# RoFL method

#### Stefan

##### Member
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 "Rotten First Layer"

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.

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#### scottishcuber

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

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

##### Member
Edit: What exactly does RoFL mean?
Oops, you're right, I didn't explicity say it anwhere. It means "Rotten First Layer".

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?

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#### scottishcuber

##### Member
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.

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

##### Member
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).

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.

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#### Stefan

##### Member
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

##### Member
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

##### Member
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.

#### Stefan

##### Member
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.

#### Escher

##### Babby
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

##### Member
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

##### Nub
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.

#### Escher

##### Babby
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

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

#### Rubiks560

##### Nub
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