The Orcuber's Hunt For The Best 3x3 Method

[Michael Wimberly]

We still have a lot of the bad habits from Spain.

lol

 

[CrossPetrus]

Another thing I don't think I've seen mentioned in this thread is inspection depth. If you want to create a method that is better than CFOP/ZB, then it needs to be able to compete with them at inspection depth as well. Currently, Yiheng and Xuanyi can see cross+3 in inspection, Xuanyi more than Yiheng, so this gives them the opportunity to 3/4-look solves depending on the method. Depending on scrambles, this could allow 2-look solves from Xuanyi if he can inspect up to ZBLS, which he has demonstrated in this video.

So, if you want to create a method better than ZB, it needs to at least be able to be 3-looked every time. This means the method needs to start out in a way that allows a top solver to be able to look as deeply into the solution as possible, so there can't be any weird movesets or patterns. Though this does restrict a lot of approaches, because with some intuitive solving styles like blockbuilding, it becomes more difficult to track what you're doing the deeper you get into inspection. The main reason F2L allows for such deep inspection depth compared to other methods we've seen is that it always has you undoing moves. This allows solvers to easily track many pieces with little effort because they don't move much, allowing for much deeper inspection. This is extremely difficult to beat when trying to create a better method because blockbuilding doesn't use the same ideology as F2L. There are a lot of one-sided movesets, which makes it difficult to track pieces as they are moved around much more without being restored.

Though this doesn't apply to most solvers, because their inspection depth is much less developed. So, the method should have a linear flow like F2L, allowing solvers to gradually learn to inspect deeper as they become more advanced. Since CFOP/ZB allow a solver to start by planning only cross, then move up to cross+1, then cross+2, then cross+3, the method needs to have a similar progression that accounts for beginner to advanced solvers.

Additionally, to create the best method, it is almost guaranteed to end with ZBLL. Even though it is 493 algs, it doesn't make it bad or difficult to learn, it's just the most optimal algset to end off a solve. So far, ZBLL has the best balance between efficiency and ability to learn, unlike 1LLL or OLL-PLL, it is a balanced middle ground that doesn't require thousands of algs, but also doesn't require multiple looks or more moves. This doesn't restrict the method to ZBLL for all skill levels, though, since, just like CFOP, it can start out ending with OLL-PLL, but have the option of ZBLL for more advanced solvers. I've seen a lot of people trying to figure out some 'better' algset than ZBLL to end off the solve, but it likely doesn't exist without having some major downside. 1LLL, for example, has the potential to average somewhere between 11-13 moves, while ZBLL is currently around 13-15 moves, so that makes it more efficient, but the major downside comes from the amount of algs which make it unviable for the final alg to end off a solve. Likewise, OLL-PLL has the advantage of being 78 algorithms, but the major downside is that it requires 2 looks to solve the cube and averages 21-23 moves. ZBLL is the current perfect middle ground, being only 493 algs, but averaging 13-15 moves using the best algs. In recent years, it has been demonstrated that it's easily possible to learn full ZBLL at the highest level and see improvement from OLL-PLL, even from older cubers like Tymon Kolasiński, Kyle Santucci, Ryan Pilat, and Luke Griesser. So, the point I'm making is that there realistically won't be a better LL method than ZBLL, and examples like L.O.T. just aren't going to best it. So the most optimisation you can get from trying to create a better method will come from building the first 2 layers rather than from optimising the LL, as ZBLL is likely the most optimised LL can get.

I 100% agree with pretty much all of this. I agree that inspection depth is very important, especially at higher levels. Also with ZBLL being the best ll technique, I would say I’m not 100% sure of that, but definitely like 97%+ sure.
Now for my yap, because I’m also a method developer, not just a guy who knows how batch solver works (btw I’m going to make a batch solver guide). To me, there is a distinction between the practical requirements and the theoretical requirements. Practical requirements are things that are needed by any skill level. These are things like good ergonomics, lookahead, good efficiency limit (possibility to have a low movecount, of course efficiency will be dependent on the solver for intuitive steps). Theoretical requirements are things needed at the theoretical limit of prefect solving: ability to be 2 looked consistently, recognition that can be automatic (and not having to double recog, ofc). I think there needs to be a balance between having all of the theoretical and practical requirements. This because a method does not only have to be good in theory for a good solver, but also a natural progression. A method has no value unless people use it and become fast with it. A key part of method development is marketing.
On a completely separate note, we are acting there is one method out there that is unanimously better than every other one. I think this is not so. There will always be tradeoffs between recog, ergonomics, movecount, lookahead/prediction, etc. I think the first thing we need to do is decide what we will value the most, and start thinking of ideas that relate to that. Not just chuck stuff at a wall and see what sticks. That won’t get us anywhere. We need structure and to be smart. We can do this!

 

[n0nco]

To me, there is a distinction between the practical requirements and the theoretical requirements. Theoretical requirements are things needed at the theoretical limit of prefect solving. I think there needs to be a balance between having all of the theoretical and practical requirements.

On a completely separate note, we are acting there is one method out there that is unanimously better than every other one. I think this is not so. There will always be tradeoffs between recog, ergonomics, movecount, lookahead/prediction, etc.

