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Objectively, the best 3x3x3 method...
- Thread starter FiWiFaKi
- Start date
@4Chan That's where the ID came from ^^
@xyzzy thank you for the long and well thought out reply, much appreciated.
Thanks for letting me know that it's not seen as good, I suppose I'd have to look at the algorithms closer to be 100% sure, but I'll take your word for it.
-VHLS + ZBLL are 32 (6.63moves) + 493 (12.08 algorithms)... Replacing VHLS with ZBLS saves 3 moves, but now we're up to 795 algs. With a LS Insert+LL move count of 15.63 (ZBLS+ZBLL is more, but ZBLS solves the F2L case, not inserts it, I tried to adjust it to only take into account the solving). Versus CFOP: LS (3.7 moves) + OLL (9.7 moves) + PLL (11.8 moves)... So CFOP LS+LL is 25.2~ moves.
-WV/SV + COALL (first time hearing this) is 108, though half are perfect mirrors, and taking your 150 for COALL, that's significantly less algs. Move count is and (8.07+9.4)/2, so 8.74 moves For WV/SV
So now we have in nice order of algorithm trade off:
CFOP: 78 algs at 25.2 moves
Wv/SV+ COALL: 258 algs at 8.74+(12)? = 20.74 moves
VHLS+ZBLL: 525 algs at 18.71
ZBLS+ZBLL: 795 algs at 15.63
Hmm, maybe I will need to look into it more, because we can see it's all tradeoffs, but I kind of like it in theory anyway. The issue with VHLS + ZBLL is that it splits the two into very uneven steps, where VHLS is way too easy compared to ZBLL, and that raises algorithm count too much. Instead this VW/SV+COALL would make the first step more difficult, and the 2nd step much faster... And edge orientation to me is quicker to notice as well... Really depends on how the algs look.
ZB method is designed when both ZBLS+ZBLL is used since then both steps are fairly "balanced", while if we did the VHLS -> ZBLS expansion for VW/SV -> solving any F2L case, you'd I think have an algorithm count in the 1,000-2,000 range, so that's no longer practical. But the entire basis for this is that ZB is balanced but requiring too high an algorithm count, while WV/SV+COALL is balanced at 1/3rd the alg count, but 5-6 moves longer. Hmm, I'll have to look at some cubing resources online to analyze this stuff, it's got me interested.
Interesting to hear that you've tried the building a 2x2x2 block, maybe I got the idea when I was quickly skimming through every wiki article, not sure.
Actually, with those 65 algorithm sets, when you start with a fully completed F2L, there's exactly 63 non-redundant solution paths. By non-redundant I mean, don't preserve EO/CO/CP/EP if you're doing an OCLL variant first step in a 4LLL.
The solution paths are:
4 modifications - 1LLL 1 case
3+1 modifications - 2LLL, OLLCP + quick finish type things 4 cases
1+3 modifications - 2LLL, ZBLL type of thing 4 cases
2+2 modifications - 2LLL, there is: OLL/PLL, CLL/ELL, LLEF+L4C, CPEOLL+2GLL, PLL/OLL (sounds awful lol), inverse of the 2GLL method (doesn't exist yet?)... I feel safe to say that out of those 6, OLL/PLL is the fastest. 6 cases
(2+1+1) or (1+2+1) or (1+1+2) modifications - 3LLL, I guess the only thing similar is was it BLL where the guy tried to get a 3LLL in under 25 algorithms? Well, there's many different options to explore here for low algorithm solving, not really practical though. 3x12 cases
1+1+1+1 modifications - 4LLL, just different order for each of the steps. I feel like the classic LL method is best, I think doing permutation before orientation on any piece is very bad, so that automatically would cut the cases in half to six. 12 cases
So these are all the 63 solution methods to last layer solving with completed F2L... Assuming you're always solving all EO, or all CO, or all, CP, or all EP in a single step, which almost every method does.
