I've been wondering lately if there will be any new speedcubing methods/techniques that are significantly better than current methods and techniques or if this is even possible. I have my half formed thoughts below and encourage other people who also dedicate too much headspace to this sort of thing to share theirs.

Consider that most speedcubing methods consist of two fairly discrete phases.

The Construction Phase - Which consists of putting pieces together that belong together( i.e. solving them immediately) while ignoring large portions of the cube (usually the last layer)

And it's best friend

The tweaking phase - Which solves the remaining portion of the cube by separating it into steps. Where each step solves the permutation and/or orientation of a group of cubies while preserving what was resolved in previous steps and in the construction phase.

I personally think that the construction techniques that we currently have fill every useful niche. That is to say I don't think that in the future a new construction process will be discovered/invented that improves considerably on current techniques.

Accepting that as a given (which is a bit of a leap) then any innovation has to come in the form of a significantly more efficient tweaking phase

Most Tweaking phases seem to begin with between 8 (LL methods) and 10(Groux, ZB..) cubies completely or partially unsolved. Each cubie has only two properties orientation and permutation. These can be considered separate problems so that each step can be considered to solve a set of Cube Properties(CPs) while preserving another set.

There really can only be as many possible steps as there are pairs of exclusive sets of CPs, a large number sure but finite. Most of these CP sets are nonsense and unusable for speedcubing e.g. Orienting DFR UF DL and FL while permuting UL UFR and DF. Most (if not all) of the 'Common sense' CP sets e.g. 'Orient Last Layer edges preserving F2L' have been widely used and many are very successful e.g.OLL PLL.

So for a tweaking phase step to be new but useful it seems it will have to use an CP set that is non-obvious but human usable and that it should be solvable with a good turn/CP ratio compared with current methods.

I think that there a few possibilities here:

that a conflation of existing common sense goals will be found to be useful e.g. ZBF2L (solve a c/e pair + orient edges)
perhaps for petrus method users we could use a similar set of sequences that solves our last c/e pair and simultaneously OLL, after all our LL edges are already oriented.


that a different (not necessarily better) construction method will lead to a non-obvious tweaking phase that has greater turn economy than current common sense steps (I think this is very unlikely)

So do you think that there will be any great new methods or not? What are your overwrought rationalizations?

Personally I think that new methods that prepare the LL further even than orienting edges during F2L and lead to a "one step LL" will prove to be useful e.g. I'm working on a method that uses petrus construction/edge orientation and builds a 2x2x1 on the last layer during F2L. This leads to a "One step LL" that is a subset of ZBLL about 40 cases IIRC. (I'm calling it goldfish becuase of it's similarity to fish and chips)

Anyway... I'll be surprised if anyone even reads all this crap let alone replies

Hrm, Heise method does something similar to what you explained in your method-in-development. In my opinion, construction phase should be the one most improved on. There's so many cases, i.e. lots of room for improvement.

I think intuitive steps and understanding are much more important than tweaking phase. Learning hundreds of algs can make you a couple seconds faster, but it doesn't really help at all.You learn nothing if you just memorize algorithms. Most speedcubers disagree with me, but I still believe I will be really fast some day even though I don't use Fridrich. (I haven't yet understood why people think it's a really good method)

Tweaking phase is bad also because there's always a delay when recognizing the case. But using intuition it's possible to solve the whole cube without any delays, because you understand what you are doing and can look ahead. (ok, you could look ahead during OLL and recognize what PLL case you'll get, but that's not really realistic)


I know 40-50 algs for that, and was going to learn a lot more. But now I understand that it would be useless.

Sorry but that makes you either blind or ignorant. Here's a reason why people think it's good:

Official world records:
- single: Toby Mao - Fridrich
- average: Anssi Vanhala - Fridrich

Unofficial world records:
- single: Andrew Kang - Fridrich
- average: Andrew Kang - Fridrich

And it's not only the #1 spots. What's the highest ranking non-Fridrich entry in any of those lists?

So the only reason is that most speedcubers use it? If >90% used Roux or Petrus or something else, it would make it a very good method, because world records would be set using it? There are only 2 color schemes that are commonly used, does it mean they are better than others?

No, the reason is that the best results were achieved with it.

Note I don't say Roux or Petrus are bad. Because I know they haven't been used as much. But you really shouldn't say Fridrich is not good when it's the method that has resulted in the best results. If you think another method is better, provide evidence. Until then...

I think that's because there are so many cubers using it. It's obvious that when hundreds of cubers use the same method, there are some really talented/motivated ones who get awesome results.


I don't mean it isn't good, but there are better ones. I simply can't see why saving 10 moves should be bad.


ok

Well yeah that's one possible explanation, another one is that the method is just good. Still, it's ridiculous to say the method that holds all the records is not good. Where's the evidence for that claim?

Got it?

No.

Btw, I didn't know speedcubing measures the number of moves. I thought it measures the time.

Oh and... whether or not this or that method is good or better or worse than another... what you (implicitly) asked for is why others believe Fridrich is good. And I think it's the records. That was my reason, at least, when I started serious speedcubing and had to decide which method to use.

I never said it measures the number of moves.

Just not explicitly.

So you think the number of moves doesn't matter? I think it makes sense to use 45 moves instead of 55.

I don't say it doesn't matter. It's a good indicator. But it's by far not all that counts. What counts in the end is the combination of all factors, measured by time. Per can quite regularly solve a cube in 25 (!) turns or less with his method, does that mean it's by far the best method for speedcubing? I doubt it. Btw, where did you get the 45 moves from? Even Lars Petrus himself says he averages 60 moves for speedsolving and Gilles Roux reports 48 and that's STM.

FMC is not the same as speedsolving.


I've heard many times that most cubers who use Fridrich average around 55 moves. If I use ~25 seconds, I average around 45 moves. That's not speedsolving really, but 45 when going full speed is easily possible for me. I don't use just Petrus, sometimes Heise or some FMC tricks.

On average?

On average. Not yet, but soon.

I trust you have evidence for that "but soon"?

I've had huge problems with step 2 for a long time. Just recently I started practising it a lot and I'm getting better, in several weeks I should be able to average around 45 moves in speedsolving.

Ok, then I wish you good luck with that, let us know when you achieve it. Can you tell how many moves you average right now when going normal full speed?

Because of the bad edges stage and the fact that I don't solve two edges in that last step it's really not that similar to Ryan's method. It's more of a petrus variant. (or a fish and chips rip off). Also it uses alot of memorisation so I'm sure ryan wouldn't want to be associated with it

edit:
My original post was more along the lines of "Will there ever be significantly better speedcubing techniques and methods then those we now have." and less along the lines of "are non-intuitive steps disgusting spawn of the dark lord"

I was hoping this would be a discussion of future methods and what characteristics of them we can predict.

e.g. what will a better construction phase be like? obviously it will use less turns. Will it clump unassociated blocks like ryan heise? will it be an improved method for CFOP F2L that allows for more double slotting? Will it go further than F2L?

Johannes is right. It's definitely possible to use very few moves when speedsolving. When I solve I use an average of 43 moves when going full speed and I'm sure there are at least a couple other people that use 45 or less.



You really shouldn't say "best" when it's pretty much the ONLY results.



Oh, sorry. I guess future methods will probably either have lots of memorization or very very little. Not many in-between. Maybe there will be even more memorization based methods since people are lazy.

Which metric is that and what are your times?


Why not? They *are* the best.

It's STM. I usually only time myself once or twice a month. I probably average around 23 I guess, best time of 18 when I last timed. I started this "change" a month or two ago.



It's like the best compared to itself. It just doesn't seem right to me to say that it's had the best results when few other things were tried.

I really want this to stop soon. This was a great topic idea and would be a nice discussion.

I think ZB has shown to be faster then fridrich on average, but there are only a handfull of people studying it.

Sure? How?

Oh and to be constructive: Gerard, how does the method that first orients edges fit into your framework?

Are you referring to Ryan Heise's Human Thistlethwaite Algorithm?

seems awsome.

