 r2 U2 R2 r2 U R U R2 r U2 r
r2 U2 R' r U2 r' U2 R2 r' U R' U' R2 r2 U2 R2 r2 U' R U' r' U2 r'
r2 U2 R' r U2 r' U2 r' U R U' R2 r2 U2 R2 r2 U' R' U' R2 r' U2 r'
r' U2 R U R' U R' r2 U2 R' r2 U r' U2 r U2 r' U' R' r2 U2 R2 r
r' U2 R r' U2 r U2 r2 U' R2 U' R r' U2 R r' U' R2 U' R2 r2 U2 r2
R2 r' U2 R r2 U r U2 r' U2 r U' R r2 U2 R r2 U' R U' R' U2 r
r2 U2 R2 r2 U' R2 U' R r' U2 R r' U' R2 U' r2 U2 r U2 R r' U2 r'
r' U2 R2 r' U' R' U' R2 r2 U2 R2 r2 U' R U r' U2 r' U2 R' r U2 r2
r' U2 r' U' R U' R2 r2 U2 R2 r2 U' R' U R2 r' U2 r' U2 R' r U2 r2
r' U2 r' U' R2 U' R2 r2 U2 R2 r2 U' R2 U R2 r' U2 r' U2 R' r U2 r2
r2 U2 R r' U2 r U2 R2 r U' R2 U R2 r2 U2 R2 r2 U R2 U r U2 r
r2 U2 R' r U2 r' U2 R2 r' U R2 U' R2 r2 U2 R2 r2 U' R2 U' r' U2 r'

(more to come?? The U perm + flip case is actually not that useful since you can just do pure OLL parity then a U perm, which is almost as fast and easier to recognise, but for other OLL parity cases, it might be possible to avoid bad COLLs.)

Edit: Regripless flip + pi, starting with thumb on bottom:
r U2 r U R' U r2 U2' r2' U R U' R2' r U2 r U2' r' U2 r2 U2' R' U2' R2
All the "U2" moves can be done either lefty or righty, but for the "U2'" moves, the right hand won't be in an appropriate position to double-flick. Not sure if this is faster than the other flip+pi alg I posted a couple of pages back, which is a few moves shorter and has a regrip near the end.

Edit: 4-flip O perm in 21 moves: r U' r2 U' R2 r2 U' r' U R' U2 R' U r' U' R2 r2 U' r2 U' r. No other 4-flip + PLL parity case can be done in 22 or fewer RrU moves.

Also, completely unrelatedly, here's a C/D perm (whatever you call it, it's that parity PLL case with no bars and edges not phased):
u' R U R' u' r2 U' R' D' R U' R' D R' r2 U2 r2 u R U' R' u
Possibly tied for the shortest known alg for this case in OBQTM (26q), but way more fingertrickable than the 26q alg on the wiki. R perm cancelling into parity might be faster depending on how bad you are at D/D' moves relative to F/F' moves and how willing you are to learn weird algs for PLL parity.

@xyzzy, as you probably know, I still have been browsing the forums from time to time, as I have added some of the other 4x4x4 parity algorithms that you have posted in this thread of late.

I was indeed thinking about making a new Section/Chapter to hold the above algorithms as well as conjugation of the "4x4x4" part of the "5 dedge flips", "7 dedge flips", etc. (as they are also 6-cycles).

But before I do, I just want to let you know that I do intend to add them, and thus if you would like to find more algorithms like this, please sort them by exact case for me. (If they all solve different cases, I apologize.)

Also, here's some more adjacent PLL parity algs (originally posted a few pages back, but I think you might've missed it):
[Uw' R U' R' Uw' Rw2 U2 : 2R2]
y [Uw' R U R' Uw' Rw2 U2 : 2R2]
y2 [Uw R U' R' Uw Rw2 U2 : 2R2]
y' [Uw R U R' Uw Rw2 U2 : 2R2]

@Aerma I just want to correct some execute tips with this alg (not trying to be picky!) because I use it. However, I execute it: R U2' R2' U' R2 U' R2 U2' R. Nothing to spectacular, but executing it like that helps it flow faster

@Aerma I just want to correct some execute tips with this alg (not trying to be picky!) because I use it. However, I execute it: R U2' R2' U' R2 U' R2 U2' R. Nothing to spectacular, but executing it like that helps it flow faster

I execute the first U2 with my right hand but the other with my left, it requires a slight regrip of my right hand after the first U2 but I can still do the alg pretty fast