# 4x4 Edge Parity can be avoided

#### ravicvn

##### Member
I got into edge parity issue with 4x4 initially but I was able to avoid it totally by using a procedure and have been successful in avoiding edge parity.

Is it usual to not to get into 4x4 edge parity at all?

#### xyzzy

##### Member
I got into edge parity issue with 4x4 initially but I was able to avoid it totally by using a procedure and have been successful in avoiding edge parity.

Is it usual to not to get into 4x4 edge parity at all?
Depends on the method you're using, and also on what exactly you mean by "edge parity".

If you're using the cage method (solve all corners and edges first, then finish the centres), handling parity is often as simple as doing a single move, followed by a single commutator if necessary.

If you're using the reduction method, where you solve all the centres and pair up all the edges first, the probability of getting OLL parity (an odd number of bad/flipped edge pairs) is 50%, as is the probability of getting PLL parity (an odd number of swaps among the corners and edge pairs). If you're trying to do something fancy and you haven't seen OLL parity (or PLL parity) in a while, chances are that you just got lucky and you're not actually forcing OLL parity (or PLL parity) to not happen.

A 50% chance of getting OLL parity means that there's a 1/1024 chance of not getting OLL parity ten solves in a row. That's a low probability, but it's not negligible.

(Obviously, caveats apply; it is possible (albeit very difficult) to avoid OLL parity in speedsolves and a few people are good enough to do it consistently, but they also know exactly what they're doing and don't need to ask if what they're doing is sensible. My point is: if you have to ask, you're not doing it right.)

#### Duncan Bannon

##### Member
Can you supply a step by step method that does this? Or did you find an algorithm that will solve it?

#### Christopher Mowla

I made a list of several topics which discuss this in detail here on the 4x4x4 parity algorithms page in the Wiki.

But it's not worth avoiding it (it takes more time than executing a parity alg for sure) unless you are doing FMC. But even then, there might be a special circumstance in which a short odd parity fix may make the overall solve shorter.

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#### ravicvn

##### Member
Depends on the method you're using, and also on what exactly you mean by "edge parity".

If you're using the cage method (solve all corners and edges first, then finish the centres), handling parity is often as simple as doing a single move, followed by a single commutator if necessary.

If you're using the reduction method, where you solve all the centres and pair up all the edges first, the probability of getting OLL parity (an odd number of bad/flipped edge pairs) is 50%, as is the probability of getting PLL parity (an odd number of swaps among the corners and edge pairs). If you're trying to do something fancy and you haven't seen OLL parity (or PLL parity) in a while, chances are that you just got lucky and you're not actually forcing OLL parity (or PLL parity) to not happen.

A 50% chance of getting OLL parity means that there's a 1/1024 chance of not getting OLL parity ten solves in a row. That's a low probability, but it's not negligible.

(Obviously, caveats apply; it is possible (albeit very difficult) to avoid OLL parity in speedsolves and a few people are good enough to do it consistently, but they also know exactly what they're doing and don't need to ask if what they're doing is sensible. My point is: if you have to ask, you're not doing it right.)

I mean I never get OLL Parity. I just position the yellow pairs in certain position and it helps me in not getting any OLL Parity. I solved it almost 15 times and never got OLL Parity. As mentioned by you above I use the reduction method.
Yes I learnt to solve the 4x4 cube recently around 15 days ago and I had problem solving the OLL Parity using algorithm as I don't like to remember lengthy algorithms. So I studied the movement of the cubes and came up to this procedure.

I am able to solve 4x4 without getting OLL Parity in around 20 min. But I sometimes still get PLL Parity. Which I solve using the procedure i learnt in YouTube

Can you supply a step by step method that does this? Or did you find an algorithm that will solve it?
Sure, I am planning to put it up in YouTube. Hope it is useful to someone

I made a list of several topics which discuss this in detail here on the 4x4x4 parity algorithms page in the Wiki.

But it's not worth avoiding it (it takes more time than executing a parity alg for sure) unless you are doing FMC. But even then, there might be a special circumstance in which a short odd parity fix may make the overall solve shorter.

I never get OLL Parity. I just position the yellow pairs in certain position and it helps me in not getting any OLL Parity. I solved it almost 15 times and never got OLL Parity. I use the reduction method.
I learnt to solve the 4x4 cube recently around 15 days ago and I had problem solving the OLL Parity using algorithm as I don't like to remember lengthy algorithms. So I studied the movement of the cubes and came up to this procedure.

I am able to solve 4x4 without getting OLL Parity in around 20 min. But I sometimes still get PLL Parity. Which I solve using the procedure i learnt in YouTube

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#### Christopher Mowla

...as I don't like to remember lengthy algorithms. So I studied the movement of the cubes and came up to this procedure.
I found this OLL parity (specifically, a single edge flip + PLL parity) algorithm late last year which basically requires you to learn 6 moves. FYI.

Rw' (F U' Lw' U)5 Rw

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#### ravicvn

##### Member
T
I found this OLL parity (specifically, a single edge flip + PLL parity) algorithm late last year which basically requires you to learn 6 moves. FYI.

