Why MGLS??

[El Veintitres]

So I've been reading up a lot lately on some of the crazy last layer methods out there. And I understand like ZB, and EJ and COLL and such, however, earlier I came across MGLS. And I am at a loss as to how it is faster than CFOP. Basically you take the last f2l slot and instead of just solving it, and then doing OLL, you instead place the edge and orient the edges of the last layer in one alg and place the corner and orient the corners of the last layer in another alg. So... why is this faster. It must be if people are willing to learn the 130 algorithms or whatever it is, but I am just at a loss as to why MGLS is faster than just placing the last slot and doing OLL. I mean you still have to recognize two cases and do two algorithms in both methods, so why is MGLS faster? I'm just curious, I don't intend to switch away from Fridrich anytime soon, but if someone could give me an explanation it would be much appreciated.

 

[Dene]

There is no evidence that this method can be faster than Fridrich at the moment. Only two (I think) people have fully learnt the method, and neither of them are at the top level of cubing. However try looking at it like this:
Fridrich: Last slot then OLL
MGLS: ELS then CLS
So there are the same number of steps here. However I am of the understanding that the overall move count for the two steps is slightly less in MGLS. Also, CLS can be done very nicely 2-gen (I'm not sure if it can all be done 2-gen someone correct me on that). This is very nice for finger tricks. OLL is not done this way.
So it seems that MGLS has a lot of potential, but overall it is roughly the same as Fridrich. If you feel the need to learn it instead of OLL then go ahead. Otherwise I'm sure you'll be fine.

 

[Lucas Garron]

No one ever said it's faster. It may be, I don't know. But I suspect that the MGLS-F and pure Fridrich are so close that practice and ability matter more than the choice between the methods.
At the very least, MGLS is not slow. The fastest official non-Fridrich was done with MGLS-F, not Roux or Petrus.
Myself, I am not particularly consistent with my solves, but I don't think I'd be significantly better with Fridrich. But I still practice 3x3x3 speed, to show that MGLS has some potential.

There are a lot of factors that distinguish the methods (mainly stemming from CLS vs. PLL), including optimal/comfortable movecount, 2-gen, recognition, number of algs, intuitiveness, community development, performance in different solving circumstances, compatibility with other methods, etc.

In particular, "130 algs" is not bad at all. The algs are often quite easy to learn, and ~half the cases are mirrors. I maintain that if anyone can learn full OLL, they are also capable of learning full MGLS and retaining it with the same ease.

So, MGLS is not "faster." It's an alternative. There aren't very many sources, but if you're really looking at Fridrich variations, I suggest that you try to understand the benefits and drawbacks of MGLS, and make an informed decision whether to use it or not.

 

[blah]

Well. You get almost twice as many skips for ELS than for the fourth slot.

 

[Stefan]

You get almost twice as many skips for ELS than for the fourth slot.

And what about CLS vs OLL?

 

[Namegoeswhere]

Petrus + MGLS seems to be quite good.
http://www.youtube.com/watch?v=1yn1wLkC1eI&feature=channel_page

 

[trying-to-speedcube...]

Chance of skipping corner last slot: 1/5*1/3=1/15
Chance of skipping CO of LL: 1/3*3=1/27
1/15*1/27 = 1/405

So that's almost twice as few skips with CLS than with OLL.
Conclusion: No real advantage when talking about skipping chances.

 

[blah]

You get almost twice as many skips for ELS than for the fourth slot.

And what about CLS vs OLL?

That was supposed to be sarcastic, sorry if I didn't make it (the sarcasm) clear enough. I believe not enough people have ever taken MGLS seriously enough, which is kinda sad, was hoping that would instil some faith in the sub-method For the record, I've learned full MGLS in different stages of my cubing, umm... "career". I've learned different CLS cases when I was experimenting with different ideas throughout the past year, if I still remember all the algs I've ever learned, then I'd know full MGLS - but I don't All I have in my long-term memory now is ELS, because the algs are pretty intuitive.

In case you still want that answer from me, I thought it was obvious enough to anyone who did *just a bit* of thinking that P(ELS skip) * P(CLS skip) = P(LS skip) * P(OLL skip) since they achieve the same thing.

