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Phasing Explained (ZZ-b)

Cride5

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A description of Phasing already exists here, but I thought I'd add some extra explanation to clarify it...


Phasing is a technique for reducing the number of ZBLL cases, thus enabling completion of the LL with 'one look' and significantly less algorithms (ZZLL). However, remember that the extra inspection required to do phasing still requires a 'look' during insertion of the final F2L block, but because phasing is very lightweight it should be possible to recognise and execute it relatively quickly.

Once Phasing is complete the LL edges will be permuted so that opposite colours (eg Blue/Green or Orange/Red) are opposite each other. If two opposite coloured LL edges are phased, then the remaining two will also be opposite each other. Looking at the LL after phasing the edges will be in one of two states. Either they are SOLVED or there is PARITY, which means that adjacent edges are not correct with respect to each other. An easy way to distinguish between SOLVED and PARITY is to attempt aligning the edges by rotating the U-layer. If its only possible to align two then it is the PARITY case.


Phasing Strategy

The strategy outlined here assumes the completed front-right block is positioned in the U-Layer (in a similar manner to Winter Variation).

With this setup there are three LL edges in the U-Layer and one is in the slot. Of the three LL edges in the U-layer, only two can easily be manipulated without breaking up the block. The third edge will be 'stuck' beside the block until the block is inserted. The stuck edge is the unlabelled LL edge in the diagram below.

The idea behind this strategy is to manipulate the remaining three free edges (labelled 1 2 and 3 in the diagram) so that they are phased after block insertion. Of the three remaining edges, find the one which needs to be placed opposite the 'stuck' edge. For example, if the stuck edge is blue, you're looking for the green edge.



If this edge is in positions 1 or 2 then the solution is fairly straightforward.

With the edge in position 1, the first R turn will place it into the correct position (replacing position 2). So the solution would simply be:
R U' R'

In position 2, it is already opposite the stuck edge, so all that's required is to ensure this state is preserved during insertion. Insertion in this case would be:
U R U2 R'

If the edge to place is adjacent to the stuck edge in the U-layer (position 3), it will initially need to be taken out of the U-layer so that it can be repositioned opposite the stuck edge. It can be done in one of two ways:
(R U R' U') R U' R'
or
(U R U' R') U R U2 R'
The part in brackets really just sets up case 1 or 2, respectively. Either of these options could be chosen depending on the position of the block in the U-layer.


Move Count

For this explanation, it is assumed that the starting point is with the block to be inserted in the U-layer (similarly to WV). Assuming a particular edge is in the 'stuck' position, there is an equal probability of its opposite edge occurring in positions 1, 2 or 3. Thus the probability of each of these cases occurring is 1/3 (~33%).

In order to find the move count, the number of moves it takes for a normal insertion (without phasing) needs to be subtracted since these moves will be required in a normal solve anyway. Here we're interested the number of 'additional' moves phasing takes.

Intuition says that the insertion in the diagram takes exactly 3 moves, but this isn't necessarily the case. If the U-face is rotated by U2 or U' then an initial AUF will be required before the 3-move insertion. Thus 2/4 cases take 4 moves and the rest take 3 moves, so normal insertion takes: (3+3+4+4)/4 = 3.5 moves


Now insertion with Phasing:

With cases 1 and 2, only one U-layer position requires no initial AUF, so the move count is: (3+4+4+4)/4 = 3.75

With case 3, because we have the flexibility in having two options, two of the U-Layer positions take 7 moves and the other two take 8. Thus the move count is: (7+7+8+8)/4 = 7.5

Because all three cases happen with equal probability the average number of moves is: (3.75 + 3.75 + 7.5)/3 = 5

So the number of additional moves that phasing (from a block in the U-layer) takes on average is:
5 - 3.5 = 1.5 moves


NOTE: This is based on the assumption that the completed block is in the U-layer. If using an insertion like R U R' or some other optimised alg which doesn't result a block in the U-layer, then an alternative phasing strategy will be required. The naive approach would be to take the completed block out and use the strategy outlined above, but much better options are available: @see Michal Hordecki's phasing algs
 
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#2
Good explanation.
Are you planning on using phasing+zzll? I learned T and U cases a while back, but I've since stopped due to time constraints/other hobbies. Learning them isn't that hard, but taking the time to find decent algs and get them to speed is a lot more time consuming than I had estimated.