Rw' (F U' Lw' U)5 Rw
Thanks Christopher, I'll try and practice the above algorithm to use in case I get stuck

#### mark49152

##### Super Moderator
Staff member
OLL parity can be avoided by tracing wings 4BLD-style during inspection and solving centres using an odd or even number of quarter slices as appropriate. I've seen it done on video - I think it was Cale Schoon. Of course, tracing wings inside 15 seconds is not easy...

#### xyzzy

##### Member
I've seen it done on video - I think it was Cale Schoon.
Yup, it was Cale:

Oliver Frost also mentioned being able to do this a while back.

(Can mods merge the posts from the three threads OP has posted in regarding this topic into a single thread?)

#### pjk

Staff member
OLL parity can be avoided by tracing wings 4BLD-style during inspection and solving centres using an odd or even number of quarter slices as appropriate. I've seen it done on video - I think it was Cale Schoon. Of course, tracing wings inside 15 seconds is not easy...
Is there a topic on this or where can we find out more info on this?

Yup, it was Cale:

Oliver Frost also mentioned being able to do this a while back.

(Can mods merge the posts from the three threads OP has posted in regarding this topic into a single thread?)
Incredible, is there more details on how he does it exactly?

Also, moved his posts from the 4x4 Discussion thread into this thread now.

#### bcube

##### Member
Incredible, is there more details on how he does it exactly?

OLL parity can be avoided by tracing wings 4BLD-style during inspection and solving centres using an odd or even number of quarter slices as appropriate. I've seen it done on video - I think it was Cale Schoon
Back in 2012, Aron Puddy-Mathew made a video about solving a 4x4x4 cube while avoiding a so-called OLL parity in less than a minute.

pjk

#### Pyjam

I don't think the method exposed in this video actually works.

If – on a solved cube – I do:
1. slice - flip edge - slice; or:
2. OLL parity alg
...in both cases there are 2 edges with the wrong orientation.

So, I don't think the number of misoriented edges is a criterium.

I've tried to count the number of pairs with only 1 misoriented edge, and it doesn't seem to work either.

#### VDel_234_

##### Member
That's a really long alg, probably would take too long in a speedsolve. I might try it though

#### xyzzy

##### Member
I don't think the method exposed in this video actually works.

If – on a solved cube – I do:
1. slice - flip edge - slice; or:
2. OLL parity alg
...in both cases there are 2 edges with the wrong orientation.

So, I don't think the number of misoriented edges is a criterium.

I've tried to count the number of pairs with only 1 misoriented edge, and it doesn't seem to work either.
Yeah, that one is complete bollocks. He mentions having a >97% success rate with his method, which is extremely strong evidence that he's a liar.

I don't think there's an easy way of determining the parity of the wings, other than just tracing all the cycles. (Rather than actually memoing the cycles, keeping track of the number of cycles is enough, but I don't know whether this is easier or harder.) Square-1 CSP has a few non-tracing-based methods, but they all exploit the fact that there are only eight corners and eight edges, and eight is a small number. Directly adapting those methods to the 24 wings on a 4×4×4 just doesn't work.

#### Pyjam

Thanks.

Indeed. Just doing F R' F' R2 with 3 bad wings + 1 good in UF and UR gives 3 good + 1 bad, reducing the number of bad edges by 2 without any slice move.

#### cubework

##### Member
Maybe checking for parity before it gets to OLL/PLL stage
Tim Koop's website proposes counting dedges to see if even/odd in number to see if there will be a parity issue. This could open up solves at an earlier stage to not undo the work done if going by a reduction method. So maybe an algorithm that does not disturb the centres?

#### xyzzy

##### Member
Maybe checking for parity before it gets to OLL/PLL stage
Tim Koop's website proposes counting dedges to see if even/odd in number to see if there will be a parity issue. This could open up solves at an earlier stage to not undo the work done if going by a reduction method. So maybe an algorithm that does not disturb the centres?
You'll still need some kind of long-ish alg to fix parity at that stage. Tim Koop's approach is to do it in a way such that most of the parity alg is "intuitive", but it doesn't circumvent the fact that it still takes a lot of moves to fix OLL parity.

Solving OLL parity after reduction but before the last layer saves approximately one move, half of the time, and in exchange you need to count the number of good/bad edges after reduction with high accuracy. Can you do that in the time needed to make half a move? Can anyone?

(Don't get me wrong; I'm not saying Tim's approach is wrong or anything. His goal is to avoid memorising a long alg, and in that sense, doing Rw then resolving the centres and edges is a very easy way of accomplishing that. I just don't think it counts as "avoiding" parity in any meaningful sense.)

#### Pyjam

Leor method for 4x4:
1. 2 opposite centers (Right and Left)
2. Left block (with corners solved, à la Roux)
3. Last 4 centers
4. Edge pairing
5. Edge orientation + Middle layer (M-centers + DF and DB edges) + obvious OLL parity detection.
6. Right block + OLL parity fixing
7. COLL + EPLL, or ZBLL, + PLL parity

During 6, you may fix the parity at the right moment, even using it to swap 2 corners in order to form a pair for insertion.

This method has a low movecount.
That said, I'm no sub-30.