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During my attempts to improve the ergonomics of LMCF, it seems clear that several edges piece must be solved at the same time as the corners. Years ago when WaterRoux was proposed, the idea was to solve Roux first block, and all the corners, in one look. Most considered that unrealistic. That would require solving 3 edges plus all the corners in one look, during inspection. An alternative, even more difficult, is to fully solve all four 3x1 columns in one look (all corners plus FR+FL+BL+BR edges). Again, most considered this nearly impossible. However, not long ago I was having a DM chat with WACWCA, who is a top 2x2 solver. He told me that he frequently can inspect three or even FOUR possible 2x2 solutions during the 15-second inspection time, and then, choose the solution that is the fastest of all of them. This implies, almost without question, that indeed it would be possible to solve many edges and the corners in one look. Instead of inspecting 3-4 corner-solving solutions in the inspection, the solver chooses only the first one, even if it might not be the fastest. That leaves most of the inspection time to figure out how to either solve the 3 edges needed for Roux first block, or, for all 4 columns. Make no mistake; if any solver can solve either roux first block plus all the corners, or all the columns, in the inspection, I believe this almost certainly would result in the fastest method ever designed. Consider that Roux solvers solve 5-7 pieces during inspection, CFOP solvers that can do XCross solve 6 pieces; LMCF solves 8 pieces in the inspection, yet now it seems that solving 11-12 pieces in the inspection is possible. If it takes 1.5 seconds on average to solve the corners (top 2x2 average), the extra time to solve 3 edges would be quite low as move freedom is extremely high, and slice moves at the start of the solve do not affect the corner solution. Not unrealistic to say that in 1.9 seconds the solver could finish Roux first block and all the corners. All that is left now is an LMCF triplet (1.1 seconds) (for waterroux), followed by LSE, or LMCF pair (0.8 seconds) + LSE for columns. In the case of columns, LSE is the same as Roux (1.5 seconds), whereas if you choose the WaterRoux style, LSE is slower because the 2-edges on one side case, allowing 1.9 seconds. This predicts an average for WaterRoux of 1.9+1.1+1.9 = 4.9 seconds, and for columns, 1.9+0.8+1.5 = 4.2 seconds. The basis of this is the claim by WACWCA that top 2x2 solvers can see 3-4 solutions in the inspection. How they 'got' to that point is beyond me, but if true, opens a great deal of possibilities to solve 11-12 pieces in the inspection. Even if I am being over-optimistic in the splits, and even if you add 1 full second, it still predicts 5.9 and 5.2 second averages.

During my attempts to improve the ergonomics of LMCF, it seems clear that several edges piece must be solved at the same time as the corners. Years ago when WaterRoux was proposed, the idea was to solve Roux first block, and all the corners, in one look. Most considered that unrealistic. That would require solving 3 edges plus all the corners in one look, during inspection. An alternative, even more difficult, is to fully solve all four 3x1 columns in one look (all corners plus FR+FL+BL+BR edges). Again, most considered this nearly impossible. However, not long ago I was having a DM chat with WACWCA, who is a top 2x2 solver. He told me that he frequently can inspect three or even FOUR possible 2x2 solutions during the 15-second inspection time, and then, choose the solution that is the fastest of all of them. This implies, almost without question, that indeed it would be possible to solve many edges and the corners in one look. Instead of inspecting 3-4 corner-solving solutions in the inspection, the solver chooses only the first one, even if it might not be the fastest. That leaves most of the inspection time to figure out how to either solve the 3 edges needed for Roux first block, or, for all 4 columns. Make no mistake; if any solver can solve either roux first block plus all the corners, or all the columns, in the inspection, I believe this almost certainly would result in the fastest method ever designed. Consider that Roux solvers solve 5-7 pieces during inspection, CFOP solvers that can do XCross solve 6 pieces; LMCF solves 8 pieces in the inspection, yet now it seems that solving 11-12 pieces in the inspection is possible. If it takes 1.5 seconds on average to solve the corners (top 2x2 average), the extra time to solve 3 edges would be quite low as move freedom is extremely high, and slice moves at the start of the solve do not affect the corner solution. Not unrealistic to say that in 1.9 seconds the solver could finish Roux first block and all the corners. All that is left now is an LMCF triplet (1.1 seconds) (for waterroux), followed by LSE, or LMCF pair (0.8 seconds) + LSE for columns. In the case of columns, LSE is the same as Roux (1.5 seconds), whereas if you choose the WaterRoux style, LSE is slower because the 2-edges on one side case, allowing 1.9 seconds. This predicts an average for WaterRoux of 1.9+1.1+1.9 = 4.9 seconds, and for columns, 1.9+0.8+1.5 = 4.2 seconds. The basis of this is the claim by WACWCA that top 2x2 solvers can see 3-4 solutions in the inspection. How they 'got' to that point is beyond me, but if true, opens a great deal of possibilities to solve 11-12 pieces in the inspection. Even if I am being over-optimistic in the splits, and even if you add 1 full second, it still predicts 5.9 and 5.2 second averages.

