# RoFL method



## Stefan (Sep 7, 2013)

I made this a while ago but didn't quite finish it, now Robert Yau's thread with the hard 2x2x2 scramble reminded me and I decided to publish it anyway:
http://www.stefan-pochmann.info//spocc/speedsolving/RoFL/
edit: "RoFL" means "*Ro*tten *F*irst *L*ayer"

If I remember correctly, I also checked *all* RoFL cases (with up to all four pieces rotten), so that would directly include Rob's scramble, and non-rotten was again the worst in HTM and QTM and the best RoFL case for QTM beats non-rotten by exactly one move and the best RoFL case for HTM also beats non-rotten by exactly one move, though the two cases differ. I sadly didn't make nice pages for this analysis, maybe I'll do them later if noone else does. But I'd probably have to redo the whole analysis, even if I find the old files again.

Edit: I just realized that a RoFL automatically means the opposite layer is also a RoFL, so you could always choose between them. And another idea I just had: You could learn algs for a selection of RoFL cases (not just one), where the selection is optimized so that you can always build one of the cases in let's say three moves (so no bad cases like Rob's with its 5 or 6 moves). Or optimize the selection for (weighted) average or so.

Edit: If you prefer, you can also call it RotFL method. I found it hard to decide which I like better.


----------



## scottishcuber (Sep 7, 2013)

Wow. I am very impressed; I really like the idea. 



Stefan said:


> selection is optimized so that you can always build one of the cases in let's say three moves



Is this always possible? How many RoFL sets would one need to know so the first layer (rotten?) can be reached in x moves?

I'm almost certain recognition will be harder than for EG due to the unfamiliarity of the orientations. And due to the over-familiarity between different RoFL sets, it may be hard to differentiate (although this will probably less of a problem if you only take one-look)

I am a little apprehensive as to how the recognition and the algs are going to be, but in time good algs come out of nowhere anyway

Edit: What exactly does RoFL mean?


----------



## Stefan (Sep 7, 2013)

scottishcuber said:


> Edit: What exactly does RoFL mean?


Oops, you're right, I didn't explicity say it anwhere. It means "*Ro*tten *F*irst *L*ayer".



scottishcuber said:


> Is this always possible? How many RoFL sets would one need to know so the first layer (rotten?) can be reached in x moves?


It certainly is possible at least for some \( x\le11 \) 

Two moves might actually suffice. At least I think there is no scramble where I can't bring the four white pieces into one layer in at most two moves. Color neutrality should improve at least average, if not worst case. I doubt one move is possible for worst case, so maybe optimize for QTM (or combination of HTM and QTM) instead. Or... well... since all that assumed you learn *all* RoFL cases, maybe the smallest or "best" subset with desired x moves worst or average case. There certainly is a trade-off, and I have no clue what subset sizes allow what x values (other than the mentioned extremes). 

Something else I forgot to mention: Compared to a solved first layer, there's also the advantage that there are several ways to build that (rotten) first layer. Just like the EG-1 cases, where you have four ways to build the first layer (for a fixed color). For average move count, solved first layer is really the worst choice, as both the first and the second layer have the highest average move count. I'm not sure, but I might've thought of RoFL after realizing that EG-1 is better than solved first layer, i.e., after realizing that it's beneficial to intentionally "mis-solve" pieces. RoFL in that way is just the extension, i.e., how much better can you get if you "mis-solve" even more?


----------



## scottishcuber (Sep 7, 2013)

Stefan said:


> Something else I forgot to mention: Compared to a solved first layer, there's also the advantage that there are several ways to build that (rotten) first layer. Just like the EG-1 cases, where you have four ways to build the first layer (for a fixed color). For average move count, solved first layer is really the worst choice, as both the first and the second layer have the highest average move count. I'm not sure, but I might've thought of RoFL after realizing that EG-1 is better than solved first layer, i.e., after realizing that it's beneficial to intentionally "mis-solve" pieces. RoFL in that way is just the extension, i.e., how much better can you get if you "mis-solve" even more?



This is what makes this method great. 



Stefan said:


> I'm not sure, but I might've thought of RoFL after realizing that EG-1 is better than solved first layer, i.e., after realizing that it's beneficial to intentionally "mis-solve" pieces. RoFL in that way is just the extension, i.e., how much better can you get if you "mis-solve" even more?



