MGLS

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MGLS
Makisumi-Garron Last Slot
Lucas Garron; June 15, 2007 & December 2007
Note: This page will render best in Firefox.
Sometime in late 2006, I was browsing through Macky's site on his old domain, and came across an obscure link on a page of miscellaneous techniques: "F2Lc+LLCO". He described a neat alternative to Fridrich he was investgating, though he never finished. I adopted his idea, found algs for every case, memorized them -and did all of that work myself. However, I probably wouldn't have tried that if it weren't for Macky. He's the inventor and I'm the engineer, so in the compound naming style of "ZBF2L" and "VH," I'm proposing "MGLS" as a speedcubing approach to solve the last F2l slot & LL of a Rubik's cube:
MGLS can simply be interpreted as a method for last slot that serves as an alternative to Fridrich; instead of placing the last slot pieces and the orienting LL, in that order, both steps are done together, first for edges (ELS) and then corners(CLS). The edges have enough free movement to require slightly fewer moves for ELS than slot placement does. CLS has quite a few more algs than OLL, but the offset involvement of the LS corner allows for nice algorithms; recognizing either CLS or OLL as the better of the two is mostly subjective (which one takes more twists, on average, depends on algs, execution, and move & metric counting scheme -though CLS is ideally shorter): I consider them very comparable.
In the course of adoption, I have found several distiguishing features to MGLS. Most of these stem from the CLS step in comparison to OLL. I had first considered using MGLS algs for 2x2x2 (get 3/4 of a face, CLS, PBL), but it turns out that porting algs is horribly inefficient -although Timothy Sun is working on finding CLS algs specifically for 2x2x2. However, the most peculiar feature of CLS is that it does not orient edges. Unlike most OLL cases, CLS cases do not need algs that turn at least 3 faces: it is possible to resolve every CLS case with an [R, U] 2-generator algorithm! This is not an amazing advantage for 3x3x3, but is very beneficial for one-handed solving and bigger cubes. Alternating between two faces without major regrip allows for faster, smoother algorithm execution. There is a tradeoff: in order to select only 2-gen algs, one loses the slight move count advantage over Fridrich. However, I believe this is a pleasant choice: How would you like it if you could replace your worst OLL's by a 14-move 2-gen alg?
Enough propagana. If you like MGLS, use it, if not, don't: no one but me will chide you for joining the mass of Fridrich clones. I gope this site makes sense and works well; I've set up a new database system that allows you to finds algs easily, feel free to browse and send me emails. I have several features under consideration, and I just might implement a few. Anyhow, have fun: May the algs be with you!

Several cubers are learning MGLS. The following lists those who are so cool that they have adopted the method and have finished learning it:

Lucas Garron (June 2007)
Justin Adsuara (Dec. 25, 2007)

A standard choice for last slot is necessary to avoid confusion. I use the front right slot as a convention, even for mirrors (so algs are reflected across FR-BL).
Need to find an alg for a case? You can browse thumbnails of all the cases!
I have made a single-page PDF alg sheet that contains everything necessary to learn both steps, a revised version of the one I used for learning all the algs. Fold it in half vertically, and then fold each half in half before closing the middle crease.
The sheet should be self-explanatory enough to be usable. Sorry if the text is a bit small right now —sometime, I will try to either add an explanation or make it simpler. I will also create a simpler version with one alg for each case, once I've decided which to use (for now, I just left every option) and received any requests. And I'll probably make a page for printing a PLL reference on the outer flaps. Depends on what's popular.

Step	Description & Notes	Goal
F2L, minus last slot	Several solutions arrive at this step; any can be used: 3 slots of standard Fridrich F2L (CF[OP]), Beginner's F2L, Working Corner/Keyhole, or any other such Cross+F2L solution. Extended Cross works well, too. Look around for this; I personally recommend Macky's page for learning F2L. Also see Fridrich's pages. Petrus up to step 4a. A Petrus solve will already have edges oriented, so ELS can often be done in only two extra twists. Heise's square-building. F2L with edge pre-orientation. This could work very well with MGLS... (See Zborowski's page) I'll experiment more with this as I get faster.
ELS	Edge step of the Last Slot: The edge of the last slot is placed while the last layer edges are oriented. 21 cases/13 algs+mirrors, ≈6.5 twists (average)
CLS	Corner step of the Last Slot: The corner of the last slot is placed while the last layer corners are oriented. 104 cases/56 algs+mirrors, ≈9.5 twists (average)
PLL	Permutation of the Last Layer: All the cubies of the last layer are permuted (placed/positioned) correctly. Macky, Vandenbergh, and "Peter" all have excellent PLL lists. 21 cases/14 algs+mirrors, ≈12 twists (average)

The only reason I brashly went ahead and named this method (with Macky's consultation) was that it became annoying telling people about "that method for which I found the algs but the idea for which Macky came up with (and also found some algs for, but not all of them, and never fully developed and employed)." So I considered the similar nature of ZB, and eventually got used to calling it MG. I cast it as MGLS, not MGF2L, because it's really only a set of two steps -not an entire solution, even for F2L- and I find it much more appropriate to make an easy choice of accurate description. Anyhow, Ryan Heise originally used ELS in his method and Andy Camann helped Macky, so it might more appropriately be called "HMCGLS" -but that loses a certain ring... If people want to call it something else, that's fine -cubing reaches a lot of standards by adoption consensus, and I'm sure that whatever happens will be appropriate.
(Incidentally, note that MG are the initials of our last names, and LS of our first names :-)
On this page, I'm simply presenting the method, and providing sufficient algs for it. I'll leave discussion and argument and criticism to the speedcubing community.
I have not configured the half-twists in the algs yet. Feel free to turn them in whatever direction you chose and make up your own finger-tricks (you can also do U3 instead of U', for all I care :-). Just don't be distracted by inefficient directions in the applets. I will fix the half twists but not add any finger tricks, except in the comments. I will leave the customization up to you.
I haven't checked every single alg and link for formatting or notation errors, though I've rarely encoutered any and always fixed them. Do inform me if you find any.
Macky found 2-gens for all - and O CLS algs. He also has a few different ones on his page (where you will find the numbering scheme used in the 2-gen text file). I'll review these sometime, and also post the first few dozen algs returned by Cube Explorer for each case. And then I'll figure out how to use ACube and ksolve commandline, and find 2-gens for everything (UR and UF), as well as 3-gens (URF, URL, URB), and rRU algs.
It's nice to also know a few tricks. Mini-ZB is useful here, if the corner is already placed at ELS (you can even learn the ones where it's misoriented, to be really prepared). Partial edge control/WV can be useful, too, for conserving the CE-pair if the LS pieces are joined at ELS.
Tell me if the design of this page, especially the frames, is causing any problem (I already got rid of the site menu, and right now I can't figure out why Firefox adds a blocked scrollbar to the bottom of this page...) in a reasonable browser like Firefox. These pages do not show up well in Internet Exploer, a consequence of its inability to render CSS properly.
I've tried to make these pages as accessible as possible; for example, each alrorithm animation displays in the lower right frame alone (tell me if on some browser you don't see the frame pop out)... I added an image-only reference, maybe someday I'll even add a text-only, if I can find a good way to do that with a monospaced font. Again, I'd like to hear about anything that's not working well.
I'll also create (a zip file for) an folder that can be used to browse this offline, once the content is sufficienty finalized. More PHP coding...
So, if for anything you have a comment, suggestion, remark, correction, etc., you can email me at lucasg (at) gmx.de [replace "(at)" with "@"]

Happy Cubing!