 

[blah]

Conclusion: No real advantage when talking about skipping chances.

I don't fully agree. I've done quite a bit of thinking about that over the past year when I was still taking MGLS very seriously (I still do, Lucas, just less seriously now ). I've had some thoughts, but none of them are fully substantiated by concrete logic yet. I'll post later when I've thought it through.

 

[blah]

P(ELS skip) = 1/80
P(CLS skip) = 1/405

P(LS skip) = 1/150
P(OLL skip) = 1/216

Now,

P(ELS skip, no CLS skip) = 404/32400
P(CLS skip, no ELS skip) = 79/32400
P(ELS skip and CLS skip) = 1/32400
P(skipping either ELS or CLS or both) = 484/32400

P(LS skip, no OLL skip) = 215/32400
P(OLL skip, no LS skip) = 149/32400
P(LS skip and OLL skip) = 1/32400
P(skipping either LS or OLL or both) = 365/32400

How about now?

In fact, P(ELS skip, no CLS skip) alone is higher than P(skipping either LS or OLL or both).

May I also mention that skipping a step is more than saving moves - you save a "look", and hence you save precious time spent staring at the cube while doing nothing to it with your hands.

If there is/are (a) logical flaw(s) here, please feel free to point it/them out

Assuming I'm right thus far, does anyone see where this whole thing is going? It's what I've been working on all this while, but to no avail, sadly

Edit: I know it's not significantly higher, and that's why I haven't switched to MGLS, considering you need to do a cube rotation to bring your LS to FR every time, and unlike OLL, some CLS cases require a cube rotation rather than just an AUF. So really, it's like Lucas said, MGLS-F and pure Fridrich are so close that practice and ability matter more than the choice between the methods.

 

[Stefan]

P(ELS skip) * P(CLS skip) = P(LS skip) * P(OLL skip) since they achieve the same thing

... and have AUFs before and between the steps. If you had two steps achieving the same but not profiting from AUFs before/between the steps, this would not have the same skip probability.

And I'd say it's more complicated than that. Above you consider the probability to skip both steps:
P(ELS skip and CLS skip) = P(LS skip and OLL skip)

That's very rare and thus I'd say less relevant than asking for *some* skip:
P(ELS skip or CLS skip) vs P(LS skip or OLL skip)

I suspect this is not equal.

Of course you also need to take into account how much a skip is worth. A beginner always solving one piece at a time will have many more skips than an expert always solving several pieces at a time, but then the beginner's skips are also worth less.

Edit: Just saw your new post...

 

[blah]

Edit: Just saw your new post...

So does that mean my math is right?

If it is, then this is what I've been working on for almost a year (and at this point, I don't think it's gonna culminate in anything reasonably good ):

I don't think I'm ever gonna change my method up to the triple x-cross stage, I have a couple of reasons to believe cross + (Fridrich F2L)*3 is the best method to achieve this.

What I've been working on, is the (probabilistically (is this even the right word?)) best alternative for LS + LL. 2-look is out of the question because I've done quite a bit of research and thinking in this direction and I have reason to believe ZB is the best 2-look method for LS + LL, but in my opinion, ZB is (no matter how many times I try to convince myself by crunching numbers and by actually practising it) pretty much unachievable unless I dedicate a couple of years to it, and I suspect I don't have a couple of years to dedicate to cubing, at least not in the near future.

So 3-look LS + LL. I've mainly been thinking about 2 things: X + Y + PLL, or X + Y + EPLL. The former for 2H and the latter for OH, well actually I'd like to use the latter for 2H if I can; I hate most PLL despite being fast at it in general. I've also been thinking about other things such as:

• X + Y + (1x2x3 block in LL to be solved)
• X + Y + (corner-edge-corner-edge-corner to be solved, kinda like an L shape if you know what I mean, not necessarily in LL)
• X + Y + (3-cycle corner commutator)
• And probably a few more which I deemed stupid and erased from memory

This is what I'm hoping for: If the probability of skipping X is 1/X and that of skipping Y is 1/Y, then we should find some X and some Y such that (X + Y -1) is as high as possible to increase the probability of step-skipping, and coupled with "next-step-influencing techniques", such a 3-look LS + LL method could be almost as effective as a 2-look one. I don't yet know.