Anyway, I keep going a bit off topic, the goal isn't to theorycraft new variations here. My goal was simply to show a bit of structure when analyzing these things... Because if we're to improve on methods, and the structure of all the information out there is really poor, then it's difficult to build on it. The imperial vs metric argument all over again, just applied to speedcubing.
As for performing this kind of experiment, I agree that it's not really feasible to be performed by a single person. I am under the impression that after 2 years of extensive practice with a method, there won't be much improvement to be made, as we can see with many of the top cubers... However to keep that motivation for an answer that isn't meaningful in the grand scheme of things, and just stuff like getting slower with age. Anyway, what you discussed is kind of the brute force method, I feel like there must be some structure to performing some experiments where we can gain new insights, and uncover fragments of the answer one piece at a time.
@Aaron Lau https://community.spiceworks.com/topic/362862-tl-dr-top-or-bottom
I think the internet is against you
@xyzzy thank you for the long and well thought out reply, much appreciated.
Thanks for letting me know that it's not seen as good, I suppose I'd have to look at the algorithms closer to be 100% sure, but I'll take your word for it.
-VHLS + ZBLL are 32 (6.63moves) + 493 (12.08 algorithms)... Replacing VHLS with ZBLS saves 3 moves, but now we're up to 795 algs. With a LS Insert+LL move count of 15.63 (ZBLS+ZBLL is more, but ZBLS solves the F2L case, not inserts it, I tried to adjust it to only take into account the solving). Versus CFOP: LS (3.7 moves) + OLL (9.7 moves) + PLL (11.8 moves)... So CFOP LS+LL is 25.2~ moves.
-WV/SV + COALL (first time hearing this) is 108, though half are perfect mirrors, and taking your 150 for COALL, that's significantly less algs. Move count is and (8.07+9.4)/2, so 8.74 moves For WV/SV
So now we have in nice order of algorithm trade off:
CFOP: 78 algs at 25.2 moves
Wv/SV+ COALL: 258 algs at 8.74+(12)? = 20.74 moves
VHLS+ZBLL: 525 algs at 18.71
ZBLS+ZBLL: 795 algs at 15.63
Hmm, maybe I will need to look into it more, because we can see it's all tradeoffs, but I kind of like it in theory anyway. The issue with VHLS + ZBLL is that it splits the two into very uneven steps, where VHLS is way too easy compared to ZBLL, and that raises algorithm count too much. Instead this VW/SV+COALL would make the first step more difficult, and the 2nd step much faster... And edge orientation to me is quicker to notice as well... Really depends on how the algs look.
ZB method is designed when both ZBLS+ZBLL is used since then both steps are fairly "balanced", while if we did the VHLS -> ZBLS expansion for VW/SV -> solving any F2L case, you'd I think have an algorithm count in the 1,000-2,000 range, so that's no longer practical. But the entire basis for this is that ZB is balanced but requiring too high an algorithm count, while WV/SV+COALL is balanced at 1/3rd the alg count, but 5-6 moves longer. Hmm, I'll have to look at some cubing resources online to analyze this stuff, it's got me interested.
Interesting to hear that you've tried the building a 2x2x2 block, maybe I got the idea when I was quickly skimming through every wiki article, not sure.
Actually, with those 65 algorithm sets, when you start with a fully completed F2L, there's exactly 63 non-redundant solution paths. By non-redundant I mean, don't preserve EO/CO/CP/EP if you're doing an OCLL variant first step in a 4LLL.
The solution paths are:
4 modifications - 1LLL 1 case
3+1 modifications - 2LLL, OLLCP + quick finish type things 4 cases
1+3 modifications - 2LLL, ZBLL type of thing 4 cases
2+2 modifications - 2LLL, there is: OLL/PLL, CLL/ELL, LLEF+L4C, CPEOLL+2GLL, PLL/OLL (sounds awful lol), inverse of the 2GLL method (doesn't exist yet?)... I feel safe to say that out of those 6, OLL/PLL is the fastest. 6 cases
(2+1+1) or (1+2+1) or (1+1+2) modifications - 3LLL, I guess the only thing similar is was it BLL where the guy tried to get a 3LLL in under 25 algorithms? Well, there's many different options to explore here for low algorithm solving, not really practical though. 3x12 cases
1+1+1+1 modifications - 4LLL, just different order for each of the steps. I feel like the classic LL method is best, I think doing permutation before orientation on any piece is very bad, so that automatically would cut the cases in half to six. 12 cases
So these are all the 63 solution methods to last layer solving with completed F2L... Assuming you're always solving all EO, or all CO, or all, CP, or all EP in a single step, which almost every method does.
