CFOP efficiency and multi-slotting

[mark49152]

There seem to be so many different LL and LS options and so much effort has been invested in devising and learning these, with new proposals emerging on almost a weekly basis. Yet, relatively little seems to have been invested in improving F2L, which is the longest and least efficient aspect of a CFOP solve. I have been wondering why that is the case, and what the potential is for improving the efficiency of F2L.

Cross is typically close to optimal and takes on average ~1.5 moves per piece solved. This is with no solved pieces to preserve, so maximum freedom to turn the cube without breaking anything.

At first I thought that steps that have to preserve more solved pieces would be less move-efficient, but that seems not to be the case (at least not until only 3-4 pieces remain). For example, optimal 1LLL has to preserve 12 solved pieces, but still takes on average ~1.6 moves per piece to solve the remaining 8 pieces. Running Cube Explorer to find a few optimal solutions for solving F2L pairs (solving 8 pieces, preserving 4 in the cross) typically found solutions in the 13-14 move range, so again ~1.7 moves per piece. Both of those are surprisingly close to cross efficiency.

What does seem to impact efficiency is the number of pieces solved in the step. Using Cube Explorer on the same examples that gave 13-14 move F2L solutions found optimal solutions of 9-10 moves to solve just the front two pairs, or ~2.4 moves/piece. And according to the wiki, the average optimal solution for one F2L slot = 6.7, or 3.35 moves/piece.

So, steps that solve a small number of pieces are generally less move-efficient. F2L is inefficient because it breaks down into four sub-steps solving two pieces each. A typical non-optimal human F2L solution is 29 moves or ~3.6 moves/piece. This is the primary reason for the high move count of CFOP. OLL/PLL work out at only ~2.8 moves/piece.

(This realization has helped me see the genius in Roux: the first two steps are broken into groups of 5 pieces each, enabling more move-efficient solutions. Second block optimal solutions seem to be in the range 8-10, or ~1.8 moves/piece, so the potential for improving efficiency is much greater than is allowed by optimal CFOP pairs. Not only that, but L6E does not have to be concerned with preserving corners or the other four edges, so can be more move-efficient while remaining intuitive.)

Staying on topic with CFOP, I started looking into multi-slotting to see if it holds potential for improving F2L efficiency. Surprisingly there are very few resources on this, so I assume it is rarely used. (Multi-slotting refers to using the insertion of one pair to help the setup of the next pair.)

I found two main resources. The page at http://f2l.net46.net/multislotting.html gives 8 different inserts and lists 80 cases where setup of the next pair is achieved by one of these insertions. The files at http://absolutemind.pagesperso-orange.fr/ms-angl.html on the other hand list 150 possible cases and give individual solutions for these, but are incomplete. Both of these resources ignore the back two slots. If the back two slots are accounted for, there are 245 cases for each of RUR’ and RU’R’ setup pairs (I suspect there are some mirrors in there but am not smart enough to work them out). Too many to learn in its entirety, but as the first page indicates, there are some simple techniques that can be applied to many cases, perhaps intuitively.

In theory, if multi-slotting could be useful in ~50% of cases, when setting up the last three pairs, and if in each case it eliminates 3 moves from the setup of the next pair without adding additional moves to the insertion, that’s an average saving of 4.5 moves/solve reducing typical F2L pairs to 24.5 moves or ~3.1 moves/piece. So multi-slotting is not a holy grail, just an interesting idea that given the inefficiency of F2L, might be worthy of further development.

Does anyone here use multi-slotting or have thoughts on its potential? Any pointers to other resources or discussions on improving F2L efficiency by merging solutions for pairs would also be appreciated. Otherwise I might just have to learn to block build .

 

[teller]

I think multi-slotting will be a huge breakthrough at some point in the future. But it presently presents a wall...once you start combining pairs, the amount of variety is ridiculous (not even considering some new avenues that have opened up recently like using the D layer more aggressively). There aren't many resources because no one has discovered a clear strategy that can be broadly applied. Longs lists of algs for R U R' is a start, but those really aren't the droids you're looking for. I suspect that many elite cubers have deep-enough look-ahead that they achieve some multi-slotting intuitively, but when I see the reconstructions it's rarely there.

Sorry that I have nothing to offer, but I agree that there's gold to be found here.