I agree with this for the most part, but the — admittedly unrealistic — goal of the thread is to find the "best" 3x3 method, so I feel like compromises are meant to be kept to an absolute minimum, despite the fact that realistically thats infeasible. (And that we have to primarily account for the best of the best solvers. I could have a wrong read on the thread though.)

Another thing I don't think I've seen mentioned in this thread is inspection depth. If you want to create a method that is better than CFOP/ZB, then it needs to be able to compete with them at inspection depth as well. Currently, Yiheng and Xuanyi can see cross+3 in inspection, Xuanyi more than Yiheng, so this gives them the opportunity to 3/4-look solves depending on the method. Depending on scrambles, this could allow 2-look solves from Xuanyi if he can inspect up to ZBLS, which he has demonstrated in this video.

So, if you want to create a method better than ZB, it needs to at least be able to be 3-looked every time. This means the method needs to start out in a way that allows a top solver to be able to look as deeply into the solution as possible, so there can't be any weird movesets or patterns. Though this does restrict a lot of approaches, because with some intuitive solving styles like blockbuilding, it becomes more difficult to track what you're doing the deeper you get into inspection. The main reason F2L allows for such deep inspection depth compared to other methods we've seen is that it always has you undoing moves. This allows solvers to easily track many pieces with little effort because they don't move much, allowing for much deeper inspection. This is extremely difficult to beat when trying to create a better method because blockbuilding doesn't use the same ideology as F2L. There are a lot of one-sided movesets, which makes it difficult to track pieces as they are moved around much more without being restored.

Though this doesn't apply to most solvers, because their inspection depth is much less developed. So, the method should have a linear flow like F2L, allowing solvers to gradually learn to inspect deeper as they become more advanced. Since CFOP/ZB allow a solver to start by planning only cross, then move up to cross+1, then cross+2, then cross+3, the method needs to have a similar progression that accounts for beginner to advanced solvers.

Additionally, to create the best method, it is almost guaranteed to end with ZBLL. Even though it is 493 algs, it doesn't make it bad or difficult to learn, it's just the most optimal algset to end off a solve. So far, ZBLL has the best balance between efficiency and ability to learn, unlike 1LLL or OLL-PLL, it is a balanced middle ground that doesn't require thousands of algs, but also doesn't require multiple looks or more moves. This doesn't restrict the method to ZBLL for all skill levels, though, since, just like CFOP, it can start out ending with OLL-PLL, but have the option of ZBLL for more advanced solvers. I've seen a lot of people trying to figure out some 'better' algset than ZBLL to end off the solve, but it likely doesn't exist without having some major downside. 1LLL, for example, has the potential to average somewhere between 11-13 moves, while ZBLL is currently around 13-15 moves, so that makes it more efficient, but the major downside comes from the amount of algs which make it unviable for the final alg to end off a solve. Likewise, OLL-PLL has the advantage of being 78 algorithms, but the major downside is that it requires 2 looks to solve the cube and averages 21-23 moves. ZBLL is the current perfect middle ground, being only 493 algs, but averaging 13-15 moves using the best algs. In recent years, it has been demonstrated that it's easily possible to learn full ZBLL at the highest level and see improvement from OLL-PLL, even from older cubers like Tymon Kolasiński, Kyle Santucci, Ryan Pilat, and Luke Griesser. So, the point I'm making is that there realistically won't be a better LL method than ZBLL, and examples like L.O.T. just aren't going to best it. So the most optimisation you can get from trying to create a better method will come from building the first 2 layers rather than from optimising the LL, as ZBLL is likely the most optimised LL can get.

These are some really good points, I whole-heartedly agree about ZBLL, and I do think we should keep "The method should have a linear flow like F2L, allowing solvers to gradually learn to inspect deeper as they become more advanced." in mind.
I'm finding it hard to write down my thoughts on inspection currently, so I'll hopefully write about it tomorrow.

 

[acrystal]

This thread reached 10K views and 300 replies

 

[Caleb Valenzuela]

Finally some progression in this thread

Another thing I don't think I've seen mentioned in this thread is inspection depth. If you want to create a method that is better than CFOP/ZB, then it needs to be able to compete with them at inspection depth as well. Currently, Yiheng and Xuanyi can see cross+3 in inspection, Xuanyi more than Yiheng, so this gives them the opportunity to 3/4-look solves depending on the method. Depending on scrambles, this could allow 2-look solves from Xuanyi if he can inspect up to ZBLS, which he has demonstrated in this video.

So, if you want to create a method better than ZB, it needs to at least be able to be 3-looked every time. This means the method needs to start out in a way that allows a top solver to be able to look as deeply into the solution as possible, so there can't be any weird movesets or patterns. Though this does restrict a lot of approaches, because with some intuitive solving styles like blockbuilding, it becomes more difficult to track what you're doing the deeper you get into inspection. The main reason F2L allows for such deep inspection depth compared to other methods we've seen is that it always has you undoing moves. This allows solvers to easily track many pieces with little effort because they don't move much, allowing for much deeper inspection. This is extremely difficult to beat when trying to create a better method because blockbuilding doesn't use the same ideology as F2L. There are a lot of one-sided movesets, which makes it difficult to track pieces as they are moved around much more without being restored.

