Hello speedcubers, my first post and thread on these forums. I've been lurking for a while, and I decided to create this post, due to the displeasure of resources I found online. A little bit about my cubing background - I started maybe 4 months ago, being 22, I cube all over the place, depending on what my ever changing work schedule allows. Some times I don't get to cube for two days, and then sometimes I have 5 hours to improve each day on the weekend. Currently, I average 30 seconds, doing algorithm F2L (I used intuition to figure out why they do the algorithms, so it's kind of like structured intuitive F2L), PLL, and 30~ OLL (rest I do 2 look OLL). My turning speed and look-ahead in F2l is rather weak, so I'm mostly practicing that while I learn the rest of the OLL's.
So onto the question I'm trying to address and discuss: What is objectively the best method to solve a 3x3x3 cube, where the goal is to achieve a fastest average time, for an average, or somewhat above average person in terms of their talent, over a period of several years (say 2-5 years), of moderate dedication (45 minutes - 2 hours average cubing every day of that several year time period).
I think naturally, many people here and cubers around the world, take a in my opinion, primitive way to improve at the Rubik's cube, maybe this can be attributed to a relatively young age of the average cuber, but I'm trying to take a more scientific (note, not mathematical) than artistic approach in figuring out what the best method is.
When someone gets into speedcubing, the structure of learning starts off very easy... You go from one of the many variants of the beginners method, to learning F2L + 4LLL (using the 3 OLL edges algorithms, 7 OLL corners algorithms, then 2 different PLL corner algorithms, then 4 different PLL edge algorithms, and voila)... After that, you learn full PLL and full OLL. Up to this point, resources are very clear and centralized, from here on out however, everything becomes all over the place, and there's in my opinion no clear way forward.
I think that the primary reason is that once you learn full CFOP, the available improvement to make is say only a 20% improvement to your time even if you use every resource available. As all of us cubers know, 90%~ of cubing improvement comes from practice, and hence why someone like Feliks Zemdegs could use an unaltered 4LLL, and still average 10-12 seconds. When the differences become this small, it becomes difficult to objectively analyze which method is better... Because someone only a little bit more practiced than me can solve the cube faster with an inferior method. The result of this becomes very vague advice to people on the forums: "get better with look-ahead, go slow to see how the pieces move with the F2L algorithms", "be able to do all the cases blind", etc.
My opinion is that the majority of people are similar enough biologically, that there should be one optimal method that fits all. Particularly after full CFOP is learnt. One of my gripes for example is when someone says: "Go to some algorithm site and try the other PLL/OLL algorithms to see if there's algorithms that are better for you"... I think we all have the same hands, and that when practiced enough, there should be one set of algorithms that is best for almost all people, just as one example.
So with the approach, let's assume that the best method to solve a cube involves solving the cube in layers, for me this is so broad, so let's take the empirical evidence that the CFOP F2L derived methods for solving the first two layers are the fastest. Which leaves us with the last layer. Now there is the tradeoff between memorization + inspection versus turns required. In the ideal world with a cyborg's mind, we would be doing 1LLL, but the 3915 algorithms has been determined to be impractical for the average (or even the best) human mind to implement effectively. Which means we need to break it down into two steps.
This can be done in many ways, but when we think about what is optimal, we know that breaking it into two steps we know that the rough trend is that: (# of moves step 1)*(# of moves step 2) = (# of moves if done in one step). Since we're trying to minimize inspection time, the less algorithms we need to recognize the better, which means it's desirable to make the size of both steps roughly the same. OLL/PLL is 57 + 21, so I'm sure that some other organization where the two steps could be broken down into say 34~ + 34~ steps would require less to remember, but OLL/PLL is really successful due to the ease of inspection, only having to look at one color blocks in OLL, and notable features in PLL.
Nothing is stopping us from doing CLL + ELL (which is 42 + 29, hence less algorithms than OLL + PLL, but the inspection suffers). Or we could do a far more imbalanced approach, such as: OLLCP + EPLL (331 + 4 algorithms, demonstrating why making both steps roughly in even quantity is preferable)... Or you could combine OCLL + ZBLL (7 + 493 algorithms, once again demonstrating why it's not good to have one step much bigger than the other). Nothing is stopping us from only having categorization of corner OLL, edge OLL, corner PLL, edge PLL, and splitting those four groups into two batches to perform them. We could have a two step method that does OLL+PLL for two edges and two corners, and then a second step that does OLL+PLL for two edges and two corners as our last layer, that might potentially create a more even last layer to solve... However this is all at the cost of inspection time, and hence why, I feel like quite comfortable to say, that if you don't to any prep moves on the last layer during the building of the F2L, then OLL+PLL is the best.
