The Roux method is not widely used but has shown its potential through many sub-15 achievements by people such as Thom Barlow and Jules Manalang. It has also achieved many sub-10 achievements by Austin Moore, Alexander Lau, and Kian Mansour. It works with block building, similarly to Petrus, but in a different fashion. You start by solving a 1x2x3 block on either the left or the right side, followed by an identical block on the opposite side. Thereafter you permute and orient all remaining last layer corners using CMLL. From here, only M and U-turns are made. The next step consists of orienting all remaining "bad edges". After orienting the "bad edges" you solve the two edges simultaneously which belong above the 1x2x3 blocks. The final and shortest step is permuting the final 4 edges.
One of the most important things to do before you start learning any speedcubing method is to know how to solve your Rubik's Cube a beginner way. If you know this, you will understand that you cannot just get all of one colour on one side, but you have to put the pieces in the right place as well. Knowing this will also help you to understand why many of the algorithms of a speedcubing method work. You also need to know the colour scheme of your cube by heart. To get a fast time, you must be able to know where pieces go relative to each other without having to think about it.
The notation that will be used here is as follows:
R-Right face L-Left face U-Up face D-Down face F-Front face B-Back face M-Slice between R and L (Middle)(Direction of L) E-Slice between U and D (Equatorial)(Direction of D) S-Slice between F and B (Side) (Direction of F) x-whole Cube in direction of R y-whole Cube in direction of U
z-whole Cube in direction of F
No Suffix-quarter turn clockwise ' or i-quarter turn counter-clockwise 2-half turn w or lowercase-double layer quarter turn clockwise w' or lowercase'-double layer quarter turn counter-clockwise w2 or lowercase2-double layer half turn
Creating a block one cube wide, two cubes tall, and three cubes deep, is the first step. This step is simple enough, and most anyone who can solve the Cube in a simpler fashion can finish this. This step is pretty self-explanatory, and there are many ways to go about it, you just have to find them. This step can usually be mentally achieved by longtime Roux uses but in the fifteen second inspection time before any given scramble. This step is mostly completed mentally, so it is almost required that you have a basic understanding of your cube before getting decent times with this method. Most speedcubers find this the easiest step.
In this step, you add a second 1x2x3 on the opposite side from the first. If you did the white side first, now you would do the yellow 1x2x3. You have to keep intact your first 1x2x3 block on the left side. This is a simpler task than many think, but you have to be resourceful and understand your Cube and its moves to imagine what needs to happen to complete this step
Corners of the last layer
First, you must orient all your top corners up. Use the algorithm R U R' U R U2 R'. This will rotate all corners clockwise, besides the front upper left corner. Position carefully to do the least number of repetitions.
Next, you may need to swap two corners. Position the corners that need to be swapped on the right side. That is, you find the two correct corners and position them on the left. Then you use the algorithm R U R' F' R U R' U' R' F R2 U' R'.
Fixing Bad Edges
During this stage, you need the U or D face center on top. From there, proceed to see if any of the edge cubes have the F or B stickers on the U or D face. Once you locate all the pieces that un-oriented, you must orient them. This can be done with a little logic, and knowledge of your Cube. (For beginners, this concept may be difficult to grasp.) But you will get it.
Placing L and R edges
All this step does is place two edges, simultaneously, above the 1x2x3 blocks from the first two steps. There are a small number of cases for this step, seeing that there are only 2 pieces you need to work with. This is can be highly optimized and brought down to only a few moves.
Permuting M edges
A fairly simple process, using any variation of M and only U2, that will correctly place the remaining 4 edges of the M slice.
There aren't many apps on the play store right now for the Roux Method, at the moment the only one is: