A collection of useful <Rw,R,U> parity algorithms for 4x4x4

[uberCuber]

So which 1 edge flip and 3 egde flip parity you guys use?

For 1-flip, I always solve OLL at the same time, which usually involves the use of the double parity alg (r2 B2 r' U2 r' etc.).

For 3-flip, I usually do B' R' setup to my regular OLL parity alg (r2 B2 U2 l U2 etc.)

 

[scottishcuber]

So which 1 edge flip and 3 egde flip parity you guys use?

I use Lucas parity (r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r') for both cases. Although, I used to use this: (Rw' U' Rw' U2') (Rw' U2 Rw' U' Rw U2) (r U2 Rw U' Rw' U2 Rw' U2') (Rw' U' Rw'). I have a vid of me executing this, which is the 5th reply to this thread.

 

[uberCuber]

Although, I used to use this: (Rw' U' Rw' U2') (Rw' U2 Rw' U' Rw U2) (r U2 Rw U' Rw' U2 Rw' U2') (Rw' U' Rw'). I have a vid of me executing this, which is the 5th reply to this thread.

Curious, why did you stop using this?

 

[scottishcuber]

I started to prefer using Lucas at one point and then I just forgot about it. I will switch back now though...I can execute it more consistently on my Aosu than when I used my SS.

 

[CriticalCubing]

For 1-flip, I always solve OLL at the same time, which usually involves the use of the double parity alg (r2 B2 r' U2 r' etc.).

For 3-flip, I usually do B' R' setup to my regular OLL parity alg (r2 B2 U2 l U2 etc.)

What is your regular Oll alg? You use only one oll alg for solving oll? I use 2LOLL to solve OLL. Am I doing something wrong?

I started to prefer using Lucas at one point and then I just forgot about it. I will switch back now though...I can execute it more consistently on my Aosu than when I used my SS.

So you are back to using this alg: (Rw' U' Rw' U2') (Rw' U2 Rw' U' Rw U2) (r U2 Rw U' Rw' U2 Rw' U2') (Rw' U' Rw') ?

And also should I learn normal alg or pure alg?

 

[Christopher Mowla]

I find this algorithm a few years back, but for some reason I forgot about it, and I didn't put it in the wiki because I thought it was too long (should I add it?).

Pure Form (1):
Rw U2 Rw2 U L U r U' L' U2 L U r' U' L' U Rw' U2 r U2 Rw' U2 Rw' = [Rw U2 Rw2: [U': [U2, L U r U' L']] [Rw' U2: r] ] (29,23)

Non-Pure Form (affects LL just as LucasParity does)
Rw U2 Rw2 U L U Rw U' L' U2 L U Rw' U' L' U Rw' U2 Rw U2 Rw' U2 Rw'

Pure Form (2)
The L turns can all be inverted to have another pure form (the algs "cousin")(but all single slice turns cannot be converted to wide):
Rw U2 Rw2 U L' U r U' L U2 L' U r' U' L U Rw' U2 r U2 Rw' U2 Rw'

What do you guys think?

 

[uberCuber]

What is your regular Oll alg? You use only one oll alg for solving oll? I use 2LOLL to solve OLL. Am I doing something wrong?

I think you are misinterpreting my post. If you have parity with 1 flipped edge, there are, I believe, 27 different OLL cases you can have. I can solve any of them in one look. The algs I use for those 27 different cases are generally of the form [a few outer-layer turns -> double parity alg -> a few more outer-layer turns], where double parity alg = r2 B2 r' U2 r' U2 B2 r' B2 r B2 r' B2 r2 B2. (note: lowercase letters = wide turns)

A couple examples are:
B2 R2 (double parity alg) U2 R2 B2
R' (double parity alg) R U R' U R

If instead of 1 flipped edge you have 3 flipped edges, there are, again, 27 different OLL cases you can have. However, unlike the 1-flip cases, I don't know separate setups/algs to solve all of the 3-flip cases in one look. So for these cases I have to do two steps.
1. AUF so that the one good edge is at UR, and then do B' R' (r2 B2 U2 l U2 r' U2 r U2 F2 r U2 l' B2 r2) R B to solve parity (orienting all the edges). The alg in parentheses is my normal OLL parity alg, and the setup makes it so that 3 edges get flipped instead of just one.
2. Solve the remaining OLL (often using COLL)

 

[CriticalCubing]

I find this algorithm a few years back, but for some reason I forgot about it, and I didn't put it in the wiki because I thought it was too long (should I add it?).

Pure Form (1):
Rw U2 Rw2 U L U r U' L' U2 L U r' U' L' U Rw' U2 r U2 Rw' U2 Rw' = [Rw U2 Rw2: [U': [U2, L U r U' L']] [Rw' U2: r] ] (29,23)

Non-Pure Form (affects LL just as LucasParity does)
Rw U2 Rw2 U L U Rw U' L' U2 L U Rw' U' L' U Rw' U2 Rw U2 Rw' U2 Rw'

Pure Form (2)
The L turns can all be inverted to have another pure form (the algs "cousin")(but all single slice turns cannot be converted to wide):
Rw U2 Rw2 U L' U r U' L U2 L' U r' U' L U Rw' U2 r U2 Rw' U2 Rw'

What do you guys think?