Currently, there's two ways that I see people trying to improve the last layer from what is seen as the classic 2LLL. One is simply to start learning more cases from the 1LLL subset, in order to essentially get a PLL skip. This is the reasoning I see with why some top cubers, learning some PLL skip cases, learning COLL, so on and so forth. The percentage of the skip is rather small, and I suppose it's fairly effective at getting one good time, but not so good at improving your average, which is the question in discussion (you might be going from 57 OLL's to say 57OLL + 42COLL + 20 PLL skips, but that's still a small percentage of the 4000~ 1LL cases).
The other method people take is to do some setup moves during F2L, which most commonly is in the form of partial edge control to not receive dot OLL cases (which are what, 1 move longer on average? lol)... Doing the Winter Variation, which shows up roughly (?) 27/864 or, 3.125% of the time saves around 5 moves (8 moves~ versus 9 moves~ for OLL, minus 4 moves for the F2L insert)... Full VLS can be learnt at a cost of 432 algorithms, for an average savings of 3~ moves (9.74 moves/ VLS versus 9 moves for OLL plus the 4 to insert)... It starts to beg the question, is it worth it? Is needing to recognize one of 432 algorithms to save 3 moves 50% of the time worth it? Or if you learn the cases selectively, you might slow your other times down, seeing you don't know this case, while you could have been inserting the F2L pair normally in that time. I believe the only other popular case to mention is VHLS (32 algorithms) or ZBLS (302 algorithms), followed by ZBLL (493 algorithms)... This is more theoretical now, but I suppose it'd be the progression for someone very dedicated. Anyway, the point is that these are all the popular extensions to CFOP, are they any good, are they worthwhile, which is the best? Do people only do them for the bragging rights at this point? There's no definitive answer that I can find of where to progress your last layer once you've mastered everything in CFOP.
So what is the best last layer method? And on that note, what is the best inspection system, is inspecting a PLL by looking at subtle differences on two edges quicker than having a quick whiff of 3 faces and getting to see larger features? Is there any method to inspecting OLL's, a better classification and data structure than simply associating the shape that you see on the top with the yellow blocks (assuming white cross), and then looking for a key pattern on the others? Is it worthwhile to learn OLL algorithms for all the different angles of OLL's to prevent a cube/top face rotation, but instead require more processing time in your brain to recall the algorithm (it'd be almost 4x the algorithms, some OLL's have symmetry and can be performed from two different angles)... If yes to some, how much is enough, what is the ideal amount? Same goes for PLL... The question once again comes back to, where to go to after learning full CFOP?
We can discuss many things, many of which haven't really been scientifically tested. People here seem to like color neutrality, but badmephisto says that the average moves from a white cross is 5.81, while dual cross is 5.39, and color neutral is 4.81. Is saving the 0.5-1 moves worth it? Sure, you can look ahead a bit more, and start thinking about your extended cross more, but you also need to spend some time finding which cross will be the best, and the obvious increased inspection time during F2L (and especially other stuff like COLL of ZBLL if you go down that route).
Some people will say, go learn some advanced F2L cases, but which ones, they're all over the place, and most people try to be more flashy than useful in the videos that I've seen. To what extent should you minimize rotations in your F2L, at what point does it just not become worth it anymore. Even the basic stuff, like is it worth going a tad slower to keep track of all your empty slots and potentially reduce your insertions by a move or two, or use the tried and true without using other slots to go faster? Is multi-slotting worth the time? Use generic algorithm to get rid of stuck pieces, or learn them for every orientation? Misaligned pairs algorithms?
anyway, like I mentioned at the start, it's difficult to quantify what is best going forward, because these are such minor improvements to CFOP, and practice will make a far larger difference than these in most cases, but once you approach your personal limit after years of practice, I believe these differences makes a noticeable impact - say the difference between a 6.5-7 second average, versus 8 second average. Naturally, most people wont get to that point, and so most people wont notice they have an imperfect system because hey, they're solving the cube in 12 seconds, which is faster than their peers, or just good enough for them. However, speaking for me personally, I'd be satisfying for me to know that what I'm learning is the best system there is for someone like me, even though I might never reach its full potential... And hence even though I know practicing instead of even typing this out would probably yield me more benefit in terms of speed, for my peace of mind, and to promote discussion, I'd like to discuss here the answer to the above question.