I think ZB has been shown to have a lower theoretical turn average than fridrich but I don't know of anyone who actually uses it. I know alot of people use ZBF2L + OLL + PLL and a bunch use ZBF2L + COLL + Permute Edges but I don't know of anyone who claims to use ZBLL in full speed solving. This leads me to believe that future successful methods will not use steps with more than a hundred distinct memorised sequences.

Does anyone know of any other methods where a step has more than a hundred cases?



If you are talking about the human thistlewaite algorithm, then I guess it's a method that has no construction phase... which is quite interesting. Can people actually get good times with it?

A phase that doesn't seem to be common among good methods is a "rough sort" phase e.g. in ring method iirc the steps are

1. solve E slice
2. put all the cubies that belong in the U layer in the U layer
3. there must be some parity fix phase?I'm not sure
4. OLL + PLL the U layer
5. OLL + PLL the D layer

Step 2 is a rough sort. Do any other methods have a rough sort?

Does anyone have a better name for the Tweaking phase it just sounds unbearably stupid.

44, 48, 47, 45, 52, (56), (41), 42, 52, 47, 53, 41 => 47.1 HTM
No lucky solves. Around 1-2 seconds slower than my normal avg because I had to count the moves.


They are the best results, and pretty much the only results. If there were hundrerds of speedcubers using Roux and Petrus, it would make more sense to compare the best averages.

For example, yes. Or any other method that orients edges first. Imagine you could build a CFOP cross and at the same time orient the remaining F2L edges so that you can solve F2L purely in without cube rotations. And if you can even include orienting the LL edges so they're already oriented after F2L...

gerard wrote:

Step 2 is a rough sort. Do any other methods have a rough sort?

I once came up with this idea: First separate the pieces into four areas of equal shape. First area is the 3x2x1 block from UFL to UR. Next area is at the same position after an x-rotation. Same for the remaining two areas. So after separation, solve the areas one by one with one alg each, possibly affecting the unsolved areas if needed or advantageous.

Fewer turns, that's correct. How does that show it's faster?

And the general question: How do you prove one method is better than another for speedsolving? Is that possible at all?


Hmm, where's that from? Chats? I admit I don't chat. But I've almost never heard someone say he can do ZBF2L, i thought it's at most a handful of people.

That is awesome.



Can you give an example solution?

I started working on "ZBLL" in the summer of 1981, though I didn't and don't call it that. Since I picked the cube up again about 4 years ago I started developing it again.



Its hard to say. Learning "ZBLL" is the first step in becoming really fast. Look at the intrinsic quality of solving the LL corners when placing the final First Level corner(s)...the end result may be a one-look solve.



Since I'm a little over 25% to the goal of "ZBLL" I guess you could call my 300 hundred plus algs part of my method...

Cheers,

David J

for speedsolving by humans? no.

there are alot of useful metrics that suggest how good a method is

Average Number of turns
Number of looks/steps
How intuitive it is
How successful have people been with it in the past

but proving it is impossible because the human's ability/drive/good looks are so variable.

about the Cross + orient all edges idea:
Would doing F2L while preserving orientation be slower than doing F2L then fixing the last layer edges?
edit: It has recently become obvious that the tiny turn restriction won't slow you down at all.

Sounds really interesting though, I'm going to learn ryan's human thistlewaite thingy so I can understand that a bit better.

As part of my ongoing saga conflating small steps has anyone tried using a set of algorithms to permute corners and finish (Petrus)F2L at the same time? because I believe you are then left with only 47 possible cases.

David J:
Are we talking about the same thing with ZBLL? A set of algos to do the last layer in one step assuming that it has oriented edges.

It sounds like you're talking about something else.

I know a couple people that use VHF2L (including myself in some dumb cases), but ZBF2L? I don't know anyone who actually uses that for anything yet.

Also, move count is not necessarily directly proportional to speed.

Keep in mind that it's not always better to have all 4 edges oriented (during F2L) before OLL(ZBF2L). Some OLL with only 2 edges oriented are faster/shorter sequences than some with all 4 LL edges properly oriented.

There's simple ways to make your solve easier, partial edge control for example. I think simple shortcuts like that would be great to hasten speedsolving times. Just have to find more like that....

uuh, can you elaborate?

