# 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.

## The Steps

See EOLine

### Phasing

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.

### 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.

## 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:

• H 1/24
• Z 1/12
• A 1/3
• E 1/12
• F 1/6
• N 1/12
• T 1/6

## 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.
• 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.

## 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.