 

[Escher]

There aren't many resources because no one has discovered a clear strategy that can be broadly applied.

This is definitely the problem. I've been thinking for a long, long time (maybe 2 years) about writing something to do with multi-slotting, but every time I begin writing I end up hitting a bit of a road-block. I don't know whether this is due a lack of explanatory powers on my part or I'm just missing the terminology to concisely describe it - perhaps I'm just missing the point.

Anyway, it becomes easier and easier the more experience you have with f2l and I would say I'm now consistently able to produce 24-27 move f2l solutions that are just a mix from my bag of tricks that individually aren't hard to understand. Basically, you need reasonably deep look-ahead (not as far as you'd think) and the ability to understand what your pair solutions do to priority pieces on the cube, and identifying those priority pieces isn't too complex a heuristic but there's definitely quite a bit of 'feel' involved. Pair selection and multi-slotting go hand in hand and I think pair selection is easier to understand and implement at first.

I would say pair selection can be well-implemented even with only 1 way of solving each f2l case (and this might be something I can explore for trying to write an article about it). Multi-slotting then, becomes a by-product of good pair selection along with having multiple options to solve pairs. I don't think the way that the pasperso pages describe multi-slotting is really hitting the mark and I actually think that they're quite misleading as to what multi-slotting means. It's more of a thought process or selection of choices rather than anything you can reasonably delineate with algorithms.

I'll try to give you an example solve and stop being so cryptic, but bear with me - sometimes it's hard to say 'why' you should do something when it's non-verbally learned as 'just better':

U L2 R2 D B2 F2 U' L2 D' B2 D2 F L2 U2 L' B' L2 R' D L U2

z2 F2 U' R' F U L' (6)

This places the formed pair on the U layer and releases what would be a trapped corner (look at the UBL piece before doing the final U L'), while only adding 1 move to the optimal cross solution here.

y R' U2 R (9)

This hides our released corner preserving it's position (it currently has a good relation to its edge). We could do U R' U R which is okay too, but our plan was to solve the FR pair next and it's preferable to stick to preserving that - it makes checking for our next pairs a little simpler. Also, consider how nice the next case will be AFTER that one given our current plan...

y' R U R2 U' R (14)

This conveniently joins up our FR pair while solving our BR. Although in a 1-slot left case that FR pair would be bad, it's good to be aware of how empty slots can help you develop pieces before you insert them.

U F R' F' R (19)

Simple trick to preserve the position of the corner but flip the orientation of the edge, giving us a nice 3 move insert.

y' U' R U R' (23)

I'd like to provide more but I'm a little hungover and this takes a reasonable amount of effort to transcribe - perhaps if I can locate a camera a short video might be better.


Btw, in regards to your numbers for the typical human non-optimal f2l solution (29) - I assume that doesn't include cross, because my guess for the average cross + f2l incidentally is 35.

 

[Bunyanderman]

http://absolutemind.pagesperso-orange.fr/msd-angl.html

 

[windhero]

Most of the algs here http://f2l.net46.net/multislotting.html are just what I and many others would do intuitively. It doesnt exactly count as multislot imo, it kinda breaks lookahead down to 2 pairs instead of 4. F2L should be free to solve whatever pops in front of you first. The true benefit of multislotting comes from diagonal multislotting, not adjacent. If 2 adjacent slots are solved chances are your empty slots are on the front side and that lookahead is ridiculously easy.

 

[ILMZS20]

well multi slotting will probably be more efficient but look ahead would be alot harder i think. if you really use multi slotting then your tps will definitely go down because you need much, much more look ahead and i guess it would be better to just simplify your solves instead of doing stuff you actually have to think about that much. so i think that this would be more efficient but still slower, but i dont have too much of a clue so i might be wrong.

 

[Renslay]

Why not blockbuilding?

 

[TDM]

Personally, I've never liked the inefficiency of standard CFOP. Whilst I understand solving a cross makes lookahead easier and is something you can continue on with from the beginner's method so you don't have to learn anything new, I can't see any advantage to solving a cross when all you have to do to complete the F2L is break it, re-solve it, break it, re-solve it, and then do that for another three F2L pairs. It really isn't efficient. I like the idea of multislotting though, as it means you don't have to break and solve the cross as much as in a solve without multislotting. I've been thinking of switching to another method where you don't solve some pieces and then unsolve and then solve them again all the time, but as I'm more experienced with CFOP, I think I'll practise multislotting and see how I find it.