Hi gerard,

What I think of as ZBLL is solving the Last Layer in one alg, and this includes all of the edge positions alone, and with corner positions. Something like 1211 algs.

What you describe is combining CLL and EPLL. That's CornersLastLevel and EdgePermutationLastLevel. I forget what it's called.

Cheers,

David J

No, ZBLL only includes cases that have edges already oriented. 493 (I think) cases, including mirrors and inverses. You are talking about 1-look LL. It's 1211 if you can inverse and mirror algs on the fly, but that doesn't sound fun. For regular humans it would be several thousands.

ZBLL is useless.It takes the focus off of basics, and basics is ALL you need.

Those are useful for comparing methods but IMO they do not show how good they are.

Average number of turns almost shows how good a method is.

Hi Mike,



This is true for CLL as well.



I rarely arrive at the LL with all four edges flipped over; usually two, though I figured out an alg for what I call "reverse headlights" that flips all four edges - in 11 moves. R B L U2 L' U2 L U2 L' B' R'

Cheers,

David J

FRUR'U'SRUR'U'f' is pretty good too.

HI guys Yes fmc and speeding are 2 separete worlds. I can keep on refining my solutions iteratively, working on many ideas. Speedsolving, then u solve the cube in one go. No way to do a certain step over again to see if it's faster to do it another way. And yes i agree that a methods avg number of moves is only an INDICATION of its potential timewise. if a method has a higher proportion of "intuitive" steps. Or it has extremely many cases for some step it will be harder (but not impossible) to go fast with the method. Fridrich is fast simpy because lots of people have contributed to finding very good optimimised algs for most cases and also the fact that 95 of speedcubers settle for that method. If those same people had used say roux-method then we would see roux method also dominate the record lists. I'm sure of it

-Per

PS! amongst the techniques i use for fewest moves i think only blocks first (Petrus) is really suitable for speeding. my edges-first approach has nothing to do with the edges-first i have done speedingwise just for fun. Likewise, not every corner-first method has to be similar. It could be done just like some 2x2x2 method regardless of edges, or while trying to get at least SOME edges solved .... etc ....

I would prefer calling the 2 steps the skeletal phase and the completion phase. And i think both those 2 phases still can be improved for most methods. For the completion phase fewest moves solving has a great advantage : insertions. When ending up after f2l with 3 edges unsolved and 3 corners unsolved the standard CFOP procedure prescribes OLL + PLL. This may be 20+ turns or even 25+ turns if using no lookahead at all. Direct solving will be at most 10 turns for the edges and 10 turns also for the corners. With insertions the chance of saving(cancelling) more than 5 turns (compared with 2 straight cycles right at the end) is quite good. In fact, the skeletal phase for fewest moves is by far the most important. It's important to pair up as much of the cube as possible while still having a high degree of freedom to utilise.

-Per

OK, theoretically u will benefit from learning many methods. But when u sit there with a scramble and ur 15 secs pre-inspection, how the h*** are u gonna be able to select the *best* method For fewest moves u can always try all the different approaches (if u have time!). Practically it's not always a good thing to learn many methods and many special cases. In the end it may end up confuse u and make choices harder, where the choice should have been automated (just do a learned case). Learning *too much* can actually make u solve slower. I have often heard cubers tell me that when starting to learn VH or ZB their times actually go worse (on average) but that they do indeed set some blazing fast times every now and then. Only after using the new stuff for a prolonged time did they se their average times go better again In the end it's the delays between steps that will kill ur times. This is described very well on Jessica Fridriech's page here.

-Per[/url]

Nice and easy to remember.

I agree with R.E.T. because as he said mostly everyone will be using the fredrich method, so there isn't often debate as to what the fastest system is, and therefore, fredrich always remains at the top simply because of odds because if 7 in 10 speedcubers use fredrich and 1 of 10 become like nationally ranked, theres a very good chance that they will use some version of fredrich, so it really isn't an accurate portrayel of the best or fastest method.

Also, I had a question...

What is the method that requires the least amount of turns?

-FireWezul