I'm aware that this isn't the place to ask questions, but I don't feel that this thread is so much about personal gain, but rather I hope it to become a somewhat scientific discussion about what best is given the limitations of the human body and mind, and hence I believe it to be acceptable for this forum. If not, feel free to move or whatever
TLDR: All resources expanding on full CFOP are all over the place, with no unanimous consensus on the way to go forward.
So onto the question I'm trying to address and discuss: What is objectively the best method to solve a 3x3x3 cube, where the goal is to achieve a fastest average time, for an average, or somewhat above average person in terms of their talent, over a period of several years (say 2-5 years), of moderate dedication (45 minutes - 2 hours average cubing every day of that several year time period).
I think naturally, many people here and cubers around the world, take a in my opinion, primitive way to improve at the Rubik's cube, maybe this can be attributed to a relatively young age of the average cuber, but I'm trying to take a more scientific (note, not mathematical) than artistic approach in figuring out what the best method is.
When someone gets into speedcubing, the structure of learning starts off very easy... You go from one of the many variants of the beginners method, to learning F2L + 4LLL (using the 3 OLL edges algorithms, 7 OLL corners algorithms, then 2 different PLL corner algorithms, then 4 different PLL edge algorithms, and voila)... After that, you learn full PLL and full OLL. Up to this point, resources are very clear and centralized, from here on out however, everything becomes all over the place, and there's in my opinion no clear way forward.
I think that the primary reason is that once you learn full CFOP, the available improvement to make is say only a 20% improvement to your time even if you use every resource available. As all of us cubers know, 90%~ of cubing improvement comes from practice, and hence why someone like Feliks Zemdegs could use an unaltered 4LLL, and still average 10-12 seconds. When the differences become this small, it becomes difficult to objectively analyze which method is better... Because someone only a little bit more practiced than me can solve the cube faster with an inferior method. The result of this becomes very vague advice to people on the forums: "get better with look-ahead, go slow to see how the pieces move with the F2L algorithms", "be able to do all the cases blind", etc.
My opinion is that the majority of people are similar enough biologically, that there should be one optimal method that fits all. Particularly after full CFOP is learnt. One of my gripes for example is when someone says: "Go to some algorithm site and try the other PLL/OLL algorithms to see if there's algorithms that are better for you"... I think we all have the same hands, and that when practiced enough, there should be one set of algorithms that is best for almost all people, just as one example.
So with the approach, let's assume that the best method to solve a cube involves solving the cube in layers, for me this is so broad, so let's take the empirical evidence that the CFOP F2L derived methods for solving the first two layers are the fastest. Which leaves us with the last layer. Now there is the tradeoff between memorization + inspection versus turns required. In the ideal world with a cyborg's mind, we would be doing 1LLL, but the 3915 algorithms has been determined to be impractical for the average (or even the best) human mind to implement effectively. Which means we need to break it down into two steps.
This can be done in many ways, but when we think about what is optimal, we know that breaking it into two steps we know that the rough trend is that: (# of moves step 1)*(# of moves step 2) = (# of moves if done in one step). Since we're trying to minimize inspection time, the less algorithms we need to recognize the better, which means it's desirable to make the size of both steps roughly the same. OLL/PLL is 57 + 21, so I'm sure that some other organization where the two steps could be broken down into say 34~ + 34~ steps would require less to remember, but OLL/PLL is really successful due to the ease of inspection, only having to look at one color blocks in OLL, and notable features in PLL.
Nothing is stopping us from doing CLL + ELL (which is 42 + 29, hence less algorithms than OLL + PLL, but the inspection suffers). Or we could do a far more imbalanced approach, such as: OLLCP + EPLL (331 + 4 algorithms, demonstrating why making both steps roughly in even quantity is preferable)... Or you could combine OCLL + ZBLL (7 + 493 algorithms, once again demonstrating why it's not good to have one step much bigger than the other). Nothing is stopping us from only having categorization of corner OLL, edge OLL, corner PLL, edge PLL, and splitting those four groups into two batches to perform them. We could have a two step method that does OLL+PLL for two edges and two corners, and then a second step that does OLL+PLL for two edges and two corners as our last layer, that might potentially create a more even last layer to solve... However this is all at the cost of inspection time, and hence why, I feel like quite comfortable to say, that if you don't to any prep moves on the last layer during the building of the F2L, then OLL+PLL is the best.
Currently, there's two ways that I see people trying to improve the last layer from what is seen as the classic 2LLL. One is simply to start learning more cases from the 1LLL subset, in order to essentially get a PLL skip. This is the reasoning I see with why some top cubers, learning some PLL skip cases, learning COLL, so on and so forth. The percentage of the skip is rather small, and I suppose it's fairly effective at getting one good time, but not so good at improving your average, which is the question in discussion (you might be going from 57 OLL's to say 57OLL + 42COLL + 20 PLL skips, but that's still a small percentage of the 4000~ 1LL cases).