Anyway, I keep going a bit off topic, the goal isn't to theorycraft new variations here. My goal was simply to show a bit of structure when analyzing these things... Because if we're to improve on methods, and the structure of all the information out there is really poor, then it's difficult to build on it. The imperial vs metric argument all over again, just applied to speedcubing.
As for performing this kind of experiment, I agree that it's not really feasible to be performed by a single person. I am under the impression that after 2 years of extensive practice with a method, there won't be much improvement to be made, as we can see with many of the top cubers... However to keep that motivation for an answer that isn't meaningful in the grand scheme of things, and just stuff like getting slower with age. Anyway, what you discussed is kind of the brute force method, I feel like there must be some structure to performing some experiments where we can gain new insights, and uncover fragments of the answer one piece at a time.
@Aaron Lau https://community.spiceworks.com/topic/362862-tl-dr-top-or-bottom
I think the internet is against you
Last edited:
mark49152
Premium Member
No, I said it's the most obvious objective measure of a method. Or at least, I can't think of one that is more obvious.
Move count is of course relevant to how fast a method can be. That's so obvious that I'm not sure I haven't misunderstood your point.
Much of your analysis seems to be focused on algorithm count. Sure, algorithm count is an objective measure, but it has no bearing on your question unless you factor in lost time caused by the difficulty of recalling large alg sets, which is subjective and not directly reflected in the alg count measure anyway.
I'm not disagreeing with taking a scientific approach to method analysis, just pointing out that there is a lot of subjectivity involved and the presence of the word "objectively" in your question really makes it impossible to answer. Even your proposed mass training/solving experiment would not tell us what is objectively the best method. That would be a statistical conclusion, not an objective one.
AlphaSheep
Veteran
Given sufficient time to learn all of the algorithms in a set, and given plenty of time to practice them until you're completely familiar with them, I really don't think a large algorithm set (hundreds of algs) is that much of a big deal.
I don't have as much experience as many others, but I'm about 100 algs into learning ZBLL and I don't find recognition for many cases to take that long. I'll try explain what its like using a non-cubing analogy. You know how to recognise many types of animals, so you can recognise cats, dogs, horses, birds, etc. You recognise these animals by identifying the features that set them apart. Say you then learn how to identify many different breeds of dog. Obviously this has no impact on your ability to recognise cats, horses, birds, etc. Once again you recognise the breeds of dogs by identifying features that set them apart. When you see an animal, you take in all of the features at once and your brain recognises what it is based on connections it has built between the animal and its features. You can see an animal of a certain size with short white fur, many black spots and a tail and know it is a dalmation without first having to recognise it as a dog.
Because recognition for large sets is typically introduced as a hierarchical system of recognising, for example, CO then CP then EP in the case of ZBLL, doesn't mean that that's how you would actually recognise it in a solve. At first you do spend more time recognising a case, but with practice you start to notice the features in a different way and recall becomes very fast. I find it no more difficult to recall algorithms now than I did when I only knew 5 algorithms.
I think it's also worth mentioning that the ZBLLs I have chosen to learn are those that I started noticing without putting in any extra effort whatsoever. They all have features that I was noticing during the course of my normal COLL recognition. That means that I did not put in any effort to learn to recognise the ZBLLs that I know. I just had to spend 2 minutes learning the algorithm, and a week or two building up the connections between the case and the algorithm in my brain. In other words, larger algorithm sets do not necessarily equate to lower recognition times or more brain processing power.
Don't forget, your brain is optimised to an incredible degree for building connections and then recalling them. You've probably got a vocabulary of tens of thousands of words, with each one connected to a meaning, appropriate usage, etc, and your brain has no problem quickly pulling up the information it needs. Compared to that, a few hundred algorithms is small fry.
The big challenge with large algorithm sets is
I don't have as much experience as many others, but I'm about 100 algs into learning ZBLL and I don't find recognition for many cases to take that long. I'll try explain what its like using a non-cubing analogy. You know how to recognise many types of animals, so you can recognise cats, dogs, horses, birds, etc. You recognise these animals by identifying the features that set them apart. Say you then learn how to identify many different breeds of dog. Obviously this has no impact on your ability to recognise cats, horses, birds, etc. Once again you recognise the breeds of dogs by identifying features that set them apart. When you see an animal, you take in all of the features at once and your brain recognises what it is based on connections it has built between the animal and its features. You can see an animal of a certain size with short white fur, many black spots and a tail and know it is a dalmation without first having to recognise it as a dog.
Because recognition for large sets is typically introduced as a hierarchical system of recognising, for example, CO then CP then EP in the case of ZBLL, doesn't mean that that's how you would actually recognise it in a solve. At first you do spend more time recognising a case, but with practice you start to notice the features in a different way and recall becomes very fast. I find it no more difficult to recall algorithms now than I did when I only knew 5 algorithms.
I think it's also worth mentioning that the ZBLLs I have chosen to learn are those that I started noticing without putting in any extra effort whatsoever. They all have features that I was noticing during the course of my normal COLL recognition. That means that I did not put in any effort to learn to recognise the ZBLLs that I know. I just had to spend 2 minutes learning the algorithm, and a week or two building up the connections between the case and the algorithm in my brain. In other words, larger algorithm sets do not necessarily equate to lower recognition times or more brain processing power.
Don't forget, your brain is optimised to an incredible degree for building connections and then recalling them. You've probably got a vocabulary of tens of thousands of words, with each one connected to a meaning, appropriate usage, etc, and your brain has no problem quickly pulling up the information it needs. Compared to that, a few hundred algorithms is small fry.
The big challenge with large algorithm sets is
- Each alg requires practice to instil in muscle memory so that you can perform it fast.
- You have to take the time to build the connection between the case and the alg.
- You have to practice regularly to maintain both of these.
mDiPalma
Veteran
- Joined
- Jul 12, 2011
- Messages
- 1,533
not that it matters, but:
cfop last pair is ~6.7 moves - not 3.7. you are also forgetting to add .75 moves between each step for AUF.
>> cfop LS & LL is actually >31 moves (assuming you use optimal oll and pll, which nobody does).
you're also discounting methods like Snyder's LL (fish & chips) and commutator-based LS/LL approaches derived from Heise which blow methods of comparable alg/case count out of the water with regards to efficiency.
Y2k1
Regular
Random question what is snyder's method?
shadowslice e
Legend
Snyder2 is essentially FreeFOP with a different LL method. Anthony Snyder proposed it a while back and claimed it to be far superior to any methods ever invented (though he claims to have been the fastest in the world until 2004 or something like that but could never go to a comp because everyone was "organising things behind his back" and never invited him because they were jealous and though he was too good). You can read about it on his website snydermind if it hasn't been dropped and stuff but I warn you he does exaggerate a lot though to be fair it is not a bad method and definitely sub-10able of you put enough practise in.
There is also the hallowed "snyder3" method which he talks about as the logical progression of this method and will always give movecounts of under 30 moves thanks to "some innovations and new concepts he came up with" and will from there be completely computer generated and takes months for "very high aptitude" people to learn but he said he was going to publish a book which would instruct people how to do it and give anyone who read the book "all the tools to get world class times" once they had finished and perfected his method.
Y2k1
Regular
Umm... Wow. Thats all I've to say. What is the ll exactly?
