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I've been using this, and have gotten sub-20 with minimal practice, and I think it could be good. the only downside, is that there are a lot of algs, though most can be done in two steps.

1. F2l-1: Solve however you like.
2. Insert corner and solve EO (33 algs) If F2L-1 was solved via petrus or ZZ, there should be no need for algs
3. COLL (42 Algs)
4. EOL5E (? algs)

Example solve: here
Scramble:
L B2 F2 L2 D2 L U2 R' F2 L F2 B R' U' B' F D' L' D B2 R2

x' r' F' D L2 D R' D2 L' R' U2 R U' R U R2 F R F' L U L F' L' F D L' U' L D' L' U L // F2L-1
y2 R U' R' U' F' U' F R U2 R' //EO+C
U R U2 R D R' U2 R D' R2 // COLL
R U R U' R U R U R U' R' U' R2 U' R' //L5E
67 HTM, but I'm am incredibly inefficient.
What do you guys think?
 
I have considered all these variants and as far as a 'Modernized Waterman' goes, I think the best variant is the rotationless variant mentioned earlier:
1. Solve FB on the left (roux style)
2. Solve DFR and BDR corners in a random permutation
3. Execute an EG1-style or CMLL algorithm to solve the top corners and permute the bottom right corners
4. Solve two R-layer edges at once in a pair algorithm (LMCF style) or if possible solve a triplet (UL, and two redges)
5. Finish with L7E or Waterman L6E

This adds 42 EG1-style algorithms, 80 L7E algorithms and about 24 LMCF algorithms to the original Waterman, which was itself heavy in algorithms. I think it would be fast and quite fun though. It is quite similar to WaterRoux though. One could honestly call it a variant of WaterRoux.
Are these EG-1 algs available? I'd definitely consider learning them. I'm mainly using Roux as my main method atm (my sig has been irrelevant for months, I should really change it) and I'm really starting to get the hang of Waterman L6E and LMCF so I could potentially use this as my main method for a while and see how it goes. Also how many LMCF algs would be necessary?
 
Are these EG-1 algs available? I'd definitely consider learning them. I'm mainly using Roux as my main method atm (my sig has been irrelevant for months, I should really change it) and I'm really starting to get the hang of Waterman L6E and LMCF so I could potentially use this as my main method for a while and see how it goes. Also how many LMCF algs would be necessary?

If we call this WaterRoux-EG, then you need to use LEG-1 algorithms which hold the bar on the left. The LEG-1 set has been generated for 2x2 here and the vast majority of them keep the Roux first block intact when used on 3x3:
http://www.cyotheking.com/leg1/

So only a few need to be regenerated with Cube Explorer.
 
So looking back a few posts ago on my Petrus/L2L variant, I realized that there's actually not nearly as many cases as I was expecting there to be. There'd only be 86 cases including EPLL, and a majority of the algs are just mirrors/inverses. THey're also pretty easy to recognize. And of course they're all 2-Gen, but some of the 2 gen algs are pretty long, so I may consider making a 3-Gen alg set for it and choose algs from there. I'll do an example solve later today and if it's good I'll post it.
 
I thought of a method that is a new version of ZZ. The main difference is the use of M-slices in EO. Almost all of the time, with x2 and y2 color neutrality, EO can be finished only <R,U,r,u,M>. This may seem cumbersome, and sometimes it is. The reason one would use it is this: if these are the only moves used, then CP does not have to be tracked, further than simply tracking the pieces to be swapped. Thus the needed swaps to solve CP can be tracked through. Now, we can simply finish the CP while placing the line edges. I don't know how difficult this would be, but I assume it is doable. It would be even easier if you placed one or both line edges while orienting edges. If you have any experience with Roux L6E, you should know how to help influence this. From there, you can do F2L and finish with 2GLL.

Example solve:
Scramble- D2 R D2 R' F2 L U2 R' B' F U' L B2 L F' D2 U R'
2GEO- r M' U R2 U2 M' U M' U M' U M' U u2 R U' R2 U' M' U M U2 M' U M -could definitely be more efficient
CPline- U2 M' U2 M2 U2 M' -pretend I did CP here, as I don't know how
Left block- R L' U L U' L2 U L' U2 L2 U2 L U2 L U L U L U L'
Right block- R' U' R' U2 R2 U R U2 R U R' U2 R U R'

Yeah, this is a bad idea. I'm not even going to finish the solve. I'll leave the concept for someone else to mold into something feasible. Honestly, you should probably use Briggs instead.
 
I made a new 4x4 direct solving method that is directed toward CFOP users. I got a 1:36 ao5 with it, and I average 1:17 with Hoya.

Step 1: Cross and centers
You can do this with Yau or Hoya, whichever you prefer.

Step 2: F3L
What you do is use F2L techniques to solve a corner and a wing, then solve the other wing using keyhole. If you cannot find the other wing, you can start solving another slot until you find it. For the last pair, you use a commutator to solve the last wing. Match it up with its center, hide it on the bottom layer using a slice move, do a sledgehammer, slice back up, and insert the pair.
EDIT: You can also insert a single wing, move it out of the way using a Uw of d move, and solve the rest of the slot using F2L techniques.

Step 3: CLL
You can use whatever OLLCP algs you want for this. The only things that matters is that you preserve the F3L and solve the last layer corners.

Step 4: ELL
You have to use commutators for this. A great way to do this is to solve 2 opposite edges, then solve the last 2 dedges with one algorithm (they can be found on the KBCM wiki page). Since I am not very good at 4x4 ELL, I solve one wing at a time using 2 simple commutators. When the top layer sticker is facing up, I do F R' F' r' F R F r. When the top layer sticker is facing to the side, I do x' r B' R B r' B' R' B. There are also cases that use flipping algs as insertions.
 
I made a new 4x4 direct solving method that is directed toward CFOP users. I got a 1:36 ao5 with it, and I average 1:17 with Hoya.

Step 1: Cross and centers
You can do this with Yau or Hoya, whichever you prefer.

Step 2: F3L
What you do is use F2L techniques to solve a corner and a wing, then solve the other wing using keyhole. If you cannot find the other wing, you can start solving another slot until you find it. For the last pair, you use a commutator to solve the last wing. Match it up with its center, hide it on the bottom layer using a slice move, do a sledgehammer, slice back up, and insert the pair.
EDIT: You can also insert a single wing, move it out of the way using a Uw of d move, and solve the rest of the slot using F2L techniques.

Step 3: CLL
You can use whatever OLLCP algs you want for this. The only things that matters is that you preserve the F3L and solve the last layer corners.

Step 4: ELL
You have to use commutators for this. A great way to do this is to solve 2 opposite edges, then solve the last 2 dedges with one algorithm (they can be found on the KBCM wiki page). Since I am not very good at 4x4 ELL, I solve one wing at a time using 2 simple commutators. When the top layer sticker is facing up, I do F R' F' r' F R F r. When the top layer sticker is facing to the side, I do x' r B' R B r' B' R' B. There are also cases that use flipping algs as insertions.
This is literally K4 but using keyhole to solve F3L rather than "algs" and changing the center/edge building techniques
 
I did a small test in regards to movecount and unfortunately it may not be as low as was predicted. It's still about the same as Roux though. Here is my rundown:

FB: 7 moves
Sq+C:11 moves (?)
TCMLL: 10 moves
Setup: 2 moves (?)
L7E: 15 moves (?)

So I'd estimate the average movecount to be 45 which is still excellent and in the range of Roux and ZZ-A, but unfortunately not as powerful as was expected. Correct me if I'm mistaken but isn't this about the same movecount projected in LMCF? I'm thinking that maybe 45 moves is about the est. average movecount that a human method can get right now but that may change in the future.
 
Hey I know it's been a while since Shiv3r or I have posted about it, but I just released a video detailing the newest version of the NS4 Method. Here's a link if you'd like to check it out:

 
So I have all of the algs generated for L6EP. It was originally concieved for my L2L variant (may continue work but it's not showing much promise), but it can be applied to ZZ/Petrus/CFOP quite easily.

There are 86 cases that are (mostly) pretty easy to recognize once you get the hang of it, and the average and median is at 12 moves simply with the 2-Gen algs. It could be good for OH or to finish CP Redux. It also makes SB REALLY easy for ZZ. The only problem is the recog on some of the cases is kinda hard (especially on the last set. oh GOD), but this may have some potential for very fast OH solvers. Enough rambling, here are the algs so you can judge for yourself:

https://docs.google.com/spreadsheets/d/1XSIM6KS0aNAMaVOQGScCCPGf_IhphhWzPbsDmyus0hE/edit?usp=sharing
 
Hey guys, I wanna generate some algs for a new method idea I have (related to WaterRoux), however I am currently on vacation and do not have access to Cube Explorer (it's complicated, but basically my laptop is a work laptop which cannot download certain software). Does anyone know of any other solvers that are just as good, if not better? I've tried ACube but it's a little too complex for me, and I don't have the time to learn how to use it.

Sent from my Moto G (4) using Tapatalk
 
This method is dumb and probably won't work very well, but I have a new ZZ variant.

Step 1: Eoline (obviously)
Step 2: solve all corners
Step 3: Using R And L moves and Epll algs, solve the R and L face edges, forcing a LL skip.

Advantages: Very intuitive, low algcount, easy to learn.

Disadvantages: A lot of M slices during last step, hard to optimize, not researched. (obviously)

Any ideas on how to improve this method, or is it just bad like I think it is?
 
crafto and I are working on a potential way to do edges in WaterRoux that we could use some help on in making algs. Basically the DB and FR edges get solved while orienting the rest of the edges so it's possible to end in L5EP. The DB and FR edges get put in the redge slots with no regards to permutation/orientation. Anyone think they can help us out? Preferably keep the algs using M U and R/r moves. I know that the sets with both DB and FR oriented have 16 algs each and there'd be 8 sets so it's not a horribly large algset (120-130 is my guess)
 
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