Though this doesn't apply to most solvers, because their inspection depth is much less developed. So, the method should have a linear flow like F2L, allowing solvers to gradually learn to inspect deeper as they become more advanced. Since CFOP/ZB allow a solver to start by planning only cross, then move up to cross+1, then cross+2, then cross+3, the method needs to have a similar progression that accounts for beginner to advanced solvers.

Additionally, to create the best method, it is almost guaranteed to end with ZBLL. Even though it is 493 algs, it doesn't make it bad or difficult to learn, it's just the most optimal algset to end off a solve. So far, ZBLL has the best balance between efficiency and ability to learn, unlike 1LLL or OLL-PLL, it is a balanced middle ground that doesn't require thousands of algs, but also doesn't require multiple looks or more moves. This doesn't restrict the method to ZBLL for all skill levels, though, since, just like CFOP, it can start out ending with OLL-PLL, but have the option of ZBLL for more advanced solvers. I've seen a lot of people trying to figure out some 'better' algset than ZBLL to end off the solve, but it likely doesn't exist without having some major downside. 1LLL, for example, has the potential to average somewhere between 11-13 moves, while ZBLL is currently around 13-15 moves, so that makes it more efficient, but the major downside comes from the amount of algs which make it unviable for the final alg to end off a solve. Likewise, OLL-PLL has the advantage of being 78 algorithms, but the major downside is that it requires 2 looks to solve the cube and averages 21-23 moves. ZBLL is the current perfect middle ground, being only 493 algs, but averaging 13-15 moves using the best algs. In recent years, it has been demonstrated that it's easily possible to learn full ZBLL at the highest level and see improvement from OLL-PLL, even from older cubers like Tymon Kolasiński, Kyle Santucci, Ryan Pilat, and Luke Griesser. So, the point I'm making is that there realistically won't be a better LL method than ZBLL, and examples like L.O.T. just aren't going to best it. So the most optimisation you can get from trying to create a better method will come from building the first 2 layers rather than from optimising the LL, as ZBLL is likely the most optimised LL can get.

I think CFOP is generally better for inspection because it’s mainly algorithmic. Algorithms are usually much better for inspection depth because, as you said, algorithms undo moves a lot. It’s also easier to study where pieces will go after an algorithm. But at the same time, a method mainly comprised of algorithms is usually higher in movecount, which is where ZB comes in. ZB compensated for the extra moves from last pair-OLL-PLL, which is why ZB is considered “better” than CFOP.
That’s where i think APB is better. APB seems to be the middle ground between an intuitive method (Roux) and an algorithmic method (CFOP/ZB). Half of the solve (223) is intuitive block building, which can be predicted in inspection at a high-enough level (iirc some roux solvers can plan up to SB or half of SB). BR pair, LXS, and ZBLL are all algorithmic which come after 223. I think the main problem though is the “evenness” of the steps. APB has one huge step (223), that has to be divided into two, then 3 smaller steps (BR Pair, EO, LXS), then one medium-sized step (ZBLL). CFOP on the other hand is relatively even, since you have cross, then four pairs, then last layer. I think evenness is important in inspection depth, since you can plan deep into one big step, but then not be able to inspect into the smaller steps later on in the solve.

PS. This is just an overly-complicated way of me adding my opinion

I hope this made sense

 

[Ralph Laurence]

Honestly I’ve read 10 over 13 of this thread before I even respond and I felt like this search for a best theory, by that I mean a theory that is better than any of the established speedsolving methods would be a far reaching goal. Perhaps a better thing to consider is a method creation that works best under specific constraints.

But given the vision of this thread, I open my mind to the possibility of something better. I believe an incorporation of other established method and integrating them, or developments of already established method and testing them.

It’s also important to note that, we are constraining the best theory in terms of the WCA procedures for speed cubing “how can we inspect better in 15 seconds” etc that rule while good, eliminates potential better theories that unfortunately demands more inspection time

I think the best move forward in this thread is to compile all the methods that were thrown around in a document, list their pros and cons, then compile all the speedcubing methods that are established as well as their pros and cons

Then we can deliberate theorizing a method based on how the past discussions gone so far, in that way, when we come up with a theory we readily have a document that we can base where we can already eliminate in our head because we know this wouldn’t work, or ae give it a try since it’s conceptually in alignment with our trial and errors so far

 

[That0newe1rdo]

guys i made this method during detention

the JOHN method (cause of the first step and my name)

1 - Make a 1x2x3 in the bottom left (like roux)
2 - solve a 1x2x2 in the back right (makes a J shape, hence the method name)
3 - Solve the CP plus DB edge in 1 alg ( 113 cases i think)
4 - Solve EO plus DF edge in 1 alg (60smth cases I think)
5 - OCLL + FR pair then edge perm thing or FR pair + 2GLL

Like ~300 algs total sadly but might have speedsolving potential idk

 

[Michael Wimberly]

guys i made this method during detention

the JOHN method (cause of the first step and my name)

1 - Make a 1x2x3 in the bottom left (like roux)
2 - solve a 1x2x2 in the back right (makes a J shape, hence the method name)
3 - Solve the CP plus DB edge in 1 alg ( 113 cases i think)
4 - Solve EO plus DF edge in 1 alg (60smth cases I think)
5 - OCLL + FR pair then edge perm thing or FR pair + 2GLL

Like ~300 algs total sadly but might have speedsolving potential idk

300 algs is doable though, ZBLL is 493 algs

 

[n0nco]

Perhaps a better thing to consider is a method creation that works best under specific constraints.

But given the vision of this thread, I open my mind to the possibility of something better. I believe an incorporation of other established method and integrating them, or developments of already established method and testing them.

I think the best move forward in this thread is to compile all the methods that were thrown around in a document, list their pros and cons, then compile all the speedcubing methods that are established as well as their pros and cons

Then we can deliberate theorizing a method based on how the past discussions gone so far, in that way, when we come up with a theory we readily have a document that we can base where we can already eliminate in our head because we know this wouldn’t work, or ae give it a try since it’s conceptually in alignment with our trial and errors so far

I personally disagree, I feel as though the previous method concepts were scattered and lacked direction. By that I mean they were all random, very underdeveloped, and lacked structure in the way of criteria, focused around the requirements for an optimal method, to tick off (Once again, I don't mean to cause any offence). It would likely be more productive to discuss what those criteria are, and how much we are willing to compromise on. Of course, it's up to the others to decide.

Another thing I don't think I've seen mentioned in this thread is inspection depth. If you want to create a method that is better than CFOP/ZB, then it needs to be able to compete with them at inspection depth as well. Currently, Yiheng and Xuanyi can see cross+3 in inspection, Xuanyi more than Yiheng, so this gives them the opportunity to 3/4-look solves depending on the method. Depending on scrambles, this could allow 2-look solves from Xuanyi if he can inspect up to ZBLS, which he has demonstrated in this video.

So, if you want to create a method better than ZB, it needs to at least be able to be 3-looked every time. This means the method needs to start out in a way that allows a top solver to be able to look as deeply into the solution as possible, so there can't be any weird movesets or patterns. Though this does restrict a lot of approaches, because with some intuitive solving styles like blockbuilding, it becomes more difficult to track what you're doing the deeper you get into inspection. The main reason F2L allows for such deep inspection depth compared to other methods we've seen is that it always has you undoing moves. This allows solvers to easily track many pieces with little effort because they don't move much, allowing for much deeper inspection. This is extremely difficult to beat when trying to create a better method because blockbuilding doesn't use the same ideology as F2L. There are a lot of one-sided movesets, which makes it difficult to track pieces as they are moved around much more without being restored.

Though this doesn't apply to most solvers, because their inspection depth is much less developed. So, the method should have a linear flow like F2L, allowing solvers to gradually learn to inspect deeper as they become more advanced. Since CFOP/ZB allow a solver to start by planning only cross, then move up to cross+1, then cross+2, then cross+3, the method needs to have a similar progression that accounts for beginner to advanced solvers.

I'm not very well versed in inspection, so I personally can't really gauge the efficacy of a given methods inspection potential.

Hypothetically, if the inspection potential isn't as good as CFOP, but the lookahead was great, would it make up for the inspection?
How much do you think you'd need to predict in inspection? I know you said a solve would have to be capable of being 3 looked, but I'd like to hear more on that.
Would you see any potential in blockbuilding within the hypothetical best method, despite inspection issues? I doubt theres much way to improve upon CFOPs concepts as is, so I don't think that's a feasible avenue to focus on.

It seems to me CFOP is so uniquely crafted in a way that perfectly suits itself towards every quality, besides movecount.

Sorry this is an incoherent jumble of thoughts, I'm finding it hard to articulate my thoughts for this.

 

[AJT17]

Hypothetically, if the inspection potential isn't as good as CFOP, but the lookahead was great, would it make up for the inspection?
How much do you think you'd need to predict in inspection? I know you said a solve would have to be capable of being 3 looked, but I'd like to hear more on that.
Would you see any potential in blockbuilding within the hypothetical best method, despite inspection issues? I doubt theres much way to improve upon CFOPs concepts as is, so I don't think that's a feasible avenue to focus on.

I think lookahead can only take you so far. Turning between 10-15 TPS, depending on the solver and the movesets, it becomes difficult to rely solely on lookahead, which lends itself to deeper inspection to reach those speeds consistently. Though under 10 TPS, lookahead can still be more viable, as I would consider it slightly easier to practice and get good at than inspection depth. So, there could be levels to this, as I mentioned earlier, with the most advanced solvers sticking to deep inspection, while intermediate solvers could plan slightly less in exchange for potentially inconsistent lookahead.

As for how much should be inspected, based on CFOP/ZB, generally cross+3 is the limit for 15 seconds of inspection for top-level cubers to 3-look. So, applying this to another method like APB means you would need to plan 223, BRPair, and EO all in inspection to satisfy the requirements for 3-look solving. If it weren't for EO, this would be moderately easier, so that is something to consider when looking for improvements. This might lead us to look at immediate EO, though that imposes some restrictions on inspection depth and movesets, as you need to be mindful to preserve EO throughout. From what I've heard, top-level ZZ solvers can plan EOCross+2, which is equivalent to cross+3, so that could be doable.