 

[Dapianokid]

I use multislotting. I believe Petrus and Roux to be more efficient ways of solving, but harder to learn with the same mastery and maturity as one can learn CFOP in the same amount of time with the same amount of practice. Because of the freedom, picking up tricks and learning hows and whys to the things you do take much longer because of the distance between solves that incorperate the same newly learned technique. CFOP is so beautiful to me because it isn't as highly intuitve as others, and we can learn to master it better and improve upon it. I believe if one focused on one substep of Petrus or Roux for a while, they might gain some level of mastery similar to that which one achieves when using CFOP for so long. I mean, building pairs optimally and easily and with sexy movements comes so naturally to an experienced CFOP solver. But building a 2x2x3 block takes time and thought.

For those who tl;dr'd,

He basically asked about how to improve this method's primarily longest stage: F2L, and the effectiveness of multislotting. Moral of the story: Efficiency in CFOP takes off .5 of a move per piece of F2L, a total of 4 extra moves. When they are finger-friendy, it takes me about as long as it takes me to open my eyes and close them again as quickly as possible to do 4 moves, so I don't feel as if I'm wasting much time by being a little bit less efficient and more focused on finger-friendly movements.

 

[rj]

Why not blockbuilding?

Freefop, and I use it. It's fun. It works.

 

[Lchu613]

I use multislotting. I believe Petrus and Roux to be more efficient ways of solving, but harder to learn with the same mastery and maturity as one can learn CFOP in the same amount of time with the same amount of practice. Because of the freedom, picking up tricks and learning hows and whys to the things you do take much longer because of the distance between solves that incorperate the same newly learned technique. CFOP is so beautiful to me because it isn't as highly intuitve as others, and we can learn to master it better and improve upon it. I believe if one focused on one substep of Petrus or Roux for a while, they might gain some level of mastery similar to that which one achieves when using CFOP for so long. I mean, building pairs optimally and easily and with sexy movements comes so naturally to an experienced CFOP solver. But building a 2x2x3 block takes time and thought.

For those who tl;dr'd,

He basically asked about how to improve this method's primarily longest stage: F2L, and the effectiveness of multislotting. Moral of the story: Efficiency in CFOP takes off .5 of a move per piece of F2L, a total of 4 extra moves. When they are finger-friendy, it takes me about as long as it takes me to open my eyes and close them again as quickly as possible to do 4 moves, so I don't feel as if I'm wasting much time by being a little bit less efficient and more focused on finger-friendly movements.

I'm sorry but I almost tl;dr'ed on both walls, despite the second wall being shorter.

Don't worry though I actually decided to read both.

 

[evogler]

mark49152, I'm trying to PM you but it says your inbox is full.

 

[Arkwell]

Doesn't Feliks use some multi-slotting? Or is it that his lookahead is so good that it just looks like multi-slotting?(Been checking some Feliks reconstructions)

 

[uberCuber]

Doesn't Feliks use some multi-slotting? Or is it that his lookahead is so good that it just looks like multi-slotting?(Been checking some Feliks reconstructions)

Read Escher's post on the first page. Those two concepts kinda merge together.

 

[elrog]

This doesn't have anything to do with multislotting and it doesn't really help, but its fun to mess around with. I was as well thinking of a way to make F2L better (but not entirely in terms of move efficiency). I was thinking that it would be alot easier to choose the best F2L pair to do and it would be easier to look ahead if more F2L pieces were in the top layer. This would also allow you to actually use the 42 F2L algorithms which never were very useful because you mostly get cases where your pieces are in other slots. So what I did was fill the F2L slots with the 8 top layer pieces and then did my F2L. This makes the look ahead extremely easy, but it was then that I realized this restricted you from using empty slots without canceling out the work you already did. I do, however, think that it would be feasible and could help to try and get 1 or 2 slots filled with top layer pieces while you make your cross.