So, do you think such a method to exists in reality, or am I just dreaming too much?

 

[Stefan]

Need more time to reply, maybe later. But...

So, do you think such a method to exists in reality, or am I just dreaming too much?

I think many dream too much. I've come to the conclusion that in cubing, you don't get anything for free, that you always get what you work for. Roughly speaking, spending equal amounts of effort on two different methods will lead to equal results. People always come up with new method ideas, but the advantages are always pretty much cancelled out by the disadvantages, which others have to point out to the over-excited inventor. Bottom line in my opinion: There's no silver bullet method.

 

[blah]

P(ELS skip) * P(CLS skip) = P(LS skip) * P(OLL skip) since they achieve the same thing

... and have AUFs before and between the steps. If you had two steps achieving the same but not profiting from AUFs before/between the steps, this would not have the same skip probability.

I understand what you're trying to say, but I was thinking a little differently and I was wondering if you could point out the logical flaw in it, or otherwise verify that it's correct.

P(ELS skip) * P(CLS skip) * P(PLL skip) = P(LS skip) * P(OLL skip) * P(PLL skip) (= P(LS and LL skip))

So dividing both sides by P(PLL skip) (which is 1/288 disregarding the benefit of AUF), it follows that P(ELS skip) * P(CLS skip) = P(LS skip) * P(OLL skip). And this can be proven without taking AUFs into consideration, no?

 

[blah]

Bottom line in my opinion: There's no silver bullet method.

Actually, I still believe there's a silver bullet method yet to be discovered, BUT, I also believe that Fridrich is so ridiculously advanced that this silver bullet method isn't ever gonna be taken seriously enough to the point that it can be a threat to Fridrich's dominance

 

[Nukoca]

I also believe that Fridrich is so ridiculously advanced that this silver bullet method isn't ever gonna be taken seriously enough to the point that it can be a threat to Fridrich's dominance

*coughpetruscough*

MGLS is more useful to the Petrus user because you can solve the last slot/OLL in one alg, since we already have EO. You just have to remember to insert the edge. I'm thinking of learning it(EJF2L first).

 

[Escher]

I also believe that Fridrich is so ridiculously advanced that this silver bullet method isn't ever gonna be taken seriously enough to the point that it can be a threat to Fridrich's dominance

*coughpetruscough*

MGLS is more useful to the Petrus user because you can solve the last slot/OLL in one alg, since we already have EO. You just have to remember to insert the edge. I'm thinking of learning it(after EJF2L, of course).

EJF2L is part of MGLS dammit you mean you're going to learn the rest of it after you've learnt cases I and Im

 

[Nukoca]

EJF2L is part of MGLS dammit you mean you're going to learn the rest of it after you've learnt cases I and Im

I know that... I was saying that EJF2L was the first part of MGLS I was going to learn, since it's only 16 algs.

 

[blah]

I also believe that Fridrich is so ridiculously advanced that this silver bullet method isn't ever gonna be taken seriously enough to the point that it can be a threat to Fridrich's dominance

*coughpetruscough*

Ha!

MGLS is more useful to the Petrus user because you can solve the last slot/OLL in one alg, since we already have EO.

Umm. How does that make it more useful? You still don't skip a step. And you don't get a significant move count advantage, if at all. (Might I remind you that CLS takes more moves than edges-oriented-OLL.) Besides, ELS is only 19 more cases, almost half of which are just mirrors. Personally, given the recognition time for Petrus EO, I'd just add a 1x2x2 block after the 2x2x3 block and do MGLS, but of course, that's just me.

Going by what you said, it's also "more useful" to the ZZ user.

 

[Escher]

EJF2L is part of MGLS dammit you mean you're going to learn the rest of it after you've learnt cases I and Im

I know that... I was saying that EJF2L was the first part of MGLS I was going to learn, since it's only 16 algs.

sorry if that came off as aggressive, you just didn't seem explicit in your post and i was picking up on it