As for the potential for blockbuilding, my current ideas lean towards a more linear approach to solving, though I'm not entirely sure how to do it yet. Followed up with some form of blockbuilding as the last part you'd see in inspection. Which might get rid of the downside of not being able to see past one-sided movesets, since it's last, it doesn't need to be undone to see deeper. This could be executed with something along the lines of an EOXCross in BL without the DR edge being solved, then do BR and FL pairs in inspection, leaving LXS-ZBLL. Or an EO223 on the left, followed by BRPair, though this would be at the tail end of inspection, and it might be difficult to see this deep consistently. Another approach could ditch immediate EO, in favour of a different approach to cross+3. Starting out with a form of 223, or cross without DR, then solving 2 pairs, followed by intuitive blockbuilding of the right square, to be left with ZBLS-ZBLL to end off. This might allow for a more structured, linear start to make inspection depth easier, while also allowing some intuition for the final square, though it would be difficult to do at the tail end of inspection. Though I wouldn't consider any of these approaches to be very different from what we currently have, or any bit better, as they involve very little blockbuilding and are more like slight variants/meshes between CFOP/ZB and APB. It might lay out a stronger foundation for working towards a 'better' method at the very least.

Two things should be relatively constant: EO during some part of the solve, whether full EO, ZBLS, or something else, and ending with ZBLL. Ideas like mid-solve CP might sound better, as they reduce alg count and end with 2GLL, but doing CP in the middle of the solve just isn't viable, and methods like Epidote that have tried to fix this haven't gained much traction. And as I've mentioned earlier, doing CP at the start of the solve just isn't worth the restriction, as it only saves a couple moves at best, while massively restricting what moves can be done.

The main focus of finding this 'better' method should definitely shift away from LSLL, since ZBLS and ZBLL are really strong and have very few drawbacks aside from a slightly high alg count, though this isn't an issue at the highest level. There are likely a good number of approaches to making cross+3 that haven't been looked into yet, potentially like I mentioned earlier, or even something I haven't thought of. This will be the biggest factor in actually improving upon ZB. With Xuanyi incorporating pseudo-F2L/pseudo-slotting, it will be even more difficult to save moves and improve ergonomics, but it is likely possible with the right approach.

This might've gotten a bit muddled and confusing as I've been writing in different sections as the ideas have come to me. If there are any confusing parts, I would be happy to clarify.

 

[Ralph Laurence]

I personally disagree, I feel as though the previous method concepts were scattered and lacked direction. By that I mean they were all random, very underdeveloped, and lacked structure in the way of criteria, focused around the requirements for an optimal method, to tick off (Once again, I don't mean to cause any offence). It would likely be more productive to discuss what those criteria are, and how much we are willing to compromise on. Of course, it's up to the others to decide.


I'm not very well versed in inspection, so I personally can't really gauge the efficacy of a given methods inspection potential.

Hypothetically, if the inspection potential isn't as good as CFOP, but the lookahead was great, would it make up for the inspection?
How much do you think you'd need to predict in inspection? I know you said a solve would have to be capable of being 3 looked, but I'd like to hear more on that.
Would you see any potential in blockbuilding within the hypothetical best method, despite inspection issues? I doubt theres much way to improve upon CFOPs concepts as is, so I don't think that's a feasible avenue to focus on.

It seems to me CFOP is so uniquely crafted in a way that perfectly suits itself towards every quality, besides movecount.

Sorry this is an incoherent jumble of thoughts, I'm finding it hard to articulate my thoughts for this.

Scattered, lack direction, are what’s observed in the previous method creation, which is important to note. While also considering already established method, a contrast between the past efforts and the analysis of the established methods is exactly what we’re doing here to elucidate and have a better chance good method development.

this thread has discuss perhaps so many but hasn’t provided a clear summary to move forward, your contributions and others that are currently posting are necessary to highlight in a well define document that is easily organized. That’s the main point of my post here. Which I’m not sure if you really disagreed as fundamentally it seems like you disregard then idea because of what you observed as a scattered pitches, which can be resolved by organizing it can thus making it clear as to why it may be, and preventing to recycle ideas that are already brought up and failed in scrutiny.

 

[n0nco]

I think lookahead can only take you so far. Turning between 10-15 TPS, depending on the solver and the movesets, it becomes difficult to rely solely on lookahead, which lends itself to deeper inspection to reach those speeds consistently. Though under 10 TPS, lookahead can still be more viable, as I would consider it slightly easier to practice and get good at than inspection depth. So, there could be levels to this, as I mentioned earlier, with the most advanced solvers sticking to deep inspection, while intermediate solvers could plan slightly less in exchange for potentially inconsistent lookahead.

As for how much should be inspected, based on CFOP/ZB, generally cross+3 is the limit for 15 seconds of inspection for top-level cubers to 3-look. So, applying this to another method like APB means you would need to plan 223, BRPair, and EO all in inspection to satisfy the requirements for 3-look solving. If it weren't for EO, this would be moderately easier, so that is something to consider when looking for improvements. This might lead us to look at immediate EO, though that imposes some restrictions on inspection depth and movesets, as you need to be mindful to preserve EO throughout. From what I've heard, top-level ZZ solvers can plan EOCross+2, which is equivalent to cross+3, so that could be doable.

