ZZ-reduction
ZZ-reduction, also called ZZ-r, is a variant of the ZZ method for 3x3x3 proposed by Adrian Currier in 2014. It focuses on a reduction of PLL cases with the added benefit of faster recognition and more frequent PLL skips. It has the lowest algorithm count of any 2LLL method at 16 total.
You can use ZZ-r as a transition from beginner to full CFOP. Full CFOP might be faster than ZZ-r once you memorize all 78 algs.
The Steps
EOLine
See EOLine
Phasing
See External links
After EOLine is completed, Phasing is employed during the insertion of the final block pair in F2L, with LL edges resulting in opposite colours (eg Blue/Green or Orange/Red) being placed opposite each other.
However, you can also employ superphasing, whereby you always permute all edges of the last layer. One way of achieving this is by first phasing, then if you notice that you have parity employ this algorithm:
R' U' R U' R' U2 R2 then phase (U R' U R U2 R')
OLC
See OLC Algorithms
OLC (Orient Last Corners) is a subset of OLL that orients corners only and also preserves two opposite or all four edge permutations.
PLL
See PLL Algorithms
Since the phased edges were preserved in OLC, you should end up with only 9 possible PLL cases, down from 21 in full PLL. These are Aa/b, E, F, H, Na/b, T, Z.
Alternatively, you can limit PLL to a different set of 15 cases (Aa/b, E, Ga/b/c/d, H, Ja/b, Ra/b, U, V, Y) by antiphasing. That is, instead of placing LL opposite edge colors when completing F2L, placing adjacent edge colors.
But, if you intentionally phase all four edges (superphase) after F2L every time and then employ OLCs that preserve this edge permutation, you can further limit PLL cases to just A, E, and H.
PLL probabilities
The probabilities for the PLL subset in ZZ-r are different than for full PLL. The probability of skipping PLL is 1/24, while the probabilities of getting each case are as follows:
- A 1/3
- F 1/6
- T 1/6
- E 1/12
- N 1/12
- Z 1/12
- H 1/24
If superphasing and OLCs that preserve all edge permutations are employed, the probability of skipping PLL is 1/12, while the probabilities of getting each case are as follows:
- A 2/3
- E 1/6
- H 1/12
Pros
- Reduced algorithm count: Only 16 algs are needed for full ZZ-r (7 for orientation and 9 for permutation), lower than any other 2LLL method. If using superphasing, only 12 algs are needed (1 for superphasing, 7 for orientation, 4 for permutation). Technically, superphasing makes ZZ-r a 3LLL method.
- Faster recognition: Because there are so few last layer cases, recognition is very quick.
- Frequent skips: The low number of last layer cases make for more frequent skip cases. Skip probabilities are as follows: orientation 1/27; permutation 1/24; skip both (LL solved) 1/648. If superphasing is used, skip probability for permutation is twice as likely: permutation 1/12; skip both (LL solved) 1/324.
Cons
- Phasing - Although not a great hindrance to move count, the phasing step adds an average of 2 7/12 moves. This may be offset by the increase in PLL skip probability and faster recognition.
- Superphasing - If edge permutation is executed every time, this adds an average of 6.5 moves (13 moves divided by 2 cases - parity or solved). This may be offset by the even greater PLL skip probability and faster recognition.
