These are my rantings. I shall type these without researching further right now, and will cover as much as I can.
This is a good method. There's absolutely no doubt about that by anyone who's paid attention to speedsolving since J. Fridrich popularized it (read: not discovered). Regarding how /good/ this method is, it seems to be the one most people get sub10 with. Or sub-20 with, etc. CFOP has been popularized to a very very appropriate extent considering its power, and I don't exactly expect to see it die out any time soon. While most of the world records have been set with this method, and slight variants, I don't believe enough research has been done for cubing, which leads me to become disappointed when a new user joins the forums and an older member straight off the bat says 'CFOP is the best; don't even bother with anything else.' Sure, CFOP is the method that's showed us very good averages, and is the most documented method, but something leads me to believe that this might not be the order that sentance should be in.
CFOP is far better documented than any other method I've seen out there, be it any puzzle (purposely ignoring LBL because as referenced it's just not as good, to be honest. More on that later). More experimentation and documentation needs to be done has far as cubing is concerned, which is why I frequently do such. Before I allude too deeply into other methods, let me just note my personal experience: I average better with pure CFOP than with any other pure method. This amounts to me averaging 17s with CFOP, and 18-22 with the other big 3. It's pretty sweet.
I honestly think that this would be my best method (of the big 4) if I were to ever bother practicing it as much as I have CFOP (or for that matter, Salvia--more on that later). I've done my fair few-hundred solves or more of this to test and play around with it, but I just never found the time/will to do such. Roux is a block-building method at heart, which means that you really have to think well, and think quickly. I believe I can think well, proven slightly by fairly decent (imo) SpeedFMC, by my abilities of thinking quickly are minimal. This has haunted me in other aspects of cubing as well, but this is notably important in methods such as Roux. A note on personal experience quickly before I forget: I average ~20 with Roux, compared to ~17 with CFOP, and this has been done with much less practice. Also notable, my movecount on linear FMC solves with CFOP is ~55 while my speedFMC solves with Roux seldom go above 45. I don't know *full* OLL or CMLL which somewhat brings about a level playing field in terms of ability, but I won't use that as an excuse here as to why one method is worse or better than the other.
I love M-slice moves. If I'm fast at any alg set, it's something with M-slices, I'm sure. This, while not shown through other methods (Petrus, ZZ, CFOP) is focused fairly well here in Roux, and for this, I get a little sense of joy about being /finally/ able to spam algs unlike what I can do in, say, CFOP. I know not everyone will get this source of joy, but that little spam of my left ring finger and my right pointer finger is more enjoyable than any other algset. This also translates into ELL, and methods that use such, but with Roux,--it's just something else. Roux's a really really good method, that's been pretty well documented (both by the creator, Kirjava, Waffle, etc), thankfully. Actually, I think Roux's documented well enough at this point. Sure, more can be done, in terms of variants, algs, etc, but Roux is a really solid method, where one really just needs to know the basics to do well. Oh, and lots of practice.
I'm not really a fan of Petrus, past the 2x2x3. I'll make that rather clear here. I love that block-building is more-so popularized by Petrus, but as a method in whole, there's just something to it that's a turn-off to me. I think it's the EO stage. I won't outright say it's "bad", because it simply isn't, but I don't think I'll be practicing it much.
Petrus is kind of well-documented. There's an obvious general hub or two of Petrus solvers (Lars' website, that site advertized on SS by some thread that's frequently on the homepage). These two sources are surely enough to get one into Petrus, but I don't feel that enough different approaches to teaching the method are yet presented. Fortunately, there are enough after-EO approaches to take that *are* well documented, somewhere or another. I think a single collaborative page *coughwikicough* divided by users' preference of approach would be pretty awesome. That's all I really have to say for Petrus. It's solid, decently-documented, and--I don't really like it. Meh, I'm not sure why. I average ~21 with it, btw.
Oh, another thing, very quickly: I've noticed that Roux and CFOP users generally like to push their methods. I've seldom seen this from Petrus users, and whether this is due to a decreasing number of users or simply a humbleness to them, I appreciate it! It's painful to see someone not open to other methods.
ZZ's really really cool, guys. This needs to be documented more. Not only is this a really nice OH method, which has been proven (most notably by kittens), but it's also a pretty good 2H method. I won't go into all of the crazy variants individually, because I just honestly don't know enough about them. Like Roux and Petrus, ZZ needs your brain. Badly. Not only is EOline hard to perform efficiently and quickly, it also CONTINUES to need your brain further on. It's pretty damn intense.