As for the potential for blockbuilding, my current ideas lean towards a more linear approach to solving, though I'm not entirely sure how to do it yet. Followed up with some form of blockbuilding as the last part you'd see in inspection. Which might get rid of the downside of not being able to see past one-sided movesets, since it's last, it doesn't need to be undone to see deeper. This could be executed with something along the lines of an EOXCross in BL without the DR edge being solved, then do BR and FL pairs in inspection, leaving LXS-ZBLL. Or an EO223 on the left, followed by BRPair, though this would be at the tail end of inspection, and it might be difficult to see this deep consistently. Another approach could ditch immediate EO, in favour of a different approach to cross+3. Starting out with a form of 223, or cross without DR, then solving 2 pairs, followed by intuitive blockbuilding of the right square, to be left with ZBLS-ZBLL to end off. This might allow for a more structured, linear start to make inspection depth easier, while also allowing some intuition for the final square, though it would be difficult to do at the tail end of inspection. Though I wouldn't consider any of these approaches to be very different from what we currently have, or any bit better, as they involve very little blockbuilding and are more like slight variants/meshes between CFOP/ZB and APB. It might lay out a stronger foundation for working towards a 'better' method at the very least.

Two things should be relatively constant: EO during some part of the solve, whether full EO, ZBLS, or something else, and ending with ZBLL. Ideas like mid-solve CP might sound better, as they reduce alg count and end with 2GLL, but doing CP in the middle of the solve just isn't viable, and methods like Epidote that have tried to fix this haven't gained much traction. And as I've mentioned earlier, doing CP at the start of the solve just isn't worth the restriction, as it only saves a couple moves at best, while massively restricting what moves can be done.

The main focus of finding this 'better' method should definitely shift away from LSLL, since ZBLS and ZBLL are really strong and have very few drawbacks aside from a slightly high alg count, though this isn't an issue at the highest level. There are likely a good number of approaches to making cross+3 that haven't been looked into yet, potentially like I mentioned earlier, or even something I haven't thought of. This will be the biggest factor in actually improving upon ZB. With Xuanyi incorporating pseudo-F2L/pseudo-slotting, it will be even more difficult to save moves and improve ergonomics, but it is likely possible with the right approach.

This might've gotten a bit muddled and confusing as I've been writing in different sections as the ideas have come to me. If there are any confusing parts, I would be happy to clarify.

I watched the follow up to the video you linked earlier on, and apparently Xuanyi typically only inspects around 2 pairs in comp, since he has to simplify his pair solutions to actually inspect 4. Of course, the video is 2 years old, so he totally could've improved since then, but I still think it shows that lookahead can make up for non-ideal inspection potential to at least some extent, even though it would be best to hypothetically surpass CFOP in that regard. (That's just my not-super-educated guess though. I know you're speaking in definites, and I don't mean to disregard what you're saying, but SURELY theres some leniency to it, right?)

Blockbuilding in the latter end of inspection is very interesting, but I don't see much efficacy in it, since it wouldn't really lean into "gradually inspecting deeper", as blockbuilding would probably be a huge jump in the learning rather than a gradual improvement, and if you can't inspect to that step of the solve, I'd imagine that step wouldn't be very fast.

Although, I tried EOCross-1 earlier, and I found some pretty efficient solutions, so I think it would lend itself to some very creative solutions. And for the EO223, I think it could work, even without BR pair in inspection (surely it's not too bad to lookahead your way through that 1 pair), although it would just be APB with EO at the start rather than mid solve, and the blockbuilding may be stunted by the lack of F/B moves(?).

If I may ask, wouldn't restricted petrus methods (as I've seen you call Lau) be better than standard petrus, due to the "structure" that would help with inspection, or are the restrictions too extreme/there are some other factor(s) at play?

In the immediate-EO-less concept, would you be abusing the S slice to avoid rotations, or would the method have rotations? Also, I noticed you mentioned 2 method concepts that utilise LXS, are you a big proponent of it?

"[We should] shift away from LSLL" LSLL as in unique Last Slot and Last Layer approaches? or something else?

By the way, thanks for these answers, they're incredibly insightful & interesting. (/genuine, just in case its not clear.)

I can’t help but notice everyone else who was messaging on this thread has gone quiet, which is unfortunate, I'd like to hear y'all weigh in on this discussion as well.

 

[Caleb Valenzuela]

I personally disagree, I feel as though the previous method concepts were scattered and lacked direction. By that I mean they were all random, very underdeveloped, and lacked structure in the way of criteria, focused around the requirements for an optimal method, to tick off (Once again, I don't mean to cause any offence). It would likely be more productive to discuss what those criteria are, and how much we are willing to compromise on. Of course, it's up to the others to decide.


I'm not very well versed in inspection, so I personally can't really gauge the efficacy of a given methods inspection potential.

