# Full LMCF 3x3 method now available

##### Member
Since LMCF has such a large range for the number of algs one has to learn (few or hundreds), I think that's one of it's biggest draws. The more you can memorize, the faster you can get.

I also like it because if someone already knows 2x2 and L6E (or L4E) then they don't even need to learn any new algs.
The E2L steps can all be intuitive! Even doing one edge at a time can be about the same number of moves as solving 2 at a time (an E2L pair). So new cubers can get into it and see low move counts (<70 anyway) right away.

I tried to record this intuitiveness for myself in an info sheet.
It's Step 2 on here: http://solvexio.cf/app/#/Corn_E_Midge

#### Spencer131

##### Member
Here's a comparison of Roux and LMCF which I think is very reasonable.

1. First square of FB is approximately equal to first side of the 2x2 phase.
2. The eg algorithm is probably slightly faster than CMLL.
3. LMCF doesn't have CMLL recognition, but Roux doesn't have E2L transition, so that roughly balances out.
4. They both have lse.
5. And all that's left is E2L for LMCF, and second pair of FB+SB for Roux. My intuition says that E2L is faster than second pair+SB.

So overall, this could mean lmcf is faster than Roux. Because of this reasoning, I am definitely considering switching.

##### Member
Here's a comparison of Roux and LMCF which I think is very reasonable.

1. First square of FB is approximately equal to first side of the 2x2 phase.
Fairly reasonable though it neglects that fact that with Roux FB is rarely built by itself without doing anything to the other pair or DR.
2. The eg algorithm is probably slightly faster than CMLL.
CMLL has less algs to practise (important with really large alg sets like eg)
3. LMCF doesn't have CMLL recognition, but Roux doesn't have E2L transition, so that roughly balances out.
CMLL is easier to predict and faster to recognise.
4. They both have lse.
true, though in roux LSE should rarely be left uninfluenced by CMLL.
5. And all that's left is E2L for LMCF, and second pair of FB+SB for Roux. My intuition says that E2L is faster than second pair+SB.
The second pair of FB should be 1 maybe 2 moves after FBsquare if done right. SB+3 moves is less moves and also significantly more ergonomic than E2L

#### efattah

##### Member
Here's a comparison of Roux and LMCF which I think is very reasonable.

4. They both have lse.

In Roux, LSE is always done by solving UL+UR plus the M-slice edges. In LMCF, half the time, two unsolved edges are on the same slice (both on the R slice, or both on the L slice). And the other slice (R/L) is fully solved. For example, FR+UR+M Slice edges. The case when the remaining edges are both on the same slice results in using Waterman's L6E method, however Waterman's L6E was not fully computer optimized back in 1988. I have spent the last several months re-optimizing the Waterman L6E set and the results are very unusual. I really felt the case where two edges were on the same side would be a disadvantage compared to the other half of the time where you are solving UL+UR (which results in a pure M/U solution). This turned out to be untrue.

Firstly, the astonishing thing is the move count, *even for the speed optimized algorithms*, is incredible. Solving FR+UR, or DR+UR, while orienting the midges, takes an average of 8.90 moves + 0.75 setup moves = 9.65 moves for the speed optimized algorithms. In Roux, full EOLR with misoriented centers can solve UL+UR+orient midges in 8.28 moves (Source: http://jeremyg.nl/home/rouxdata).

So again it seems like having both edges on the same side is a disadvantage in terms of movecount. What actually turns out is that this is not the case. In one case you have 8.28 STM moves that are pure M/U. In the other case (Waterman) you have 9.65 moves that are generally RrUM and sometimes (if ergonomic) FRrUM, and in UR/DR cases RrUMD. What ends up happening is due to the extra freedom of movement (not constrained to pure MU), the number of possible algorithms to solve each case is enormous, typically yielding 12 or more candidates that are ergonomic, allowing us to be VERY PICKY when choosing an algorithm. The end result is incredibly fast algorithms that are significantly faster than pure MU. So the 9.65 move [F]RrUM ends up faster than the 8.28 pure MU algorithm. My TPS on the FRrUM sets is significantly faster than my max M/U TPS (my TPS is around 11 on the Waterman cases and around 8 to 8.5 on the pure MU). So what ends up happening is that having the last 2 edges in LMCF L6E being on the same side of the cube ends up being an advantage. The disadvantage is the large number of cases (around double the number of cases vs. Roux EOLR+MC).

