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I developed an algorithm to discover if your 4x4x4 is in parity long before it is almost solved. You might find it interesting.
Oh yeah, I remember your thread. But isn't your idea and his have conflicting objectives for a beginner's guide? He's not against using move sequences, for example.

But it's ironic, because if one aims to do something similar to resolve PLL parity (which this thread is about) as you advertise to do to resolve OLL parity (after they see that they have it by counting the number of good dedges as you explain how to do), something cool happens!
  1. Do a half turn to induce/fix PLL parity (move sequences like this and this (that I found) prove that PLL parity is technically resolved with two slice quarter turns):
    2R2

  2. Correct the top and bottom centers like you would when doing reduction.
    U2 2R2 U2 2R2

  3. From this point, they can either learn the very useful 4 move commutator to exchange center pieces:
    2R2 2U2 2R2 2U2

    Which gives:
    2R2 U2 2R2 U2 2R2 2R2 2U2 2R2 2U2 = 2R2 U2 2R2 Uw2 2R2 2U2 (a familiar sight)

    Or, since he is in favor of conjugation, he can tell them to just do the setup move 2U2 before and undo it after so that they don't have to learn that 4 move sequence:
    2U2 2R2 U2 2R2 U2 2R2 2U2

    If we make those setup moves wide turns, it becomes the very algorithm that he thinks is good for beginners:
    (So this can be an explanation of how the algorithm works, which in of itself can help to memorize it to long-term memory much easier.)
    Uw2 2R2 U2 2R2 U2 2R2 Uw2

Also, based off of the guide he has written so far, I don't think he would recommend them to do a quarter turn and then have to redo a portion of the reduction phase and start completely over with solving the pseudo 3x3x3 as a 3x3x3, because that requires much more than one extra algorithm (which seemed to be what he was trying to avoid when handling the adjacent PLL parity case . . . I suspect that he wanted to avoid having them do a U-Perm and then opposite PLL parity to resolve the adjacent PLL parity case).

Instead, since (2R U2)4 2R is the simplest of odd parity algorithms, and he's comfortable with the idea of conjugation, then maybe he would be in favor of: (2R2 F Rw' F' Rw') (2R' U2)4 2R' (Rw F Rw F' 2R2) to resolve adjacent double parity (for any big cube size).

Or maybe he would like Floyd Newberry's (Rw B' z')(r' F U2 F')4 r' (z B Rw') for the single dedge flip (which also works on any big cube size).
 
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I felt like making this thread because I haven’t found any yet so I thought this would be a good idea to post some interesting/new algorithms

New algorithm for Aa perm:
Basically Tperm just with wide R’ moves
r U r’ U’ r’ F r2 U’ r’ U’ r U r’ F’
(Orientation)
1645108029937.png
from JPerm’s PLL trainer
 
I felt like making this thread because I haven’t found any yet so I thought this would be a good idea to post some interesting/new algorithms

New algorithm for Aa perm:
Basically Tperm just with wide R’ moves
r U r’ U’ r’ F r2 U’ r’ U’ r U r’ F’
(Orientation)
View attachment 18679
from JPerm’s PLL trainer
Thanks for the idea, but this isn't really a new algorithm. Most everybody knows it. I would suggest looking at Speedcubedb if you want to find abnormal, more interesting algs.
 
eazy ZBLL

regular OLL alg is R2 D R' U2 R D' R' U2 R'

this easy ZBLL you only need to do do this alg = R2 D Rw' U2 Rw D' R' U2 R'

you can use one of edge parity alg for 5x5 to ZBLL alg.
the parity alg for 5x5 is Lw' U2 Lw' U2 F2 Lw' F2 Rw U2 Rw' U2 Lw2

can be used for zbll alg . just ommit the wide moves
L' U2 L' U2 F2 L' F2 R U2 R' U2 L2

usually this ZBLL U case will be solved with regular oll alg + T perm with cancelled moves.
but i prefer to use oll parity alg from 4x4 which is Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'
on 3x3 it will be R U2 x R U2 R U2 R' U2 L U2 Rw' U2 R U2 R' U2 R'
 
you can use one of edge parity alg for 5x5 to ZBLL alg.
the parity alg for 5x5 is Lw' U2 Lw' U2 F2 Lw' F2 Rw U2 Rw' U2 Lw2

can be used for zbll alg . just ommit the wide moves
L' U2 L' U2 F2 L' F2 R U2 R' U2 L2
r U' r U2 R' F R U2 r2 F

One of the 10-move 1LLL cases, very occasionally useful in FMC.

usually this ZBLL U case will be solved with regular oll alg + T perm with cancelled moves.
but i prefer to use oll parity alg from 4x4 which is Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'
on 3x3 it will be R U2 x R U2 R U2 R' U2 L U2 Rw' U2 R U2 R' U2 R'
Is OLL cancel into T perm really a common solution? I know Feliks did it in one of his world record averages or something, but I haven't seen that recommended as an alg on its own.

I've been using R' U R U' R' U L' U' r B' U2 R' U2 R2 (x'), and I think Jabari's sheet had the front-back mirror of that? In any case, it's hard to get a 25q alg faster than a 17q alg with similar regrips.
 
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