Hypothetically, if the inspection potential isn't as good as CFOP, but the lookahead was great, would it make up for the inspection?
How much do you think you'd need to predict in inspection? I know you said a solve would have to be capable of being 3 looked, but I'd like to hear more on that.
Would you see any potential in blockbuilding within the hypothetical best method, despite inspection issues? I doubt theres much way to improve upon CFOPs concepts as is, so I don't think that's a feasible avenue to focus on.

It seems to me CFOP is so uniquely crafted in a way that perfectly suits itself towards every quality, besides movecount.

Sorry this is an incoherent jumble of thoughts, I'm finding it hard to articulate my thoughts for this.

Scattered, lack direction, are what’s observed in the previous method creation, which is important to note. While also considering already established method, a contrast between the past efforts and the analysis of the established methods is exactly what we’re doing here to elucidate and have a better chance good method development.

this thread has discuss perhaps so many but hasn’t provided a clear summary to move forward, your contributions and others that are currently posting are necessary to highlight in a well define document that is easily organized. That’s the main point of my post here. Which I’m not sure if you really disagreed as fundamentally it seems like you disregard then idea because of what you observed as a scattered pitches, which can be resolved by organizing it can thus making it clear as to why it may be, and preventing to recycle ideas that are already brought up and failed in scrutiny.

I have an idea for everyone.

What if we just search and analyze a bunch of methods we already know or don’t know, gather all the pros and the best steps of each method and combine them into a spreadsheet, then rank each pro/step by priority or most important, then base a method off that?

Right now I feel like we’re kinda getting more stuck by discussing phase 0 (yes, we’re kinda still in phase 0 gng)

Xuanyi typically only inspects around 2 pairs in comp, since he has to simplify his pair solutions to actually inspect 4. Of course, the video is 2 years old, so he totally could've improved since then, but I still think it shows that lookahead can make up for non-ideal inspection potential to at least some extent

I would also like to clarify some things.
Usually, when people think of lookahead (at least this is how I always accidentally think about it), they think of the normal: “solve pair x, then look for pair y while doing pair x”. But for higher level solvers like Xuanyi, while doing cross+2, they’re already looking ahead to third and fourth pair, even if they just finished cross+1. So in a way, they’re sort of still “inspecting” while their hands are already beginning to solve the cube.

If I may ask, wouldn't restricted petrus methods (as I've seen you call Lau) be better than standard petrus, due to the "structure" that would help with inspection, or are the restrictions too extreme/there are some other factor(s) at play?

from a personal standpoint point, I think Lau is a bit too restricted, but since he did mention that it was specifically designed to avoid F and B moves, I guess it explains the rigidness. The best method (in my opinion) lies in between “flexibly intuitive” and “rigidly structured”. And coincidentally, CFOP, ZB, and APB all lie within that range, with CFOP/ZB leaning toward the more “rigid structured” side, while APB leans slightly more to dead-center, but overall more on the intuitive side due to 223. (taking that flexibly intuitive and rigidly structured are on opposite sides of a line)

In the immediate-EO-less concept, would you be abusing the S slice to avoid rotations, or would the method have rotations? Also, I noticed you mentioned 2 method concepts that utilise LXS, are you a big proponent of it?

I think using S slices often will butcher TPS. It would just be better to rotate in that case. LXS is also, from an objective perspective, a very good step since in APB it’s just solving F2L with RU gen (idk if you used the 2-gen function on csTimer, but LXS essentially turns the rest of the solve into that, which is very good)

it was a relief to be able to finally release all these thoughts

 

[Ralph Laurence]

I have an idea for everyone.

What if we just search and analyze a bunch of methods we already know or don’t know, gather all the pros and the best steps of each method and combine them into a spreadsheet, then rank each pro/step by priority or most important, then base a method off that?

Right now I feel like we’re kinda getting more stuck by discussing phase 0 (yes, we’re kinda still in phase 0 gng)

I would also like to clarify some things.
Usually, when people think of lookahead (at least this is how I always accidentally think about it), they think of the normal: “solve pair x, then look for pair y while doing pair x”. But for higher level solvers like Xuanyi, while doing cross+2, they’re already looking ahead to third and fourth pair, even if they just finished cross+1. So in a way, they’re sort of still “inspecting” while their hands are already beginning to solve the cube.


from a personal standpoint point, I think Lau is a bit too restricted, but since he did mention that it was specifically designed to avoid F and B moves, I guess it explains the rigidness. The best method (in my opinion) lies in between “flexibly intuitive” and “rigidly structured”. And coincidentally, CFOP, ZB, and APB all lie within that range, with CFOP/ZB leaning toward the more “rigid structured” side, while APB leans slightly more to dead-center, but overall more on the intuitive side due to 223. (taking that flexibly intuitive and rigidly structured are on opposite sides of a line)


I think using S slices often will butcher TPS. It would just be better to rotate in that case. LXS is also, from an objective perspective, a very good step since in APB it’s just solving F2L with RU gen (idk if you used the 2-gen function on csTimer, but LXS essentially turns the rest of the solve into that, which is very good)

it was a relief to be able to finally release all these thoughts

To clarify, the F and B move restriction is in this discussion, just me giving an example of method incorporation, lau doesn’t have to follow that although that method itself lower the chances for the F and B moves. As per whether it is better than standard petrus it depends on someone’s look ahead skills, I have already saw some top level petrus solver choosing lau due to it’s algorithmic approach, and easy inspection for the First 5 Edges. In some way it can be better, is the question is not about move count efficiency.