 

[rj]

This doesn't have anything to do with multislotting and it doesn't really help, but its fun to mess around with. I was as well thinking of a way to make F2L better (but not entirely in terms of move efficiency). I was thinking that it would be alot easier to choose the best F2L pair to do and it would be easier to look ahead if more F2L pieces were in the top layer. This would also allow you to actually use the 42 F2L algorithms which never were very useful because you mostly get cases where your pieces are in other slots. So what I did was fill the F2L slots with the 8 top layer pieces and then did my F2L. This makes the look ahead extremely easy, but it was then that I realized this restricted you from using empty slots without canceling out the work you already did. I do, however, think that it would be feasible and could help to try and get 1 or 2 slots filled with top layer pieces while you make your cross.

This is a good idea. I will try this.

 

[ianliu64]

Bleh.
Multislotting isn't my thing.

 

[ncube]

I think it could be a good idea to memorize how solving standard f2l cases affects the other corners and edges. Then instead of tracking a pair, one would be able to predict where it would be and I think this would allow for much, much better lookahead and allow faster tps. I think just from practice, many people already do this a bit. But, I think it could be pretty hard to memorize how exactly each f2l case affects others and so it's not really feasible.

 

[mark49152]

For those who tl;dr'd, .... Moral of the story: etc.

OK good point, it was rather long. For those who TL;DR'ed, here's the moral of my story:-

• Optimal CFOP pairs done one at a time takes average ~3.35 moves per piece solved.
• Optimal Roux blockbuilding takes ~1.8 moves per piece.
• Multislotting won't realistically reduce the CFOP average much below about ~3 moves/piece.

All of which leads to the question, can multislotting or F2L in general be improved or developed further, to break this barrier? Perhaps the result would be a sort of hybrid, retaining much of the simplicity of F2L while gaining some blockbuilding characteristics and efficiency. Assume that ultimately, with mastery, move efficiency doesn't necessarily mean lower TPS.

There aren't many resources because no one has discovered a clear strategy that can be broadly applied.

Yes that's the impression I got. As Escher explained well (thanks for that and the helpful walkthrough!), multislotting seems to be an extension of lookahead to intuitively do some advance work on the next pair rather than just track it. That sounds like a natural progression, but if the expected saving is only 4-5 moves and yet it requires a level of lookahead and cube-awareness approaching that needed to do efficient blockbuilding, the effort is probably better spent on the latter.

I don't think the way that the pasperso pages describe multi-slotting is really hitting the mark and I actually think that they're quite misleading as to what multi-slotting means. It's more of a thought process or selection of choices rather than anything you can reasonably delineate with algorithms.

I prefer the Absolute F2L resource. Although it looks like an alg list and, as you say, it's probably not reasonable to try to learn these as algorithms, I like the idea of studying a small selection of alternative inserts and what they do to other pieces, and Absolute F2L is better organised than Pagesperso for that.

The true benefit of multislotting comes from diagonal multislotting, not adjacent.

I think only the RUR' cases are affected, but yes it would be good to see some L(...)L' options added to that list for when the BL slot is open. If I understood you correctly, which maybe I didn't...

I can't see any advantage to solving a cross when all you have to do to complete the F2L is break it, re-solve it, break it, re-solve it, and then do that for another three F2L pairs. It really isn't efficient.

Not sure I agree with that. It's a popular viewpoint, probably because it seems intuitive and Petrus said it, but if you fire up Cube Explorer and look at the optimal solutions for any of these stages they pretty much break apart everything and put it back together. What makes CFOP inefficient is not the cross, it's that in each step you are only solving two pieces at a time, and missing the opportunity to use all those turns to do something else useful as well.

 

[Lchu613]

This doesn't have anything to do with multislotting and it doesn't really help, but its fun to mess around with. I was as well thinking of a way to make F2L better (but not entirely in terms of move efficiency). I was thinking that it would be a lot easier to choose the best F2L pair to do and it would be easier to look ahead if more F2L pieces were in the top layer. This would also allow you to actually use the 42 F2L algorithms which never were very useful because you mostly get cases where your pieces are in other slots. So what I did was fill the F2L slots with the 8 top layer pieces and then did my F2L. This makes the look ahead extremely easy, but it was then that I realized this restricted you from using empty slots without canceling out the work you already did. I do, however, think that it would be feasible and could help to try and get 1 or 2 slots filled with top layer pieces while you make your cross.

Meh.
1. Algorithmic F2L. No. No.
2. Wasting moves beforehand that don't do that much
3. What's wrong with pieces in slots? Makes for a lot of really nicely fingertrickable F2L cases.

All in all a good concept based on, imo, a skewed idea.