There was another method that was proposed like this. It involved solving 3/4 corners and mis-orienting the last, then solving that corner and the last layer in one-look. I suppose RoFL is like that but just making it more rotten to open up so many possibilities. /non-relevance

I love the way you are essentially describing that you can advance and progress a method by 'mis-solving' to greater and greater extents.


----------



## Stefan (Sep 7, 2013)

scottishcuber said:


> There was another method that was proposed like this. It involved solving 3/4 corners and mis-orienting the last, then solving that corner and the last layer in one-look. I suppose RoFL is like that but just making it more rotten to open up so many possibilities.



I didn't know about that, is there a thread about it? And yeah, RoFL is kind of a generalization of that as well. In my table, they're cases DFR_LFD, DFR_FDL, FRD_DLF and RDF_DLF. Near the bottom, just above EG-1 and EG-0 (the bottom two).



scottishcuber said:


> I love the way you are essentially describing that you can advance and progress a method by 'mis-solving' to greater and greater extents.



Me, too. No idea whether it could be good in practice, but it sure is interesting.


----------



## antoineccantin (Sep 7, 2013)

Fast layer for the pictures on top:

R U' R U' R


----------



## Stefan (Sep 7, 2013)

antoineccantin said:


> Fast layer for the pictures on top:
> 
> R U' R U' R



Yes, that pic actually shows the "winning" RoFL case from the 18 in the table.

As can also be seen from the table, there's a case (actually two, but they're equivalent) that even allows a 4-moves last layer (and two 5-moves last layers).


----------



## AustinReed (Sep 7, 2013)

Wow. What a pleasant find to wake up to. I might learn _one_ set. I'm not really up for learning an additional 43*(howevermanysets) algs. Albeit, some of the algs are really nice and short. 

Good job!


----------



## Stefan (Sep 7, 2013)

AustinReed said:


> I might learn _one_ set. I'm not really up for learning an additional 43*(howevermanysets) algs. Albeit, some of the algs are really nice and short.



Just to be clear: None of those algs have been optimized for finger-friendliness, just for HTM/QTM. So I wouldn't recommend learning those algs. Extra effort would be needed to find the best algs for execution, and I'm admittedly probably not good/interested enough to do it.


----------



## Coolster01 (Sep 7, 2013)

Someone should learn all of EG and this... 881 algs...

EDIT: More like 901, not including the solved case.

EDIT2: Nope, 902.


----------



## Stefan (Sep 7, 2013)

Coolster01 said:


> Someone should learn all of EG and this... 881 algs...
> 
> EDIT: More like 901, not including the solved case.



Don't know how you get those numbers. I'd say it's 730 algs.


----------



## qqwref (Sep 7, 2013)

Very clever idea. I'm too lazy to even learn C*LL but if I wasn't I'd consider looking to this. Nice and counterintuitive...


----------



## Escher (Sep 7, 2013)

Neat 
If I remember correctly, Justin began building algorithms for this starting step, except solving U layer orientation and ignoring D layer permutation, and then using PBL to finish - I wonder if he still has his algs lying around...


----------



## qqwref (Sep 7, 2013)

Honestly, PBL kinda sucks. Any method that ends with PBL will probably not have the potential to compete with partial/full EG in terms of ergonomics or movecount.


----------



## Rubiks560 (Sep 7, 2013)

qqwref said:


> Honestly, PBL kinda sucks. Any method that ends with PBL will probably not have the potential to compete with partial/full EG in terms of ergonomics or movecount.



This.

Seems like recog would be a pain for this method. I like the idea though.


----------



## Coolster01 (Sep 7, 2013)

Stefan said:


> Don't know how you get those numbers. I'd say it's 730 algs.



43 * (18+3)

= 903 - 1 = 902, whoops.


----------



## Escher (Sep 7, 2013)

qqwref said:


> Honestly, PBL kinda sucks. Any method that ends with PBL will probably not have the potential to compete with partial/full EG in terms of ergonomics or movecount.