 

[Caleb Valenzuela]

To clarify, the F and B move restriction is in this discussion, just me giving an example of method incorporation. As per whether it is better than standard petrus it depends on someone’s look ahead skills, I have already saw some top level petrus solver choosing lau due to it’s algorithmic approach, and easy inspection for the First 5 Edges. In some way it can be better, is the question is not about move count efficiency.

I can definitely see Lau being highly TPS spammable given the right lookahead/planning skills, but it sort of runs into a problem the CFOP had, which of course, given enough recognition and usage, will probably be resolved later. But the topic of this thread isn’t about Lau (respectfully). We could talk about it in the actual Lau method thread I think.

 

[Ralph Laurence]

I can definitely see Lau being highly TPS spammable given the right lookahead/planning skills, but it sort of runs into a problem the CFOP had, which of course, given enough recognition and usage, will probably be resolved later. But the topic of this thread isn’t about Lau (respectfully). We could talk about it in the actual Lau method thread I think.

Yes, I’m clarifying just to prevent further misinformation to happen as the most viewed tutorial of my method have done enough misinformation

it also have a similar drawback with cfop, which is why I recommend it only when one can already inspect the five initial edges that are crucial for lau as it is considerably the most optimal for those instances, scambles, perhaps another is, lau plus APB, given APB’s spammable and ergonomic function will work well

Lastly, you are welcome to discuss it on the thread I have created yes

Regarding your idea of compiling methods, we may do that and use the wiki speedcube also as a basis for documentation

 

[Martyt7777]

ok chat
I have a new idea
THE IDEA
I will be calling this 3MPLL (3 Move Pair Last Layer)
Here’s what it will be like for CFOP users
step 1: solve cross+3 pairs
step 2: solve EO
step 3: form a 3 mover for your last pair
step 4: solve the pair and the entire last layer in one step

I know what you’re thinking
It seems inefficient compared to solving OLL+PLL or ZBLS+ZBLL right? But that’s because this method was designed as a substep for APB. In APB, you already solve EO before even solving F2L, which turns the 4 step LL into a 3 step LL. I’ve also observed that most F2L pairs will always have you forming a 3/4 mover as part of the F2L alg, which is where I also got inspiration for this method. The problems I can see right now though is that the alg count might be way too high. Take this with a grain of salt though because I don’t know if this last layer method exists.

I think its at max 3984, maybe the alg count is around few hundred less, because 493 (usual ZBLL count, including PLL) * 4 (ZBLL AUF) 2 (2 possible 3-4 move pairs with EO solved) = 3984 (alg count is 984 because of ZBLL symmetries).

Just wanted to clarify, the method has 3888 algs. If anyone wants to develop this method in the future, you can gen the algs in batch solver like this:

Spoiler: Batch solver scrambles

Unpaired pair: < U , R U R' F' R U R' U' R' F R2 U' R' , R U R' U R' U' R2 U' R' U R' U R , R U R2 U' R2 U R U R' U' R U R U R U' R' > R U' R'

Paired pair: < U , R U R' F' R U R' U' R' F R2 U' R' , R U R' U R' U' R2 U' R' U R' U R , R U R2 U' R2 U R U R' U' R U R U R U' R' > R U R' U'

 

[CrossPetrus]

Just wanted to clarify, the method has 3888 algs. If anyone wants to develop this method in the future, you can gen the algs in batch solver like this:

Spoiler: Batch solver scrambles

Unpaired pair: < U , R U R' F' R U R' U' R' F R2 U' R' , R U R' U R' U' R2 U' R' U R' U R , R U R2 U' R2 U R U R' U' R U R U R U' R' > R U' R'

Paired pair: < U , R U R' F' R U R' U' R' F R2 U' R' , R U R' U R' U' R2 U' R' U R' U R , R U R2 U' R2 U R U R' U' R U R U R U' R' > R U R' U'

Btw, just as a note, you can have Sune instead of R U R2 U' R2 U R U R' U' R U R U R U' R. And use [ ] to generate the 3 mover and the pair at the same time. Overall it would look like this: < U, R U R' F' R U R' U' R' F R2 U' R', R U R' U R U2 R', R U R' U R' U' R2 U' R' U R' U R> [R U' R', R U R' U']
But good job with using batch solver!

 

[Deleted member 27249]

The cases ZBLL with block 1x1x3 are 12.
If you create cross and block 1x1x3 when you solve Last Pair F2L?
How many Algs to learn for solve block 1x1x3 and cross Yellow when you solve Last Pair F2L?

 

[Martyt7777]

Btw, just as a note, you can have Sune instead of R U R2 U' R2 U R U R' U' R U R U R U' R. And use [ ] to generate the 3 mover and the pair at the same time. Overall it would look like this: < U, R U R' F' R U R' U' R' F R2 U' R', R U R' U R U2 R', R U R' U R' U' R2 U' R' U R' U R> [R U' R', R U R' U']
But good job with using batch solver!

K thanks, I just used that because that was the ZBLL scramble orekahstrah used in his batch solver guide video