# Difference between revisions of "ZZ-reduction"

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− | 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. | + | 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 == | == The Steps == | ||

+ | |||

+ | === EOLine === | ||

+ | |||

+ | ''See [[EOLine|EOLine]] | ||

=== Phasing === | === 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. | + | ''See [[ZZ-r#External_links|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. | ||

=== OLC === | === OLC === | ||

− | See [[OL4C|OLC]] | + | ''See [[OL4C#OLC_Algorithms|OLC Algorithms]]'' |

− | OLC (Orient Last Corners) is a | + | 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|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. | 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. | 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 == | == Pros == | ||

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==Cons== | ==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 | + | * '''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. |

== External links == | == External links == | ||

* [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained] | * [http://www.speedsolving.com/forum/showthread.php?t=14501 speedsolving.com: Phasing Explained] | ||

+ | * [https://www.youtube.com/watch?v=QpSw6bMBu6s Example solve] |

## Latest revision as of 21:57, 5 December 2014

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.

## Contents

## 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.

### 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.