ZBLL

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ZBLL
Information
Proposer(s): Lars Petrus, Bernard Helmstetter
Proposed: 2002
Alt Names: ZZ-a, Steps 5+6+7 (Petrus method)
Variants: 1LLL
Subgroup: 1LLL
No. Algs: 493
Avg Moves: 12.08 (Optimal HTM)
Purpose(s):


ZBLL is a step in many methods which involves solving the entire last layer in one step, assuming that the edges are already oriented. This is part of the ZB method, but it can be useful for any other method which leaves the edges of the last layer oriented after F2L is solved (such as the Petrus method, or ZZ Method). According to Zborowski's webpage, Bernard Helmstetter created the original algorithms for Lars Petrus, who proposed solving the last layer in one step. For this reason, some in the community prefer calling this subset PHLL or HPLL and believe that the acronym ZBLL (short for Zborowski-Bruchem Last Layer) does not give proper credit to the original proposers.

ZBLL indeed sounds like a very useful step to learn, but the main reason that it is not in wide use is that it involves a massive total of 493 cases (including PLL). Only a handful of people have ever learned this step in its entirety. If you wish to learn it, it is useful to start by learning either OCLL/PLL or COLL/EPLL before you learn ZBLL, so that you will always be able to finish the cube relatively quickly even if you do not yet know the ZBLL case. Past that, the learning process is done however you'd like to do it. Many choose to skip learning the S and AS subsets due to their already very easy OLL cases. However, you will benefit if you also learn S and AS.

Learning Approach

The ZBLL cases are divided into 8 sets: T, U, L, Pi, Sune, Anti-sune, H, and the PLL (or O) cases, in which all pieces are oriented. The sets are then divided further into 6 subsets. They are recognized by their COLL case as well as a corresponding edge cycle. Every subset contains 12 cases, which are all different edge cycles possible with the COLL case of that set. Many people recognize ZBLL by looking at the UFR corner and its neighboring stickers. Whether the stickers are adjacent, or opposite allows for a quick recognition. Another way to recognize is through blocks of colour or simply the edge cycle.

Edge recognition

For the T, U and L cases (there are 3*6*12=216 algorithms in this set) recognition goes as follows:

1. Recognize the orientation case.

2. Recognize the COLL case.

3. Recognize the edge cycle by looking at the UFR corner and the edge stickers around it.

4. Apply the corresponding algorithm.

Step 3 may look a little complicated, but it's actually not too bad. In total there are 12 cases, but those are recognized by 2 minor sub-cases, of which there are 3:

C: If the FU sticker is the same as the FRU sticker, and if the RU sticker is the same as the RUF sticker.

A: If the FU sticker is an adjacent color to the FRU sticker, and if the RU sticker is an adjacent color to the RUF sticker.

O: If FU and FRU are opposite, and if RU and RUF are opposite.

A case is recognized by the combination of those. First comes the FU/FRU relation, then the RU/RUF relation, divided by a slash. That means there are 9 possibilities with these cases: C/C, C/A, C/O, A/C, A/A, A/O, O/C, O/A, O/O. However, there are 12 cases. That's because the A case can mean 2 stickers. That's why the last 3 cases are known as C/OX, O/CX and OppX. This means that you don't look for the relation between FU/FRU and RU/RUF, but between FU/RUF and RU/FRU. In the C/OX case, FU and RUF are the same, and RU and FRU are opposite to each other. The same goes for the O/CX case, but vice versa. In the OppX case, both FU/RUF and RU/FRU are opposite. This looks like a Z-permutation. Note that all of these cases can be seen as A/A cases at first, but whenever you have an A/A case, you should always look if it isn't the other one.

Pros

  • Smaller movecount than doing OLL/PLL
  • Faster than doing OLL/PLL because you only need 1 look

Cons

  • There are a total of 493 algorithms
  • Long and hard recognition
  • Requires edge orientation before doing ZBLL
  • Only shows up 1 in 8 solves, however you can make it show up more often by learning ZBLS

Recognition Methods

Various recognition methods have been developed for the step.

BH

First determine the orientation of the U face corner stickers. Then check pre-determined corner locations for a pattern and compare this with the edges currently around the corner at UFR (the UF and UR edges). The U layer may need to be adjusted if patterns haven’t been learned for all four angles of each case. BH was created by Dan Harris and Jason Baum.

Blocks

Working sort of like 2 sided PLL recognition, patterns of groups of stickers are checked. Adjacent or matching pairs of stickers, a 1x2x2 block, and other patterns.

Twisty PLL

Like two sided PLL recognition the five pieces within the UF and UR bars are used to determine the case. The corners are mentally twisted, with deduction occasionally involved, to picture the six sticker two sided PLL recognition case. This PLL case, combined with the corner orientation, reveals the case.

Tran

Similar to BH, the COLL case is first identified. Then locate the two edges that belong around the UFR corner of the chosen U layer angle, rather than the edges currently in those positions. This recognition system was suggested by Chris Tran.

Tran V2

The original Tran recognition chooses a corner among the seven non-PLL orientations to be considered the UFR corner for locating specific edges. An issue is that if that UFR corner is at UFL, ULB, or UBR and one or both non U face stickers aren’t visible, deduction has to be used in order to know the exact corner and to be able to proceed with locating the edges that belong around it. Tran V2 solves this problem by assigning a corner reference sticker to each U orientation set that is always on the U face, and the edges to be found are changed to become the one matching the corner reference sticker and the one opposite to it. Ryan Hudgens developed the Tran V2 system.

NCP (No CP)

After checking the U sticker orientation, the corner permutation pattern is ignored. Instead, look at the 1x2x2 around the UFL corner and the 1x2x2 around the UFR corner. These two patterns narrow down the exact case. This recognition system was developed by Ryan Hudgens.

Straughan (positional)

Only the visible stickers within UFL, the UF edge, UFR, the UR edge, and UBR are checked. The UBL corner and the LUF and BRU stickers aren't used. This combines the pattern based recognition of BH with Twisty PLL's checking of fewer pieces. The result is fewer pieces and fewer stickers, and no deduction or mental corner twisting. It is a requirement to learn the four angles per case, meaning more learning effort from the beginning, but being fully multi-angle from the start. The differences between positional Straughan recognition and Twisty PLL are that the positional Straughan recognition doesn’t involve reducing to PLL recognition and there is no mental corner twisting or deduction. This recognition method was developed by Michael James Straughan.

Straughan (object)

The minimum number of stickers necessary to determine any ZBLL case is six. The primary form of this recognition involves locating the six stickers that belong at FLU, FU, FUR, RFU, RU, and RUB. Those six stickers are enough to narrow down the exact case. The stickers that belong oriented to the U face aren't checked. The intended use is for prediction during the solve or for one-looking during inspection, and not for recognition upon arriving at the step. This recognition method was developed by Michael James Straughan.

Polar

This recognition method is focused on checking the location of all stickers that belong on the left and right or front and back. First, the left and right corner sticker orientation is checked, then two additional corner stickers are checked to determine the COLL case (a recognition system called ATCRM). Then the left and right edges are found. This recognition method was developed by Michael James Straughan.

Algorithms

Trainers

Documentation

See also

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