As far as documentation goes, I have to give a huge shout-out to Conrad Rider for doing what he's done. More credit needs to be given to him, not only for this method, but for VisualCube, his algorithm translator, his immense work on the wiki, etc. Conrad's page is definitely the place to go for ZZ users. After that, it seems as though ZZ users just PM each other. This should be fixed. I would revive the old ZZ discussion thread, but I'm just not enough into the method any more to do such. I average roughly ~18-19s with this, and have practiced it only a tad bit more than Roux. I still often use this method, especially for OH.
Although I did not invent/discover this project, it's certainly become my baby. For this reason, I'm going to go on and on about how much I like it, similar to how a mother brags about how her son just won some worthless little-league game that he won't remember in a week.
First, let me clear up something. L2L4 was not named such for solving the 'Last 2 Layers in 4 steps.' Rather, it was the fourth proposition by Duncan Dicks to solve the L2L (last 2 layers). I had first believed that the other definition was true, until corrected by Thom. Thanks for that. On the note of L2L4: it's pretty good. It's not going to blow other methods out of the water, but sub20 is easily possible with it, and sub15 with practice. With hopes that this won't become too much of a tutorial: Duncan's 4th proposal (again, L2L4) was to solve the first layer in one step, then solve each E-Slice edge while performing a permutation or orientation (of either the corners or edges) of the last layer, individually. Being 4 steps after the first layer, solving in the order of CO, CP, EO, EP, this is where the false definition of L2L4 comes from. Although this is pretty neat, the EO and EP steps don't match up to the speeds of the L2Lk approach.
L2Lk is the method I'm currently learning. At a whopping 210 total cases, it looked to be a fairly daunting task. Rather than doing EO and EP last, like what L2L4 does, L2Lk sets up an ELL case by solving both of the E-Slice edges at the same time, then of course does ELL. Some quick advantages before I discuss alg count: alg-count ( ), move-count, sexiness of algs (<3), and use of an alg set within another method (L2E and ELL are both pretty sweet, and I've used them a number of times in CFOP solves).
Onto L2Lk alg-count in order to hopefully encourage others to learn: while there *are* 210 cases to L2Lk, you only need to learn about 80 algs. Not yet /entirely/ documented, this algs in their currently most final form will be released shortly. "How are there only 80 algs for 210 cases?!" Simple, we ignore 80 cases of CO, and we use commutator magic. Ask me personally this, or wait a bit for further documentation.
That's all. That's my baby. I'll shut up now before this becomes even more of a tutorial.
That'll be coming soon, though.
It'd be a shame if I just willy-nilly lumped all of the corners-first methods together, SO I'LL MAKE SUBSECTIONS.
{beginners corners first} Documented most heavily of course by Waterman, this is an alright method for a beginner. There's not much to say about this, as I don't have much personal experience here, so I won't pretend like I do, and I'll stop here. I'd rather not go into beginners' solutions here, as beginners' solutions are designed in order to teach how to cube, not how to cube quickly.
{sammich} I don't even think anyone /really/ does this. It's a pretty awesome method for 4x4, and if I ever bothered doing that puzzle I might switch to it, but for 3x3--well, it's still pretty good. Averaging less moves than CFOP for me, this corners-first method has proved to be a pain. It makes you learn new approaches for dealing with edges, as you have to pay attention to a lot while making use of your high doses of freedom. This is a really neat method to play around with, and I'd encourage anyone that wants to have their mind bent to do a hundred solves of this.
{Waterman} This is the king of corners-first 3x3 methods as far as I know. An influence of Roux solving, Waterman has a really low movecount, at only a bit over 100 algs. When I say low, I mean sub-45 linear is common (read: STM). I've only done, erm, 50 solves with this, if that. For that reason, I'd rather not go too much into detail, at risk of either giving misinformation or embarrassing myself, independent cares. Anyway, check it out, it'll thwomp your mind.
This--you have to really use your brain for this one. It's like block-building--but a bunch of little blocks that you have to build separately while making note that you can't use a certain color. It's fairly intense. And by intense, I mean rage-inducing, unless you know what you're doing. Oh, and guess what? After you do those crazy blocks, you have to form yet two more pairs. Oh, and then use a commutator. Have fun with that.
