Difference between revisions of "ZBLL"
(Not sure why someone added NMLL as a ZBLL variant. The second step is a subset of ZBLL, but then so are a lot of things. I'm sure having NMLL listed as a variant helped give it some recognition. However, either it shouldn't be there at all or every LL method for an edges oriented LL should be listed.) 

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−  +  {{Substep Infobox  
+  name=ZBLL  
+  image=ZBLL.png  
+  proposers=[[Zbigniew Zborowski]], [[Ron van Bruchem]], [[Lars Petrus]]  
+  year=2002  
+  anames=[[ZZa]], Steps 5+6+7 ([[Petrus method]])  
+  variants=  
+  subgroup=  
+  algs=493  
+  moves=12.08 (Optimal [[HTM]])  
+  purpose=<sup></sup>  
+  * [[Speedsolving]], [[FMC]]  
+  previous=[[LL:EO cube state]]  
+  next=[[Solved cube state]]  
+  }}  
−  ZBLL  +  '''ZBLL''' (short for ''[[Zbigniew ZborowskiZborowski]][[Ron van BruchemBruchem]] Last Layer'') is a step of a method which involves solving the entire [[last layer]] in one step, assuming that the [[edge]]s 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]]). 
−  +  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 7 sets: T, U, L, Pi, Sune, Antisune, H, and the Pll 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. However, this method only works for the T, U and L subsets of ZBLL, because in the other cases the UFR corner is not correctly oriented. 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:  For the T, U and L cases (there are 3*6*12=216 algorithms in this set) recognition goes as follows:  
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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 Zpermutation. 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.  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 Zpermutation. 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.  
−  == See  +  == 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  
+  
+  == See also ==  
+  
+  * [[ZB Method]]  
+  * [[ZBLS]]  
+  * [[ZZa]]  
+  * [[VH Method]]  
+  * [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=ZBLLT ZBLL Algorithms] (complete set)  
+  * [[H ZBLL]] (Algorithms)  
+  * [[ZBLD]]  
+  * [[OPLL]]  
−  * [  +  == External links == 
+  * [https://bestsiteever.ru/zbll/ Roman Strakhov's ZBLL trainer]  
+  * [https://taoyu.github.io/AlgTrainer/ Tao Yu's trainer]  
+  * [http://lar5.com/cube/270/index.html Lars Petrus' Onelook 2alg ZBLL system]  
+  * Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer SubSteps, Subsets of OLLCP and ZBLL]  
+  * [http://bit.ly/ZBLLankidecks Anki Deck]  complete (2H and OH)  
+  * Speedsolving.com: [http://www.speedsolving.com/forum/threads/bindedsasalgorithms.55518/ BindeDSA's Algorithms]  complete (2H and OH)  
+  * Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=18172 Happy New Year! Also, ZBLL Algorithms]  complete  
+  * [http://www.ai.univparis8.fr/~bh/cube/solutions_567.html Bernhard Helmstetter's ZBLL algs]  complete, but excludes mirrors/inverses  
+  * [http://wwwpersonal.umich.edu/~dlli/Hardwick/zbll.html Chris Hardwick's ZBLL algs]  incomplete  
+  * [http://algdb.net/puzzle/333/zbll AlgDb Algorithms]  complete  
+  * [http://tading.gitee.io/zbll/ TaDing's algorithms]  472/493 (OH)  
+  * [https://www.speedcubingtips.eu/zbllzborowskibruchemlastlayer/ Speedcubingtips.eu ]  complete  
+  * [https://docs.google.com/spreadsheets/d/1uwmZHf4vwJxFgeB3TiF8MQ0RFSS30d5CUK96PoIwk Juliette Sébastien's Algorithms]  excluding sunes (2H and OH)  
+  * [https://cdn.discordapp.com/attachments/479068012637585419/482557378605088799/ZBLL.pdf&sa=D&ust=1589197725716000&usg=AFQjCNGpVwcFU50jZ4RgIvcwQPlHCd_onA Jack314's Algorithms]  complete  
+  * [https://docs.google.com/spreadsheets/d/1uXwshDSwMPIxmAyrf40FxRNewGnlo8hTHHGQbHP8Mbk Tao Yu & Justin Taylor's Algorithms]  complete  
+  * [https://docs.google.com/spreadsheets/d/1MDpQbtErO2FRHEaMdLiZ8sqO6hqTuagL1228M3Sk28Q Brant Holbein's Algorithms]  complete (2H and OH)  
+  * [https://docs.google.com/spreadsheets/d/1lERUMmQHtVcovzeTCCQx7iOe0ku_uIXGE2SnrMZGAQ Nicolas Gertner's Algorithms]  complete  
+  * [https://docs.google.com/spreadsheets/d/1ty7aLoEGTgJMKp_qqA5nuPKBIWbV4tFmTej46k0GRw goodforthewin's Algorithms]  complete (2H and OH)  
+  * [http://www.brookscubing.com/wpcontent/uploads/2016/03/AnthonyBrooksZBLL.pdf Anthony Brooks' Algorithms]  excluding sunes  
−  [[Category:  +  [[Category:3x3x3 last layer substeps]] 
−  [[Category:  +  [[Category:Acronyms]] 
−  
−  
− 
Latest revision as of 02:09, 4 October 2020

ZBLL (short for ZborowskiBruchem Last Layer) is a step of a method 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).
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 7 sets: T, U, L, Pi, Sune, Antisune, H, and the Pll 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. However, this method only works for the T, U and L subsets of ZBLL, because in the other cases the UFR corner is not correctly oriented. 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 subcases, 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 Zpermutation. 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
See also
External links
 Roman Strakhov's ZBLL trainer
 Tao Yu's trainer
 Lars Petrus' Onelook 2alg ZBLL system
 Speedsolving.com: Hierarchy of Last Layer SubSteps, Subsets of OLLCP and ZBLL
 Anki Deck  complete (2H and OH)
 Speedsolving.com: BindeDSA's Algorithms  complete (2H and OH)
 Speedsolving.com: Happy New Year! Also, ZBLL Algorithms  complete
 Bernhard Helmstetter's ZBLL algs  complete, but excludes mirrors/inverses
 Chris Hardwick's ZBLL algs  incomplete
 AlgDb Algorithms  complete
 TaDing's algorithms  472/493 (OH)
 Speedcubingtips.eu  complete
 Juliette Sébastien's Algorithms  excluding sunes (2H and OH)
 Jack314's Algorithms  complete
 Tao Yu & Justin Taylor's Algorithms  complete
 Brant Holbein's Algorithms  complete (2H and OH)
 Nicolas Gertner's Algorithms  complete
 goodforthewin's Algorithms  complete (2H and OH)
 Anthony Brooks' Algorithms  excluding sunes