#### SomeRandomZZUser

##### Member
In Roux, LSE is always done by solving UL+UR plus the M-slice edges. In LMCF, half the time, two unsolved edges are on the same slice (both on the R slice, or both on the L slice). And the other slice (R/L) is fully solved. For example, FR+UR+M Slice edges. The case when the remaining edges are both on the same slice results in using Waterman's L6E method, however Waterman's L6E was not fully computer optimized back in 1988. I have spent the last several months re-optimizing the Waterman L6E set and the results are very unusual. I really felt the case where two edges were on the same side would be a disadvantage compared to the other half of the time where you are solving UL+UR (which results in a pure M/U solution). This turned out to be untrue.

Firstly, the astonishing thing is the move count, *even for the speed optimized algorithms*, is incredible. Solving FR+UR, or DR+UR, while orienting the midges, takes an average of 8.90 moves + 0.75 setup moves = 9.65 moves for the speed optimized algorithms. In Roux, full EOLR with misoriented centers can solve UL+UR+orient midges in 8.28 moves (Source: http://jeremyg.nl/home/rouxdata).

So again it seems like having both edges on the same side is a disadvantage in terms of movecount. What actually turns out is that this is not the case. In one case you have 8.28 STM moves that are pure M/U. In the other case (Waterman) you have 9.65 moves that are generally RrUM and sometimes (if ergonomic) FRrUM, and in UR/DR cases RrUMD. What ends up happening is due to the extra freedom of movement (not constrained to pure MU), the number of possible algorithms to solve each case is enormous, typically yielding 12 or more candidates that are ergonomic, allowing us to be VERY PICKY when choosing an algorithm. The end result is incredibly fast algorithms that are significantly faster than pure MU. So the 9.65 move [F]RrUM ends up faster than the 8.28 pure MU algorithm. My TPS on the FRrUM sets is significantly faster than my max M/U TPS (my TPS is around 11 on the Waterman cases and around 8 to 8.5 on the pure MU). So what ends up happening is that having the last 2 edges in LMCF L6E being on the same side of the cube ends up being an advantage. The disadvantage is the large number of cases (around double the number of cases vs. Roux EOLR+MC).
Pretty cool!

#### efattah

##### Member
We know the corners can be solved in 1.5 seconds by experts, and we know LSE can be done in around 1.3 to 1.7 seconds. So with LMCF the only 'unknown' area is the E2L phase in the middle, between the start (corners) and the end (LSE), as well as the 'transition' between the three phases. Giving conservatively 1.9 seconds for the corners and 1.9 seconds for LSE (=3.8 seconds), then to get a 6.8 average we need to solve E2L in 3.0 seconds. We have 6 edges to solve, either in three pairs (1 second each), or two triplets (1.5 seconds each). I'm not a super fast cuber (yet) and my TPS is pretty slow; still, despite non-optimized E2L mechanics I have routinely gotten 4.5 second E2L phases in real solves. So we are not too far from the goal of a 3 second E2L.

The problem with the initial LMCF versions (up to and including v4.xx), is the E2L phase was not very optimized. First, the E2L algorithms were not super speed optimized. Second, the E2L algorithms often required as many as three setup moves (L setup, R setup, M setup). That is way too many setup moves. In my original document, I only gave E2L cases from one of the four possible orientations/reflections, and I simply said to use the L/R or F/B reflections for the other cases. What that meant is that the ergonomics of some of the reflections were very poor.

The E2L phase has tremendous potential, and this is what I have been improving lately:
- For the very common E2L cases, I have been ignoring reflections and treating all 4 (reflected) cases as unique and generating customized highly ergonomic and fast algorithms for EACH reflection. Furthermore I have found that by relaxing the movecount, and allowing for an extra 1-2 moves, the algs are way faster (despite a move or two longer). In this fashion all 'B' moves are eliminated, and all awkward regrips are eliminated
- Also for the common cases, I have found that certain situations have awkward setup moves. In some cases doing an L2 move in order to setup up the E2L algorithm is pretty slow. To compensate for this, it is possible to execute a different algorithm that solves to the DL slot instead of the UL slot, eliminating the awkward set up move

Some people have commented by early experiments that solving one edge at a time gives almost the same move count as solving pairs or even triplets. While this is almost true, it is absolutely not true of the speed of the entire E2L phase.

When solving SINGLE edges by the old fashioned keyhole method, you have
(A) a look ahead challenge between each edge you solve
(B) setup moves between each edge you solve
(C) often you have rotations between edge solves
(D) awkward move combinations

The flow is usually broken, and the TPS low. Solving is all intuitive, and non-algorithmic. TPS is more of the intuitive class.

By executing pairs or triplets, you greatly reduce the number of 'looks', you increase the TPS a lot by using algorithmic execution, and you reduce or eliminate rotations. The algorithmic method, by using super ergonomic algs, ensure all moves are fast and ergonomic, versus SINGLE edge-by-edge solving that often uses awkward L/M/R combos that need regrips and are really slow.

I have also been developing two new classes of triplet algorithms. Currently the triplets only solve DF+UR+UL at the same time, and only the case where the target keyhole edge moves to the opposite layer it is on. These are pretty fast, but they only occur (randomly) in about 30-50% of solves. By expanding the class of triplets, you can get triplets in almost every solve. It would take too long to explain the new class of triplets and I will leave it for the next document revision, but the ultimate goal of LMCF is to solve E2L in two triplets each taking just over 1 second. Allowing 1.1 seconds for each triplet, and a more aggressive 1.7 seconds for corners and 1.6 seconds for LSE, yields an average of 1.7+2.2+1.6 = 5.50 seconds which is pretty on-par with the best CFOP and Roux solvers. Of course, lucky singles would be way faster.

#### Neuro

##### Member
I’ve concluded that the best way to do LMCF on big cubes is probably just reduction while influencing/tracking corners. I’d probably try and make algs using primarily face moves but you’ll basically need a magnetic cube to use the method effectively. I have no suggestions for improvement for OH, it just doesn’t seem good enough to match other methods.

#### efattah

##### Member
I’ve concluded that the best way to do LMCF on big cubes is probably just reduction while influencing/tracking corners. I’d probably try and make algs using primarily face moves but you’ll basically need a magnetic cube to use the method effectively. I have no suggestions for improvement for OH, it just doesn’t seem good enough to match other methods.

One of the major revisions/improvements I have made to LMCF recently is changing M-U algorithms to R-U and L-U 2-gen sets. This goes both for LSE and for E2L. The end result is solves that sometimes have as few as 4 M moves.

Examples for L5E-BDR:
Previous algorithm:
U2 M U M' U M U M' U'
New algorithm:
R U R' U' r' R U R U'

Examples for E2L:
Old: U M' U' R' U M U'
New: U r' U r R' U' r U'

Not only does this speed up the algorithms (TPS wise) but makes a limited case for LMCF in FMC, although it will never beat true FMC methods.

I have also created sets of L5E and pure edge flips that displace the L/R slices with respect to each other such that by selecting the correct variant you eliminate the irritating L/R slice adjustment during L6E. These algorithms do not use any more moves than their variants, meaning the move count for the entire method is reduced by about 0.75.

#### Neuro

##### Member
Wait instead of redux what if we did this

1) 2 opposite centers
2) 3 random edges on L
3) Last 4 Centers
4) 1 random edge to finish "cross," rotate z'
5a) Pair First x Edges, place 2 corners on bottom, rotate to back
5b) Pair remaining edges, place last 2 corners. Layer done!
6) 3x3 stage

Here's a solve

128 moves. Got super lucky on centers and 3 edges on L but had parity. Unfortunately we can't use the standard edge flip alg so OLL parity is much longer than in other methods. I had trash E2L ergonomics but hey you're improving it so good luck

#### Sue Doenim

##### Member
When are all of these new developments going to be released?

#### CeBeMind

##### Member
I'm learning this (actually it's my main method). It's very funny.

#### 1001010101001

##### Member
Wait instead of redux what if we did this

1) 2 opposite centers
2) 3 random edges on L
3) Last 4 Centers
4) 1 random edge to finish "cross," rotate z'
5a) Pair First x Edges, place 2 corners on bottom, rotate to back
5b) Pair remaining edges, place last 2 corners. Layer done!
6) 3x3 stage

Here's a solve

128 moves. Got super lucky on centers and 3 edges on L but had parity. Unfortunately we can't use the standard edge flip alg so OLL parity is much longer than in other methods. I had trash E2L ergonomics but hey you're improving it so good luck
I proposed this way back in the New Methods and Substeps thread, although a bit different

#### efattah

##### Member
Yeah, I'm thinking the same... @efattah

Sorry I have been really busy with other life stuff, but despite that I keep making improvements to LMCF daily, I was kind of hoping the 'improvements' would slow down and 'stabilize' so I could actually publish them, but each improvement is then improved upon again and again making the evolution seemingly endless. Hopefully I can compile something together in the next few months.

In terms of the change list, almost all of the E2L algorithms have been improved to be much faster and more ergonomic; almost all of Waterman Set 2 is now way faster and more ergonomic, and the L5E sets have been greatly improved. Pure M slice edge flips have been modified to eliminate the L/R correction move at the end by incorporating it into the edge flip algorithm (similarly with L5E). More triplet cases have been added and some quadruplets as well.

On another note I will say that this method has much better lookahead than I originally expected. My lookahead keeps improving without limit, and I can often breeze through E2L seeing way into the future the whole time and never lose track of the next pieces to solve.

I guess the easiest thing would be to do a partial update and at least update the E2L and WS2 sets. That would only take a few hours of edits. I could add the more complex modifications later.

#### obelisk477

##### Member
Sorry I have been really busy with other life stuff, but despite that I keep making improvements to LMCF daily, I was kind of hoping the 'improvements' would slow down and 'stabilize' so I could actually publish them, but each improvement is then improved upon again and again making the evolution seemingly endless. Hopefully I can compile something together in the next few months.

In terms of the change list, almost all of the E2L algorithms have been improved to be much faster and more ergonomic; almost all of Waterman Set 2 is now way faster and more ergonomic, and the L5E sets have been greatly improved. Pure M slice edge flips have been modified to eliminate the L/R correction move at the end by incorporating it into the edge flip algorithm (similarly with L5E). More triplet cases have been added and some quadruplets as well.

On another note I will say that this method has much better lookahead than I originally expected. My lookahead keeps improving without limit, and I can often breeze through E2L seeing way into the future the whole time and never lose track of the next pieces to solve.

I guess the easiest thing would be to do a partial update and at least update the E2L and WS2 sets. That would only take a few hours of edits. I could add the more complex modifications later.

What were you averaging with it in the beginning, and what are you averaging now?

#### Sue Doenim

##### Member
Sorry I have been really busy with other life stuff, but despite that I keep making improvements to LMCF daily, I was kind of hoping the 'improvements' would slow down and 'stabilize' so I could actually publish them, but each improvement is then improved upon again and again making the evolution seemingly endless. Hopefully I can compile something together in the next few months.

In terms of the change list, almost all of the E2L algorithms have been improved to be much faster and more ergonomic; almost all of Waterman Set 2 is now way faster and more ergonomic, and the L5E sets have been greatly improved. Pure M slice edge flips have been modified to eliminate the L/R correction move at the end by incorporating it into the edge flip algorithm (similarly with L5E). More triplet cases have been added and some quadruplets as well.

On another note I will say that this method has much better lookahead than I originally expected. My lookahead keeps improving without limit, and I can often breeze through E2L seeing way into the future the whole time and never lose track of the next pieces to solve.

I guess the easiest thing would be to do a partial update and at least update the E2L and WS2 sets. That would only take a few hours of edits. I could add the more complex modifications later.
Sorry if I came across as rude. I was really excited about the method at that point. I guess I can't really say you've been slacking off, because I still haven't even come close to finishing my stuff with HD. I've done some stuff as far as alg optimization goes, and I've introduced different NLLs depending on the position of the D layer. It looks really nice so far, but I'm busy with lots of school and stuff for now.

#### SomeRandomZZUser

##### Member
Sorry I have been really busy with other life stuff, but despite that I keep making improvements to LMCF daily, I was kind of hoping the 'improvements' would slow down and 'stabilize' so I could actually publish them, but each improvement is then improved upon again and again making the evolution seemingly endless. Hopefully I can compile something together in the next few months.

In terms of the change list, almost all of the E2L algorithms have been improved to be much faster and more ergonomic; almost all of Waterman Set 2 is now way faster and more ergonomic, and the L5E sets have been greatly improved. Pure M slice edge flips have been modified to eliminate the L/R correction move at the end by incorporating it into the edge flip algorithm (similarly with L5E). More triplet cases have been added and some quadruplets as well.

On another note I will say that this method has much better lookahead than I originally expected. My lookahead keeps improving without limit, and I can often breeze through E2L seeing way into the future the whole time and never lose track of the next pieces to solve.

I guess the easiest thing would be to do a partial update and at least update the E2L and WS2 sets. That would only take a few hours of edits. I could add the more complex modifications later.
No problem. I was just a little frustrated but I completely understand.

#### CeBeMind

##### Member
Sorry I have been really busy with other life stuff, but despite that I keep making improvements to LMCF daily, I was kind of hoping the 'improvements' would slow down and 'stabilize' so I could actually publish them, but each improvement is then improved upon again and again making the evolution seemingly endless. Hopefully I can compile something together in the next few months.

In terms of the change list, almost all of the E2L algorithms have been improved to be much faster and more ergonomic; almost all of Waterman Set 2 is now way faster and more ergonomic, and the L5E sets have been greatly improved. Pure M slice edge flips have been modified to eliminate the L/R correction move at the end by incorporating it into the edge flip algorithm (similarly with L5E). More triplet cases have been added and some quadruplets as well.

On another note I will say that this method has much better lookahead than I originally expected. My lookahead keeps improving without limit, and I can often breeze through E2L seeing way into the future the whole time and never lose track of the next pieces to solve.

I guess the easiest thing would be to do a partial update and at least update the E2L and WS2 sets. That would only take a few hours of edits. I could add the more complex modifications later.

#### Burnsy101

##### Member
I would like the update as well. Can fell E2L be solved intuitively, and for someone trying to get sub 10, what should the 2x2 stage be done in?

#### efattah

##### Member
E2L can be solved intuitively which usually means solving edges one at a time or at most, the 2-3 really simple pair cases. Using algorithms to solve E2L reduces the move count only slightly; the major benefit is a great improvement in ergonomics. Solving E2L with singlets and simple pairs usually means a lot of L/R slice adjustments and x/x' rotations and regrips.

For sub-10 solves, a realistic split is corners: 2.6, E2L: 5.0, L6E: 2.3 = 9.9 seconds. Most of my sub-10's actually have sub-5 E2L phases, but in my case I need to get pretty lucky to get a sub-5 E2L.

The corners and L6E take similar amounts of time; if you consider top 2x2 solvers averaging around 1.70, and top Roux solvers finishing L6E in 1.70. Yet, record class 2x2 is 1.30 - 1.50, and some Roux guys like Kian Mansour have 1.30 - 1.50 averages on L6E.

Generally E2L will take twice as long as those stages, i.e. ratio of corners:E2L:L6E being 1:2:1.

So a world class solver would do 1.5:3.0:1.5 = 6.00 average.

Then you have solves where you get a CLL skip (i.e. 4-5 move corner solve), and/or L6E partial skip (L6E in 3-6 moves), and then there are solves where 2-3 edges pieces are pre-solved in E2L. All of these obviously result in really fast singles.

An interesting note is that in 2x2 solving, scrambles are 'screened' to make sure the solve is more than 4 moves. This is not the case in 3x3. In other words, 3x3 scrambles are not 'screened' to make sure the corners can't be solved in less than 4 moves. So you can get scrambles where the corners can be solved in 1-3 moves. Some guy earlier in this thread posted a home scramble (PC generated) that had the corners already completely solved to start off with. Obviously illegal in 2x2 solving, but not illegal for 3x3.