I don't mean to push anyone away from this method. Just the oppositte. Just know that you're not alone in your frustration. You really can learn a lot solving this way, even if you never use it after your first 30-odd solves.
Ha. I remember when I thought this was potentially a really good method. That's when I was solving about a minute, and anything that would allow me to think I knew what I was doing was a pleasant surprise. Sorry folks, edges-first doesn't look promising, nor did it ever--unless you're doing BLD, in which case go ahead!
This is intense. The only real posts about this method are in the Random Cubing Discussion thread. It uses the same idea as the computer Thistlethwaite algorithm to solve a cube (fairly efficent, definitely not optimal), but allows processing by a human to be possible. I'll link those posts here in an edit if I remember. Otherwise, just do a quick ‘site:speedsolving.com "random cubing discussion"+"Human Thistlewaite"‘ google search and you should find stuff quickly enough.
This method got me to my first sub25 average. Noting that: this method really isn't good. It doesn't have any positive features that I can name that counteract its bad features. I used this method because I was dumb and didn't know better. It's not /terrible/ but it's definitely not amazing. Or even good. At all. It's a lot of awkward slices in places that fingers just shouldn't go.
I put (Method) here because it's been only recently that I've seen this method referenced without it there. Often referenced by ‘TFM' this method was created seeming for lulz, but is actually more promising for speedsolving than methods created for speedsolving. Erzz is doing a pretty good documentation of this, which is really cool, and I'm slowly helping him find better algs for CSO.
Things I left out on purpose:
Hahn, because it's not very promising.
Belt, because it has rediculously long move-counts rendering it nearly useless for speedsolving.
Tripod, because I simply don't know enough to utter more about it apart fromteh fact that I don't know it. Oh, it's called ‘tripod,' so maybe something like "gogo make f2l-LS with some method ___"?)
First, I have to complain about the naming of ZBF2L. I really wish it were named ZBLS, corresponding to the naming of CLS, CPLS, ELS, etc. Sure, you can do the edge orienting during some other slot, but it's typically documented otherwise. Can we please call this ZBLS now? As for the actual method: it could have benefits over standard F2L, {OLL, PLL} or {CLL, ELL}, but considering only 3 people that I know of know it (I'm counting you in this, Spef!) and there hasn't been any notable improvement of times with ZB that I know of, this direct comparison between CFOP and ZB(LS, LL) leaves me thinking that it's just not worth it. Please, though, prove me wrong!
Seldom used by common MuGgLeS, this ironically-named wizardly system of solving LS+LL has intrigued me more than most methods. Having a pretty good move-count, apt documentation, and good algs [takes slight bow], I'm somewhat surprised this hasn't yet taken off. There's not really much to rant about here. Maybe people are put off by the alg count? Or maybe people are just happy with their little CFOP world? Either way, I suggest checking it out. Macky's site for algs, Lucas' for most info.
I don't think anyone uses this, besides Snyder himself. Correct me if I'm wrong. The wiki page is decent enough, and algs are--I'm not sure if they're available actually. I think that this is just too similar to other methods to attract anyone to research it. Maybe he'll release his super-secret third(?) system if you give him money! [if you don't get the reference, don't worry about it]. I'm not sure whether I'd consider this a full method or just a LS+LL method, or for that matter, a LL method. I'll just throw this here.
This was simply the top-of-my-head and arbitrary name that I gave the system of CPLS+2GLL. Totalling 100 algorithms to solve LS+LL (after EO, sorry), I wish more people knew (of) this. It's pretty neat, in my opinion, and while the CPLS recognition takes a bit to get used to, I'm sure someone could come up with a better system for it if they had another angle of looking at it. Oh well, just another method that no one cares about.
Being the de facto LL method, I think I should be able to assume you know what these are, both OLL and PLL.
You solve the corners of the last layer. K, now do the edges. That's it.
The only think I can really rant about here is how I think CLL/ELL is better. At least for me. It has less moves on average, less algs, and--well, I just honestly love <M,U>spamming.
I included stuff that I have more knowledge of than others. This post was made without looking up stuff, so I could keep a rant-flow going, but I understand your disappointment.
Also, I forgot about Columns I'll add those in later.
So those are my rantings. Usually when I have time at work where I'm given little to do, I program a secret cubing thing, but I decided to take the first 2 hours out of my day to write this. I was in the writing mood, and thought someone might be interested on someone else's perspective.
-statue