Some things I don't like:
-You have to slow down on the last pair for lookahead; even if you make 0 extra moves you've lost time.
-Half of the corner cases (by rate of occurrence) are sune/antisune. I can't imagine phasing+recognition+zzllsune to be faster than sune+pll, though maybe it will be in the long run.

I do like the 'thrill' of finishing off with a T or a U case, even though my recognition+execution time is quite bad.
If I get more time maybe I'll start looking into it again, for now I'll just be working on EOL and ZZF2L.

Here's my T and U cases if anyone's interested, just don't expect me to put up any other cases in the near future: http://stubers.org/jamesstuff/cube/zzll.php
 

Cride5

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Cheers :)

Because of the stage I'm at (~30 sec) I think it deffo makes sense to be concentrating on my EOLine and F2L at the moment. For my LL I'm just on the bog standard OCLL/PLL, which I'm probably going to stay with until I reach sub-20 territory. The good thing about it is that the small number of algs make it really easy to get fast at (especially OCLL!) If I get good enough to start moving in the ZZLL direction it would start by gradually adding COLL algs (probably starting with the pi case), then after COLL i'd learn to do Phasing quickly, gradually adding ZZLL algs. The good thing about it is that you can always fall back onto the more basic system if you need to.

I think ZZLL probably has potential to be faster than the basic 2LLL, but only with a lot of practice. I see what you mean about the recognition for Phasing. I'd imagine recognition for OCLL is probably faster (plus both can be 2-gen). The main advantages are the move-count, and possibly that phasing flows better because it's part of the last block insertion. If you had the memory and dedication for it, eliminating Phasing all together and going for ZBLL would probably be better.

This is extremely hypothetical, but here's a time breakdown you might expect from a sub-20 cuber well practised in their LL method:

  • OCLL/PLL = (0.25 + 1.25) + (1 + 3) = 5.5
  • COLL/EPLL = (0.75 + 3) + (0.25 + 1.25) = 5.25
  • PHASING/ZZLL = (0.5 + 0.25) + (1 + 3.25) = 5
  • ZBLL = (1.25 + 3.5) = 4.75

Its based on these assumptions:
  1. Recognition/Exection for OCLL and EPLL are the same
  2. Execution for PLL and COLL are the same, but recognition for COLL is slightly faster
  3. Recognition for Phasing is slightly slower then OCLL, but execution is negligable
  4. Recognition and Execution for ZZLL is slightly slower than COLL
  5. Recognition and Execution for ZBLL is slightly slower than ZZLL

What do you think?

I hope you don't mind, I've linked to your ZZLL algs from my ZZ page :)
 
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#5
great explanation, I have learnt ZZ method, but for the LL I still use OLL/PLL
sometimes I also use COLL and ELL
maybe I would switch to ZZ for my OH
 
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#9
Can this always be done with the front-right block or is it better to learn to do it for all blocks?
 

TDM

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#10
Can this always be done with the front-right block or is it better to learn to do it for all blocks?
It's best to learn it for all last slots. It's very easy to reflect, unlike other LS techniques e.g. WV, CPLS. You'll also not have it in FR most of the time, so you do need to know it for FL/BR/BL too if you want to use ZZLL.
 
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#13
I thought the idea of phasing was to permute the edge pieces so that they are completely solved for the rest of the solving. Certain of the algorithms to deal with the corners will swap the edge pieces around so that only two opposite are solved and the other two sets are swapped around.
 
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I thought the idea of phasing was to permute the edge pieces so that they are completely solved for the rest of the solving. Certain of the algorithms to deal with the corners will swap the edge pieces around so that only two opposite are solved and the other two sets are swapped around.
No, I'm pretty sure that you just make sure opposite edges are opposite each other so blue and green are opposite and red and orange are opposite each other
 
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#15
Hey guys, I had an Idea for a lower algorithm count last layer(as opposed to OCLL+PLL), which could possibly be an easier 2look last layer for beginners. it goes like this:
-OCLL+ phasing(14 algorithms)
-PLL with edges phased(9 algorithms)
so 9+14 = 23 algorithms. a few less, and also the algorithm cound os distrubuted equally so learning the first look doesnt take a tenth of the time as learning the second look.
 
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