For the most part I agree, but, as I'm sure you know, there would probably be quite a few very nice cases that are essentially an EG solution but including cancellations. Not that I made it clear but personally speaking whenever I talk about the possible benefits of methods it's usually in terms of 'how much will this improve my average solve if I incorporate it into my general strategy'. Though I don't do 2x2 any more, I think pro 2x2 solvers these days still have a lot of improvement to go through in terms of branching out from just using full EG and giving themselves more easy solves, and imo something like 'SS+' would be one viable route to add, just as this might be for some specific subsets of cases.


----------



## JustinJ (Sep 7, 2013)

Rubiks560 said:


> This.
> 
> Seems like recog would be a pain for this method. I like the idea though.



It's the same as CLL, plus the new orientations, is it not? I think you could do pretty much the same kind of recognition.

Ex. setup with R U R U' R2

you can recognize by the opposites on top and FUL/RUF


----------



## scottishcuber (Sep 7, 2013)

Rubiks560 said:


> Seems like recog would be a pain for this method. I like the idea though.



But if you one-look then that's less of a problem.


----------



## Rubiks560 (Sep 7, 2013)

Hmm. I suppose. The new orientations is what I was worried about.

Edit: what I was saying was recognition in general. If you can't recognize the case you can't one look it


----------



## scottishcuber (Sep 7, 2013)

Yeah. I guess with EG each set contains the same LL orientations which means recognition and familiarity aren't affected, but with this there are far more sets with unique orientations. 

And I think I was mixing up recall with recognition. I recall algs in inspection if they are recently learnt and the solve will be just as fast because there is no recog. time.


----------



## KongShou (Sep 7, 2013)

this is a cool method, but too many alg

*too many!*


----------



## Stefan (Sep 7, 2013)

To clarify again maybe: The idea was *not* to learn all ~700 algs of all 18 sets. The idea was to learn the 43 algs for _"the one best"_ set of the 18 sets. Of course you *can* combine several, like EG does, but you don't have to, and the number of sets can be low.



Rubiks560 said:


> Seems like recog would be a pain for this method.



Don't know how much recog of the first layer is affected, but if you meant the second layer, you can just pick a RoFL case where the second layer isn't "misoriented", i.e., where the cases are the exact same as in normal CLL, so recog would be the exact same (have a look at its HTM and QTM pages). As mentioned on the bottom of my page, my case FDL_FRD is the best of the 18 (saving on average about 0.86 moves during CLL).



Coolster01 said:


> 43 * (18+3)
> 
> = 903 - 1 = 902, whoops.



That doesn't make sense. First of all, 43 * (18+3) = 903 - 1 is false.
Also, EG-0 and EG-1 are already included, so you only have to add EG-2.
Also, only-DFR-misoriented and only-DLF-misoriented are equivalent.

43 * (18+1-2) - 1 = 730



KongShou said:


> this is a cool method, but too many alg
> 
> *too many!*



It's only one more than CLL, which I believe many people use.


----------



## KongShou (Sep 7, 2013)

i see, but surely we have decided that EG1 and 2 are the best sets?

also what is the point of naming all 18 cases and finding algs for them then?


----------



## Stefan (Sep 7, 2013)

KongShou said:


> i see, but surely we have decided that EG1 and 2 are the best sets?



Define "best". Movecount-wise, EG-0 (CLL) is the worst among the 18 in my list, EG-1 is the second-worst, and I believe EG-2 is about as bad as EG-0 (from vague memories of my full RoFL study).



KongShou said:


> also what is the point of naming all 18 cases and finding algs for them then?



Well, in order to possibly find the best, of course I have to analyse all of them.

If you meant to ask why I *showed* all of them:


To present all results of the analysis, so we can see which cases are how good (this also allows to judge combinations of sets).
Pure optimal HTM/QTM counts don't necessarily reflect how well they work in practice (after optimizing algs for finger-friendliness), so the best sets judged that way might not actually be the best in practice.
There isn't "the one best" set, because:
The top two (RDF_FDL and FRD_LFD) have the lowest movecount, but leave the second layer misoriented, which people might not like.
Those two cases also lose against DLF_RDF and LFD_DFR, which have better best cases (allowing 4-moves last layers, might be optimal for people interested in non-lucky single records).
In the full study (up to all four pieces rotten), there's no case that wins both HTM and QTM.