So, on a similar note, I've been thinking about ECE. Based on your analysis, if it is possible to plan columns in inspection, planning psuedo-columns could be very feasible. Following this I believe that generating NLL algs from HD-G would be an excellent idea. NLL would mean that you would combine separation and permutation of corners into one step with the caveat that you need to force L cases on top and bottom. You could generate all NLL cases but that would increase the alg count significantly. Based on the move count from HD-G, NLL would save around 3 moves. Then you can choose any L8E variant to finish the solve. This could lower the average movecount to 40 with EZD. This would also make it into a 3.5-4 look method. Pseudo-columns => NLL => EO/Separation => EZD. In HD-G you can predict the subset of NLL in inspection and then you just need to recognize the case which accounts for the 'half' look. This would also be done in only around 100 algs !!

if anyone here is good at metha try this?
basically, you do ZZ EO
FB, 3/4 belt (do on oriented side)rotate to have block on left
from here, you want to reorient the E slice edges by doing a E/u move
to make the edges reoriented to the new side.
than just do whatever mehta variant you want-having to orient edges.

if anyone here is good at metha try this?
basically, you do ZZ EO
FB, 3/4 belt (do on oriented side)rotate to have block on left
from here, you want to reorient the E slice edges by doing a E/u move
to make the edges reoriented to the new side.
than just do whatever mehta variant you want-having to orient edges.

idk it prob a bit less efficient than normal mehta,
the only reason this solve was so inneficient is because I don't know what im doing lol.
the R U L belt is kinda nice, aswell as doing EO at the begging of the solve since doing eo midsolve is considered pretty sucky from what i've heard.
not as good as normal mehta I think (efficiency,1 rotation) but has some potential
update:
you can do block on left and don't have to rotate

EO+FB is quite difficult to plan in inspection; one idea being explored is EO+Square in inspection followed by extension to FB, and belt using only u2 (or u R2 u type stuff). Not sure where it'll go, it's a work in progress.
I'm not a huge proponent of the idea, because EO midsolve isn't always bad (it's done in both CFOP and Roux); but it could have potential we don't see yet.

I have a 3x3 method idea, that to me, just sounds really nice.

1. Left 1x2x3
2. EO + DFDB
3. Right 1x2x3
4. ZBLL (or 2lll)

Spoiler: Example Solve

Scramble: D B R L' U' L2 B F2 D R2 B2 U2 F2 L2 U' L2 D' B2 L U2
(x2 y)
U D B L' U' B // Left 1x2x3 (6)
r U' r' U' r U2 r U2 r2 // EO + DFDB (9)
U2 R U2 R' U2 R2 U' R' U' R2 U' R // Right 1x2x3 (12)
U2 R' U' R U' R' U2 R U' // ZBLL (9)
36 HTM ! (and 92% R and U moves!!)

Maybe I’ll name it LEOR or something. Thoughts on this method?

I know this comment is old .... But what happened to the method? I saw it a long time ago, I found it very interesting and I have discussed it with friends .... I don't know what happened but I would like to develop or help develop this method

Sorry if I express myself badly, English is not my native language

I know this comment is old .... But what happened to the method? I saw it a long time ago, I found it very interesting and I have discussed it with friends .... I don't know what happened but I would like to develop or help develop this method

Sorry if I express myself badly, English is not my native language

this is LEOR I didn't see it said that lol
its a popular method probably like the 5th most popular behind petrus and is bassically just a slightly diffrent eo223 method

During my attempts to improve the ergonomics of LMCF, it seems clear that several edges piece must be solved at the same time as the corners. Years ago when WaterRoux was proposed, the idea was to solve Roux first block, and all the corners, in one look. Most considered that unrealistic. That would require solving 3 edges plus all the corners in one look, during inspection. An alternative, even more difficult, is to fully solve all four 3x1 columns in one look (all corners plus FR+FL+BL+BR edges). Again, most considered this nearly impossible. However, not long ago I was having a DM chat with WACWCA, who is a top 2x2 solver. He told me that he frequently can inspect three or even FOUR possible 2x2 solutions during the 15-second inspection time, and then, choose the solution that is the fastest of all of them. This implies, almost without question, that indeed it would be possible to solve many edges and the corners in one look. Instead of inspecting 3-4 corner-solving solutions in the inspection, the solver chooses only the first one, even if it might not be the fastest. That leaves most of the inspection time to figure out how to either solve the 3 edges needed for Roux first block, or, for all 4 columns. Make no mistake; if any solver can solve either roux first block plus all the corners, or all the columns, in the inspection, I believe this almost certainly would result in the fastest method ever designed. Consider that Roux solvers solve 5-7 pieces during inspection, CFOP solvers that can do XCross solve 6 pieces; LMCF solves 8 pieces in the inspection, yet now it seems that solving 11-12 pieces in the inspection is possible. If it takes 1.5 seconds on average to solve the corners (top 2x2 average), the extra time to solve 3 edges would be quite low as move freedom is extremely high, and slice moves at the start of the solve do not affect the corner solution. Not unrealistic to say that in 1.9 seconds the solver could finish Roux first block and all the corners. All that is left now is an LMCF triplet (1.1 seconds) (for waterroux), followed by LSE, or LMCF pair (0.8 seconds) + LSE for columns. In the case of columns, LSE is the same as Roux (1.5 seconds), whereas if you choose the WaterRoux style, LSE is slower because the 2-edges on one side case, allowing 1.9 seconds. This predicts an average for WaterRoux of 1.9+1.1+1.9 = 4.9 seconds, and for columns, 1.9+0.8+1.5 = 4.2 seconds. The basis of this is the claim by WACWCA that top 2x2 solvers can see 3-4 solutions in the inspection. How they 'got' to that point is beyond me, but if true, opens a great deal of possibilities to solve 11-12 pieces in the inspection. Even if I am being over-optimistic in the splits, and even if you add 1 full second, it still predicts 5.9 and 5.2 second averages.

Also, for WaterRoux, would it be better to do 2x2 and then plan the rest of the corners? Then solve FL + any edge on R. Than any two edges on R + EO and then L6E? 1x2x2 + Corners seems easier than planing 1x2x3 + corners. Optimally you solve all 8 corners + BL + DL or more realistically do so in 1.5 looks; predicting a corner case partial case and then recognizing the rest afterwords. All-in-all solving 10-12 pieces in inspection seems not extremely likely but solving 8 + orientation of 2-3 pieces or maybe just tracking the 2-3 pieces? I think the limit for solving pieces in inspection is probably 8 or in what I'm suggesting 8.5 - 9 pieces ( the .5 - 1 pieces being partial solved ). This style or solving is what is suggested in HD-G as far as just partial prediction to narrow the cases.

Based on my conversations with WACWCA, solving corners + 2 edges (i.e. 2x2x1 + corners) should be easy. More is still possible. But, if you could solve the left back 2x2x1 every solve (+ corners), and perhaps on some solves, solve the entire Roux-FB + Corners. If you do solve Roux-FB + corners, obviously you have much greater freedom than with Roux because you can use LEG-1 algorithms (or even L5C) instead of just CMLL.

This is definitely easier said than done. I'm not sure that this idea will necessarily transfer over from 2x2. I think theoretically you may be able to plan all of this but especially for consistency I think that doing a 1.5 look would be the best bet. I also don't think that this would be much shorter than planning all 10 pieces.. I think that lookahead goes much farther than people estimate. This is something that was pointed out when discussing whether or not 3-style would be the fastest method given that it can be one-looked. Efficiency aside I think that optimizing lookahead is probably, long run, better due to much be consistency.

I thought you could make the first 2 blocks like Roux then finnish F2L like you would with Roux then go into CFOP and do OLL and PLL. Let me know what you think the potential of the Combo method is!

I thought you could make the first 2 blocks like Roux then finnish F2L like you would with Roux then go into CFOP and do OLL and PLL. Let me know what you think the potential of the Combo method is!

You are not the first to have thought about it but nobody does it because it's very bad.
In 20 years many have tried to improve Roux. Everybody has failed. This method is born perfect.

I thought you could make the first 2 blocks like Roux then finnish F2L like you would with Roux then go into CFOP and do OLL and PLL. Let me know what you think the potential of the Combo method is!

This is a very commonly thought of concept, and the reality is that if you’re doing the F2B anyway, it’s faster to do CMLL then L6E then it is to fill in two edges and do OLL and PLL.

Also, whenever you have an idea, try posting in the megathread for it

This is a very commonly thought of concept, and the reality is that if you’re doing the F2B anyway, it’s faster to do CMLL then L6E then it is to fill in two edges and do OLL and PLL.

Also, whenever you have an idea, try posting in the megathread for it

or you could do f2b, cmll/coll, EO, DF/DB, epll.
that's how I solve roux because I can't figure out l6e and that's closer to roux than finishing with OLL PLL
I need to practice more