Adding them to the wiki should be helpful. I like the pure alg

I think you are misinterpreting my post. If you have parity with 1 flipped edge, there are, I believe, 27 different OLL cases you can have. I can solve any of them in one look. The algs I use for those 27 different cases are generally of the form [a few outer-layer turns -> double parity alg -> a few more outer-layer turns], where double parity alg = r2 B2 r' U2 r' U2 B2 r' B2 r B2 r' B2 r2 B2. (note: lowercase letters = wide turns)

A couple examples are:
B2 R2 (double parity alg) U2 R2 B2
R' (double parity alg) R U R' U R

If instead of 1 flipped edge you have 3 flipped edges, there are, again, 27 different OLL cases you can have. However, unlike the 1-flip cases, I don't know separate setups/algs to solve all of the 3-flip cases in one look. So for these cases I have to do two steps.
1. AUF so that the one good edge is at UR, and then do B' R' (r2 B2 U2 l U2 r' U2 r U2 F2 r U2 l' B2 r2) R B to solve parity (orienting all the edges). The alg in parentheses is my normal OLL parity alg, and the setup makes it so that 3 edges get flipped instead of just one.
2. Solve the remaining OLL (often using COLL)

Can you get me where to learn these 27+27 algs? and sorry I misinterpreted them

 

[uberCuber]

Can you get me where to learn these 27+27 algs? and sorry I misinterpreted them

Assuming this attachment thing works, here are the 1-flip cases: View attachment 4x4 parityOLL 1-flip.doc

The 3-flip cases I don't have anything for. (if I did, I'd probably know and use them by now )


Looking back at that file, apparently there is actually one case that I don't have anything for. I haven't seen it in any solves recently, so I guess I forgot about it. Anyone have anything interesting to do with that case?

 

[CriticalCubing]

Assuming this attachment thing works, here are the 1-flip cases: View attachment 3946

The 3-flip cases I don't have anything for. (if I did, I'd probably know and use them by now )


Looking back at that file, apparently there is actually one case that I don't have anything for. I haven't seen it in any solves recently, so I guess I forgot about it. Anyone have anything interesting to do with that case?

Thanks You for that uber! It was silly of me to ask that in first place .Just a quick question. The DP in the alg is pure alg or normal alg? (I am guessing pure alg)

 

[uberCuber]

Thanks You for that uber! It was silly of me to ask that in first place .Just a quick question. The DP in the alg is pure alg or normal alg? (I am guessing pure alg)

DP is r2 B2 r' U2 r' U2 B2 r' B2 r B2 r' B2 r2 B2, with lowercase letters = wide turns (not slice turns). In other words, not pure.

 

[scottishcuber]

DP is r2 B2 r' U2 r' U2 B2 r' B2 r B2 r' B2 r2 B2, with lowercase letters = wide turns (not slice turns). In other words, not pure.

Side note: Have you tried the mirror (with a y2)?

[r2 F2 r U2 r U2 x U2 r U2 r' U2 r U2 r2 U2 x']

It's much nicer doing R' F' R [DP]* U2 R' F R than L' B' L [DP] U2 L' B L

Edited.

 

[Mollerz]

I started to prefer using Lucas at one point and then I just forgot about it. I will switch back now though...I can execute it more consistently on my Aosu than when I used my SS.

I use both, obviously 3flip when I have to flip 3 edges and lucas when flipping just a single edge.

 

[TDM]

r2 F2 r U2 r U2 x U2 r U2 r' U2 r U2 r2 U2 x'

This alg is awesome. I still can't see permutation parity before OLL, so I won't use it as a double parity alg, but I'll definitely change to this for OLL parity. Thanks!

 

[uberCuber]

Side note: Have you tried the mirror (with a y2)?

[r2 F2 r U2 r U2 x U2 r U2 r' U2 r U2 r2 x']

It's much nicer doing R' F' R [DP]* U2 R' F R than L' B' L [DP] U2 L' B L

Hmm. In the future it would be nice to use this for the cases that currently have uncomfortable setups. There are some cases where I specifically like using the B2 alg over this one. But I probably won't switch anytime soon because I don't feel like relearning recognition/setups for a bunch of cases. In particular I don't want to have it right now so that some cases require putting the bad edge in back and others require putting the bad edge on front.

 

[CHJ]

I use qtparity as my main as it's pure and completely 2-gen and 3-flip (same as sameers) i started to use once rob posted it a while back

qtparity: Rw' U2 Rw U' Rw' U Rw U' Rw U2 Rw U2 Rw' U2 Rw U2 Rw2 U' Rw2' U Rw U' Rw U' Rw' U2

 

[scottishcuber]

Oh yh and I always use qtparity for a pure flip. I suppose for you Callum you can always have a one-look OLL.

@TDM I can't see any pll parity either at the OLL stage, but I called it double parity because uber did. Also I think that it is usually referred to as the double parity alg anyway

 

[CHJ]

Oh yh and I always use qtparity for a pure flip. I suppose for you Callum you can always have a one-look OLL.

@TDM I can't see any pll parity either at the OLL stage, but I called it double parity because uber did. Also I think that it is usually referred to as the double parity alg anyway

likewise, if i can force an OLL skip after parity of which i know of ways how then i will use lucas (only recent, i used beginner parity for a long time)

 

[scottishcuber]

(Rw' R2 U' R' U R' Rw U' R U2' R' U' R' Rw U R Rw' U' Rw' F Rw2 U' Rw' U') (Rw U Rw' F')

Breakdown:
3 wing cycle: (Rw' R2 U' R' U R' Rw U' R U R')
Another 3 wing cycle: (R U R' U' R' Rw U R U' Rw')
Wide T perm: (Rw U Rw' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F')
6 moves cancelled.

I know it's not <Rw,R,U>, but I thought it was worth sharing anyway

 

[DavidCip86]

How fast can you do T perm + parity? and would you use this in a solve? I'm thinking about learning some of these but they look kinda long