Edit: Maybe I shouldn't have called this thread "RoFL method" but rather "RoFL 2x2x2" like the webpage, as it's not really a fixed method (at least I haven't picked one) but more of an analysis which can lead to different actual methods. And if eventually the one and only actual "RoFL method" does get picked, I should probably rename the thread to "ROFLMAO" (ROtten First Layer Method And Others (or I have to get Tyson or Toby to use RoFL (yes, I know, I'm trying too hard now))).


----------



## KongShou (Sep 7, 2013)

Stefan said:


> Define "best". Movecount-wise, EG-0 is the worst among the 18 in my list, EG-1 is the second-worst, and I believe EG-2 is really bad, too (from vague memories of my full RoFL study).
> 
> 
> 
> ...



really interesting, this might be better than EG


----------



## elrog (Sep 8, 2013)

I once had a similar idea, but never thought to only use a few of the sets and just choose the best ones. To find the "best" set though, you would not only have to get good algorithms for all of the cases, but see which ones are easier to form the first layer. There may be some sets that cover bad cases in another sets first layer making them work well together despite the actual algs.


----------



## Stefan (Sep 14, 2013)

Something that just occurred to me: If intentionally "missolving" the first layer more and more allows better and better average move counts to solve the rest in one step, what if I go to the extreme of "missolving": not solving anything at all. Just leave the cube scrambled. The average move count needed to solve a random cube is about 8.756 (using Jaap's table). That's not much worse than the 8.463 after fully solving one layer, which I think didn't count AUFs. So solving one layer on average only gets you slightly closer to a solved cube, or maybe (if you do count AUFs) actually further away from a solved cube. Weird.


----------



## scottishcuber (Sep 14, 2013)

Weird indeed. 

I guess the premise is that partially solving the cube (either a first face, layer or RoFL) greatly reduces the amount possible positions of the remaining corners. 

There are 3,674,160 possible positions on a 2x2x2 cube and 730 cases for RoFL.

How many moves on average does it take to build any type of rotten FL? 
In a previous post on this thread, you quoted the max number of moves required to make the rotten FL at 2. Let's go with that.

Basically, we reduce the cube to a RoFL case with 2 moves. In doing so we are using a method that lets us solve the cube after the rotten FL in an average of 7.769 moves QTM (I averaged the QTM column on the table on your website). 
What if we were able to reduce the cube in a different way such that we were even closer to reaching 8.756? What would that method be? More radical than RoFL for sure, but what is it? 

So instead of reducing the cube to 730 cases, this number would be different (certainly bigger)...the number of moves needed to reduce the cube would be less (less than 2 anyway), and on top of that ,each case after reduction will take even fewer moves to solve on average. 

p.s. I'm not necessarily asking you all these questions Stefan, it's just what I'm thinking. Thats why it's a little disjointed as well lol.


----------



## Stefan (Oct 16, 2013)

[post=911869]Stats for three rotten corners[/post] added in Chris Olson's TCLL thread.


----------



## BlazingDragon (Apr 11, 2015)

Ok i really dont get this, like whats the difference between RDF and FRD? arent they the same thing? they are both right down front corners right? I mean switching the order of the right or down doesnt affect the orientation right? or have i been missing things the entire time?

Edit: also when you say DBL and DBR are solved do you mean just oriented or completely solved?

Edit2: Oh! for RDF do you mean the D holds the R color, the F holds the D color and the R holds the F color?


----------



## Stefan (Apr 11, 2015)

BlazingDragon said:


> I mean switching the order of the right or down doesnt affect the orientation right?



Um, that's precisely the one thing it does.



BlazingDragon said:


> Edit: also when you say DBL and DBR are solved do you mean just oriented or completely solved?



When I say solved, I mean solved.


----------



## Stefan (Apr 11, 2015)

BlazingDragon said:


> Edit2: Oh! for RDF do you mean the D holds the R color, the F holds the D color and the R holds the F color?



Yes. Because I don't just say "RDF", I say "DFR holds RDF" (the first being a position, the second being a piece).

It's also well-known in blindcubing, maybe you've seen people say stuff like "shoot to FLU" or "shoot to *F*LU" and actually meaning the F sticker position there (the "LU" following it makes clear which of the eight possible F sticker positions is meant). "Shoot to LUF" thus means a different orientation.


----------