Thanks for the description btw.
mDiPalma
Veteran
- Joined
- Jul 12, 2011
- Messages
- 1,533
doing an alg (fish) followed by a corner commutator (chips).
https://www.speedsolving.com/forum/threads/snyder-method-fish-v2-step-fish-step-ver-2.37503/
this doesn't fall into the OP's categorization because it doesn't solve an entire 'phase' at once. Yet in doing so, it outperforms most other methods. The "mathematical advantage" that Snyder likes to tout is legitimate.
Weston
Premium Member
You scrub. KiwiKaki was never on liquid.
4Chan
Premium Member
I WAS TRICKED BY THE AVATAR OH NOYou scrub. KiwiKaki was never on liquid.
AHHHHHH
mitja
Regular
this is becoming quite an interesting discussion, and it will probably bring us nowhere. I think, if you want to be fast, it is all muscle memory and TPS on the end. I believe CFOP is so popular as you need the least time to make most of the stages into muscle memory. What I see is, that people get faster when they bring last layer into muscle memory and even faster when they do it with F2L and the cross.
When does intuitive F2L become unintuitive? When you do it almost like a reflex movement. And the fastest speedcubers do just that.
Most alternative methods need much more rehearsal and time to become muscle memory.
Well, those Snyder solves that he does on his (horrible)webpage look amazing. I can just imagine how fast it could be if he could do it fast like Felix. But then it would not be described intuitive anymore. Ultimately in the future somebody will just do it in "gods" number, that would be the fastest. How much do they need for 20 or less moves? 1-2 sec?
For so called very intuitive methods you need time, years, maybe decades. But then you get older, slower with muscle memory.
So what are you searching for? The fastest way to become world level speedcuber? Probably CFOP? Maybe roux? And definitely, stay young. I can see on older cubers thread, guys with years ( I am also 49) can be pretty fast, like Mark above. But for real TPS (like Felix's 12) it is better to be young.
Just practise, you will feel when you start with muscle memory, when you start with lookahead and when F2L( or block building stage in other methods) doesn't feel intuitive any more.
Somebody complained over the words:
"do solves"
"look ahead"
"learn that other alg set"
"do this thing blind"
Yeah it sounds boring, but it is 100% true
When does intuitive F2L become unintuitive? When you do it almost like a reflex movement. And the fastest speedcubers do just that.
Most alternative methods need much more rehearsal and time to become muscle memory.
Well, those Snyder solves that he does on his (horrible)webpage look amazing. I can just imagine how fast it could be if he could do it fast like Felix. But then it would not be described intuitive anymore. Ultimately in the future somebody will just do it in "gods" number, that would be the fastest. How much do they need for 20 or less moves? 1-2 sec?
For so called very intuitive methods you need time, years, maybe decades. But then you get older, slower with muscle memory.
So what are you searching for? The fastest way to become world level speedcuber? Probably CFOP? Maybe roux? And definitely, stay young. I can see on older cubers thread, guys with years ( I am also 49) can be pretty fast, like Mark above. But for real TPS (like Felix's 12) it is better to be young.
Just practise, you will feel when you start with muscle memory, when you start with lookahead and when F2L( or block building stage in other methods) doesn't feel intuitive any more.
Somebody complained over the words:
"do solves"
"look ahead"
"learn that other alg set"
"do this thing blind"
Yeah it sounds boring, but it is 100% true
obelisk477
Veteran
It doesn't really matter if there is a consensus on a way to go forward since there actually *is* a way to go forward. I think your discussion would be useful if we were all stuck and not really improving, as if there were some inherent roadblock in CFOP that kept people from getting better. But that just isn't the case. People just keep getting better, including Feliks.
tbh, what OP reminds me of is just an intelligent and well worded version of the usual noob question 'what do i learn after OLL and PLL to get faster'. But no matter how well you state the question, the answer is always the same -- practice. Practice is the way forward with CFOP, and that has served everyone pretty well so far who has just kept practicing.
