# Playing With Roux Orientations

#### cubacca1972

##### Member
I am starting this thread because I hijacked another (sorry about that).

I came up with the idea of parking the UL and UR edge cubies in the DF and DB positions (either order), and solving one of eleven possible orientation patterns, so that all remaining edges are oriented, and UL and UR are still in DF and DB positions, ready to be slotted home with U (or U', or U2), M2, then U or U'.

The original algorithms that I found via Ron's sticker mode solver were:

M U' M U M' U2 M U' M U' M (11,12)
M U M' U2 M U M' (7,8)
M' U2 M' U2 M' U' M U2 M U2 M (11,15)
M' U M' U2 M' U M' U M U' M' (11,12)
M' U M U' M' U2 M (7,8)
M U' M U2 M U' M U' M' U M (11,12)
M U' M' U M U2 M' (7,8)
M' U' M' U M U' M (7,7)
M' U2 M' U2 M U' M' U' M2 (9,12)
M U M U M U M (7,7)
M' U M' U M' U M2 U' M U2 M' U' M (13,15)

Athefre was able to find several amazing shortcuts to several of the algorithms as above, and we learned about some blind spots that computer solvers have when looking for optimal solutions to the orientation step with the roux method.

#### Athefre

##### Member
That was the part I hated most, I didn't even bother memorizing the corner sequences until 2 years after I started using the method.
Yeah, its a bit daunting to digest all those cases. It kinda goes against my inherent laziness. That's also why I love the waterman method, but will never learn the full system.

Probably at least most of them are like that. Not all shortcuts are useful when solving for speed though. Some are hard to recognize fast.
Generally, if you have more special cases than you have orthodox cases, you are drifting into fewest move challenge territory, and farther away from speedsolving, specifically because of the time burned up trying to recall which particular special case you are looking at.

Can you explain what exactly you are doing? Are you getting ACube to give all possible sequences, then you check each one to see what it does?
Man, I only wish it was that easy. I am manually checking all 2 187 possible algorithms in the 7 move set. I did not run A Cube. I reviewed what my data entry options were, and what the program checks for. Assume that a solved cube starts with yellow on top, orange on the left, red right, green back, white down, blue front.

What A Cube will check is how to get all six edges oriented with the yellow center on top. The problem is that we need to check for all possible cases which meet our requirements, which are:

LU and RU oriented in DF and DB position (or swapped)

With the white center on top, with white or yellow edge facelets on the U face

OR

With the yellow center on top, with white or yellow edge facelets on the U face

OR

With the green center on top, with green or blue edge facelets on the U face

OR

With the blue center on top, with green or blue edge facelets on the U face

So if I were to just check those cases generated by one of the conventional programs, I would potentially miss out on 75% of the potential algorithms. This is why you were able to find shorter algs than the originals I found using Ron's sticker mode solver. It can't recognize end states that we like as solved.

Here's what my theoretical orientation program would do, and how it would work, keeping the following assumptions and visuals in mind:

Our cube only has 4 colors:

L face yellow
R face white
F face red
B face red
U face green
D face green

Our cube only allows for 6 moves: U, U2, U', M, M2, M'

Our program only checks the location of the 6 edges, which facelet of each edge cubie (except for UL and UR) is on the U or D face (red/green), and what color center is in the U face (red/green). UL and UR edges are either oriented (Y, W), or flipped (y,w)

Data for the start position is entered to make a 7 character string which follows this form: UL UR UB UF DF DB Center

So and all flipped start position would be entered as:

GGGGywR

or

RRRRywG

or as above, with yw transposed. The program could just have yy or ww if we didn't care to track UL or UR as unique,

Solved would be entered like this, assuming that we were looking to find one of the 11 cases:

GGGGYWG

or

RRRRYWR

or as above, with UL and UR represented by the same color.

Then, the program would apply algorithms and check the resulting string with the set of acceptable end states, and print out those algorithms which match one of the defined strings in our set.

No program out there right now can do this.

I can totally write this out in pseudocode, but am programming language illiterate. I might try to write it out in Liberty Basic, but am short on time to do so right now.

I completely understand your idea, but I don't know much programming either so I wouldn't be much help with that.

cubacca1972 said:
Just to update:

M U' M U M' U2 M U' M U' M (11,12) - UF/UB
Alternative: M'U2M'UMUM'U'M' (9) - I also found F2M'UMUM'UMUF2 but it isn't comfortable.
There is a problem with your first alternative. If you do the inverse of my algorithm to set up the pattern and do your first alternative, it leaves all U layer edges flipped! I do not understand why that is though.

In your original solution, the two misoriented edges have to be at UF/UB before performing the sequence, in the first alternative they have to be at UL/UR.

#### cubacca1972

##### Member
Oops. I was worried for a second that the whole solution set might have sub cases where the algs didn't work. I am relieved.

As far as the pseudocode goes, I think I could get some of the subroutines working, but I have no ideas how to write a subroutine that would start with 1 alg, then check the next one, etc. Sigh.

#### Athefre

##### Member
As far as the pseudocode goes, I think I could get some of the subroutines working, but I have no ideas how to write a subroutine that would start with 1 alg, then check the next one, etc. