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It seems rumors of my 28-move speed solve have reached as far as top cubers in China and I have recently received various requests for a more detailed description of this LMCF (low movecount corners first) method. I have now created a 43-page elaborate description of the method with tips tricks and all the algorithms. This can serves a very fast beginner's method with only 26 algorithms, or an extremely fast method for experts (with a LOT more algorithms, 99 to 776 based on the variant), capable of sub-3 second lucky solves. While I am not a fast turner (circa 3.80 TPS), the low movecount still allows me to get frequent 8-10 second singles, and fast turners could get insane times.

About the pdf: I definitely don't think method neutrality should be encouraged. It's far too much work for relatively little gain. If you want to get fast, pick a method and stick with it.

About the method itself: (super small point, but I don't think making steps algorithmic means you need a new name for a method. People call CFOP the same thing whether your F2L is algorithmic or intuitive. I would just call this CF)
It does look really efficient though - but I feel like the rotations and transitions between L/R would mean you couldn't get the ~10 TPS you assumed in the last sentence of the intro. Perhaps algorithmically solving three L edges followed by three R edges would improve the fingertricks?

It's a very good point about the ergonomics of the E2L phase. You're totally right, the E2L phase will never achieve the same TPS as the other two phases (corners, and L6E). However it doesn't really matter. You max out the TPS on the corners like a 2x2 solver (circa 1.7 second average), you max out TPS on the L6E phase like a Roux solver (1.7 seconds L6E Alex Lau), and the E2L phase will have slower TPS but only accounts for about 18 moves and even much less on a lucky solve.

If you go with 8 TPS on the corners and L6E and 6 TPS on E2L, then the full method would have predicted splits of:
Corners 13 @ 8 TPS = 1.62
E2L 16 @ 6TPS = 2.67 seconds
L6E 13 @ 8 TPS = 1.62
Total average = 5.92 seconds

Looking at real world data, my global splits at the moment are corners (5 sec), E2L (7.8 sec), L6E (3.3 sec). However my corners suck because I average 1 second recognition on the CLL/EG1 and I get 4 second corner solves on 1 looks. So eliminating that skew and focusing on TPS with 1-looking corners and my splits are 4/7.8/3.3.

Scaling that down to a 1.9 second 2x2 phase gives a predicted high TPS split of 1.9/3.7/1.56 = 7.16 average, and that shows indeed the E2L phase has lower TPS than the other two phases. While that average is nothing spectacular, LMCF excels in fast singles, and if you scale some of my faster low movecount singles by the same amount it is interesting.

A full step 9.10 had 2.02/4.74/2.34 splits on csTimer; that scales down to 0.96/2.25/1.11 = 4.32 second full step at expert TPS, which seems about right since on that solve the corners would definitely have been a sub-1 by a 2x2 expert and L6E was very fast as well.

My 8.3 single with CLL skip would scale down to 3.94. So a 4.32 full step and 3.94 with skip are in the ball park of top CFOP ZBLL or VLS solves.

I cannot find in your PDF algorithms for orienting M-slice edges, if all R-edges and L-edges are solved. How do you realize this case? Unsolve one edge?

Okay here is the 2nd version (31 pages) which includes pure midge orientation algorithms as requested by Miro. It also includes FULL documentation and graphics for the complex Waterman L6E step which I think is the first time this step has ever been properly documented. Theoretically a Roux solver could leave any edge in the second block disoriented and it would be fixed if using Waterman's L6E to finish.

That a great, informative PDF, efattah. A lot of work has obviously put into it.

I'm interesting in giving it a go, but I want to start with the "Basic" set.
I didn't readily see the 3 E2L algorithms and 11 L6E algorithms for all that would be needed for the "Basic" solving, though.

Yes, it is true I did not expand much on the 'Basic' version of the method, I wasn't sure how much interest there would be; however I will say that I have had MANY solves in the 12.xx to 13.xx range using only the basic algorithm set of 26; a faster turner could easily get sub-10 with the basic set, making it possibly the fastest method for so few algorithms.

The LMCF basic set is:

1. Ortega for 2x2 (12 algorithms) (or any more advanced method you know for 2x2)

2. E2L algorithms (3)
Algorithm 7 (page 8) U' M U2 M2 U' (shown graphically on page 9 top left)
Algorithm 14 (page 8) M U M U2 M' U (shown graphically on page 11 top left)
Algorithm 18 (page 8) U M' U' (shown graphically on page 11 top left)
These are BY FAR the fastest situations to recognize. In the early phase of learning E2L, recognition of the cases is difficult, but with these three cases, recognition is super fast even for a beginner. The rule for recognition is simple:
Solve the DF edge into the UR slot. Does the UR slot contain an edge of the opposite color (i.e. going on to the opposite side)? If so solve it with either U M' U' (if the edge is disoriented) or M U M U2 M' U (if the edge is oriented). If the UR slot does not contain such an edge, does the UL slot contain an edge which is solved but disoriented? If so solve it with U' M U2 M2 U'. These are three very easy sequences; learn them intimately by watching what is happening with the cube and learn to execute these sequences from ANY angle (there are four reflections for each case). You can take a solved cube and execute the algorithms backwards and see exactly what they are solving (inverse is U M2 U2 M' U and U' M U2 M' U' M', and U M U').

3. L5E algorithms (8)
Learn the DFL set (page 14), 8 algorithms (solving DF->UL while orienting the midges). Using just this one set you can always solve the last ledge/redge while orienting the midges. If you end up with a reflected case, you can do D2 or U2 or y2 to 'transpose' the cube into a reflected situation for which you know the algorithm. For example, execute D2 [then do the DFL algorithm] then D2 again. Or U2 [then do the alg] then U2 again.

4. Midge permutations (3)
U2 M2 U2
E2 M E2
U2 M U2

To 'complete' your knowledge of the Basic LMCF set, the following SEVEN algorithms would be the next most important to learn in terms of how often they occur by accident. These are all midge orientation algorithms of special cases:

UR and UL both solved by accident (page 18)
2 disoriented midges DF UB: U' M U M U2 M' U M' U
2 disoriented midges UF DF: U M U M U2 M' U M' U'
4 disoriented midges: precede with U' M U M U' M' U then finish with DFL algorithm you already know (U2 M' U M U M' U M U') [this is longer than the 'fixed' version of this case but it is very easy to learn because it incorporates an algorithm you already know)

Page 16: learn all four of the situations at the top of page 16 (one edge inverted)
U L' U M' U2 M2 U L U'
U' R U' M2 U2 M2 U' R' U
M' U M' U M' U M' U [extremely easy, just [M' U]x4)
M' U' M' U' M' U' M' U' [extremely easy, just [M' U']x4)

So start with the 26 algorithm set then move up to the 33 algorithm set. I would comment that since most people know Ortega and the midge permutations are intuitive as is U' M' U, there are really only TEN algorithms to learn to get going with the basic set, or 17 if you learn the extended basic set. That means that most people can learn the basic set of 10 in a single day!

I would comment that one of the extremely beautiful (and fun) aspects of this method is that it takes so few algorithms to get started (around 10-17 as I mentioned), but you can keep growing with the method and gradually learn more and more cases until you know all 776. This prevents the terrible problem of the 'plateau'. So many speedcubers get stuck around 20 seconds and don't see improvement for years. In most cases long hours of drills are needed for them to increase their TPS and recognition. While that does work, what I find a more fun way to improve is to learn new cases. Every week I learn a few new cases and it is really fun when one of the cases comes up in a solve and I can finish the cube faster than before, and the result is every single month my average times go down steadily with no end in sight.

Wow! what a response! thanks so much for the details. I'm excited to give it a try even though I'm not a super fast solver.

I'm a fan of methods with few algorithms which is why I asked about the basic version.
I currently do CFOP with only 12-15 algs (depending on how one counts them)

Here is revision 4, which now includes two extended L6E sets, the rDFR set and the xDFL set. The rDFR set is a new trick, when solving the last 6 edges you are better off solving UL/UR inverted which drops the move count of the orientation step to 7.87.

I'm going to create a tutorial for both the beginner's method and the advanced variations within the next couple of days. These will be posted to my youtube channel. In the meantime I got video of a Waterman L6E finish on a real speed solve! Ok it took me 7 seconds to remember the algorithm but c'mon there are 372 cases and I am still learning them.

What's about algorithms for L5E, which solve whole rest of cube? Solving UR edge + Midges orientation + Midges permutation with one algorithm. If I am not wrong and UR edge is on M-slice it is 88 new cases + mirrors. (If UR edge is flipped on own position, it is another 88.)

What's about algorithms for L5E, which solve whole rest of cube? Solving UR edge + Midges orientation + Midges permutation with one algorithm. If I am not wrong and UR edge is on M-slice it is 88 new cases + mirrors. (If UR edge is flipped on own position, it is another 88.)

This was explored in a thread I created a while back called 'Roux L6E in one look'. There are at least 110 cases and recognition is slow; I explored it extensively and decided there was little to nothing to gain as recognition takes around the same time as permuting the midges.

I had a nice single today with csTimer, managed to reconstruct

Scramble: B2 L2 U' B2 F2 U L2 D' L2 B2 U2 L R B L' R F R' D' R
z2 U R2 U l U' R' // green face and CLL skip
M U2 M' // solve blue-red edge
D' M' D2 M // solve green-orange edge on D face
z x' L' U' M2 U // E2L pair
x2 r' U' M2 U r R // set up
M2 U' r' R' U M U' r2 U R2 // Waterman L6E Set 2 case 6C