3x3 PBL Theoretical Method (3BL) (CFOP Variant)

[Duncan Kimmett]

Isn't it 168?
Bottom can be Ua, Ub, W, Oa, Ob, H, Z, Adj, Diag
Top can be all 21 pll's
H bottom is nonsense, you can just do D2 after cross
This leaves 8 x 21 = 168 cases excluding normal PLLs

Wait. When bottom isn't an alg top isn't a legit PLL. How do I figure these algs out?!?!?!

 

[Duncan Kimmett]

Wait. When bottom isn't an alg top isn't a legit PLL. How do I figure these algs out?!?!?!

I have a shaky plan which is do a ton of solves with that cross on bottom then see the PLLs

 

[Jorian Meeuse]

Wait. When bottom isn't an alg top isn't a legit PLL. How do I figure these algs out?!?!?!

What do you mean 'when bottom isn't an alg'? The line and W cases?

 

[Duncan Kimmett]

What do you mean 'when bottom isn't an alg'? The line and W cases?

So, W and adjacent edges and opposite edges give combined PLL cases. I can give a screenshot.

 

[Jorian Meeuse]

So, W and adjacent edges and opposite edges give combined PLL cases. I can give a screenshot.

Yeah that's just like PLL parity on 4x4. Since the bottom has an odd number of swaps, the top must too. The easiest case is M2 U2 M2.

 

[Duncan Kimmett]

Yeah that's just like PLL parity on 4x4. Since the bottom has an odd number of swaps, the top must too. The easiest case is M2 U2 M2.

Exactly! But I need help on figuring out how to find all the cases. How can I know if I didn't find a case?

 

[Jorian Meeuse]

Exactly! But I need help on figuring out how to find all the cases. How can I know if I didn't find a case?

Well if you have 126 cases total, you have all algs. If you want to know which cases there are possible on the top, just imagine taking each regular pll and doing a single swap of edges, e.g. a diagonal swap, to each of them. That means there are 22 possible PLL cases. Wait I'm just now realizing that changes the math. 21 cases on the top for Ua, Ub, Z, 22 cases for Adj, Diag, W, gives 21 x 3 + 22 x 3 = 129 cases.

 

[Duncan Kimmett]

Well if you have 126 cases total, you have all algs. If you want to know which cases there are possible on the top, just imagine taking each regular pll and doing a single swap of edges, e.g. a diagonal swap, to each of them. That means there are 22 possible PLL cases. Wait I'm just now realizing that changes the math. 21 cases on the top for Ua, Ub, Z, 22 cases for Adj, Diag, W, gives 21 x 3 + 22 x 3 = 129 cases.

Thank you so much! You make me feel like an idiot!

 

[Jorian Meeuse]

Thank you so much! You make me feel like an idiot!

Nope you're not
If you want to check if you have every case, this video is about 4x4 PLL parity, but it covers every possible case so you can maybe use it as a checklist.

 

[Duncan Kimmett]

OMG THIS IS AMAZING!!!!!

 

[Duncan Kimmett]

also imma get back to making algs now. I'll check this every once in while

 

[Duncan Kimmett]

Just finished all the U Perm Cross Cases!

 

[Silky]

PLL parity only occurs if you have O, W, Adj, or Opp on the D face. To avoid PLL "Parity" you can preform M2 U2 M2 ( this transforms your O, W, Adj, Opp into a EPLL ). All EP cases have already been generated and can be found here, both with and without "Parity".

Also there are 109 non-Parity cases ( including PLL ) and 110 Parity cases. 219 in total.

 

[Cubinginatree]

How do you generate the algs?

 

[Duncan Kimmett]

How do you generate the algs?

If you're asking me, I use a thing called "cube explorer" which finds optimal algs for every case by the click of a button.

 

[Duncan Kimmett]

PLL parity only occurs if you have O, W, Adj, or Opp on the D face. To avoid PLL "Parity" you can preform M2 U2 M2 ( this transforms your O, W, Adj, Opp into a EPLL ). All EP cases have already been generated and can be found here, both with and without "Parity".

Also there are 109 non-Parity cases ( including PLL ) and 110 Parity cases. 219 in total.

I think that might be too many algs for my taste. Imma just stake with our current strat. Do people agree with that?

 

[Duncan Kimmett]

I'm just gonna assume Ob-Perm cycles to the left while Oa perm cycles to the right?

 

[Imsoosm]

I would suggest you to use the Batch Solver as cube explorer's optimal algorithms usually have very bad ergonomics. Batch Solver can generate a set of algorithms at a time, and can also check for the alg with highest ergonomics.

Here is the link to the original thread, you might need to watch the tutorial:

The Batch Solver - Generate large algorithm sets automatically!

The Batch Solver Batch Solver Tutorial by OreKehStrah Batch Solver Documentation Introduction Before the batch solver, generating algorithms involved inputting each and every case into Cube Explorer, running the search for that one case, testing out the generated algorithms to determine the...

www.speedsolving.com

 

[hyn]

I would suggest you to use the Batch Solver as cube explorer's optimal algorithms usually have very bad ergonomics. Batch Solver can generate a set of algorithms at a time, and can also check for the alg with highest ergonomics.

Here is the link to the original thread, you might need to watch the tutorial:

The Batch Solver - Generate large algorithm sets automatically!

The Batch Solver Batch Solver Tutorial by OreKehStrah Batch Solver Documentation Introduction Before the batch solver, generating algorithms involved inputting each and every case into Cube Explorer, running the search for that one case, testing out the generated algorithms to determine the...

www.speedsolving.com

ur signature says 3x3 Qiyi MS

didn't u have a gan 12?

 

[Duncan Kimmett]

I would suggest you to use the Batch Solver as cube explorer's optimal algorithms usually have very bad ergonomics. Batch Solver can generate a set of algorithms at a time, and can also check for the alg with highest ergonomics.

Here is the link to the original thread, you might need to watch the tutorial:

The Batch Solver - Generate large algorithm sets automatically!

The Batch Solver Batch Solver Tutorial by OreKehStrah Batch Solver Documentation Introduction Before the batch solver, generating algorithms involved inputting each and every case into Cube Explorer, running the search for that one case, testing out the generated algorithms to determine the...

www.speedsolving.com

Thank you very much! I'll try it out! Do you think it would be worth re-doing an absolute ton of algs just for this, or should I just continue with it?