The other method people take is to do some setup moves during F2L, which most commonly is in the form of partial edge control to not receive dot OLL cases (which are what, 1 move longer on average? lol)... Doing the Winter Variation, which shows up roughly (?) 27/864 or, 3.125% of the time saves around 5 moves (8 moves~ versus 9 moves~ for OLL, minus 4 moves for the F2L insert)... Full VLS can be learnt at a cost of 432 algorithms, for an average savings of 3~ moves (9.74 moves/ VLS versus 9 moves for OLL plus the 4 to insert)... It starts to beg the question, is it worth it? Is needing to recognize one of 432 algorithms to save 3 moves 50% of the time worth it? Or if you learn the cases selectively, you might slow your other times down, seeing you don't know this case, while you could have been inserting the F2L pair normally in that time. I believe the only other popular case to mention is VHLS (32 algorithms) or ZBLS (302 algorithms), followed by ZBLL (493 algorithms)... This is more theoretical now, but I suppose it'd be the progression for someone very dedicated. Anyway, the point is that these are all the popular extensions to CFOP, are they any good, are they worthwhile, which is the best? Do people only do them for the bragging rights at this point? There's no definitive answer that I can find of where to progress your last layer once you've mastered everything in CFOP.
So what is the best last layer method? And on that note, what is the best inspection system, is inspecting a PLL by looking at subtle differences on two edges quicker than having a quick whiff of 3 faces and getting to see larger features? Is there any method to inspecting OLL's, a better classification and data structure than simply associating the shape that you see on the top with the yellow blocks (assuming white cross), and then looking for a key pattern on the others? Is it worthwhile to learn OLL algorithms for all the different angles of OLL's to prevent a cube/top face rotation, but instead require more processing time in your brain to recall the algorithm (it'd be almost 4x the algorithms, some OLL's have symmetry and can be performed from two different angles)... If yes to some, how much is enough, what is the ideal amount? Same goes for PLL... The question once again comes back to, where to go to after learning full CFOP?
We can discuss many things, many of which haven't really been scientifically tested. People here seem to like color neutrality, but badmephisto says that the average moves from a white cross is 5.81, while dual cross is 5.39, and color neutral is 4.81. Is saving the 0.5-1 moves worth it? Sure, you can look ahead a bit more, and start thinking about your extended cross more, but you also need to spend some time finding which cross will be the best, and the obvious increased inspection time during F2L (and especially other stuff like COLL of ZBLL if you go down that route).
Some people will say, go learn some advanced F2L cases, but which ones, they're all over the place, and most people try to be more flashy than useful in the videos that I've seen. To what extent should you minimize rotations in your F2L, at what point does it just not become worth it anymore. Even the basic stuff, like is it worth going a tad slower to keep track of all your empty slots and potentially reduce your insertions by a move or two, or use the tried and true without using other slots to go faster? Is multi-slotting worth the time? Use generic algorithm to get rid of stuck pieces, or learn them for every orientation? Misaligned pairs algorithms?
anyway, like I mentioned at the start, it's difficult to quantify what is best going forward, because these are such minor improvements to CFOP, and practice will make a far larger difference than these in most cases, but once you approach your personal limit after years of practice, I believe these differences makes a noticeable impact - say the difference between a 6.5-7 second average, versus 8 second average. Naturally, most people wont get to that point, and so most people wont notice they have an imperfect system because hey, they're solving the cube in 12 seconds, which is faster than their peers, or just good enough for them. However, speaking for me personally, I'd be satisfying for me to know that what I'm learning is the best system there is for someone like me, even though I might never reach its full potential... And hence even though I know practicing instead of even typing this out would probably yield me more benefit in terms of speed, for my peace of mind, and to promote discussion, I'd like to discuss here the answer to the above question.
I'm aware that this isn't the place to ask questions, but I don't feel that this thread is so much about personal gain, but rather I hope it to become a somewhat scientific discussion about what best is given the limitations of the human body and mind, and hence I believe it to be acceptable for this forum. If not, feel free to move or whatever
TLDR: All resources expanding on full CFOP are all over the place, with no unanimous consensus on the way to go forward.
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SB quickly becomes as "algorithmic" as F2L (i.e. requires lookahead but is still just spamming algs), and I'd actually say it's easier to get a high TPS on SB because it's rotationless <R, Rw, U>. I agree with you for FB - but the same could be said for cross.
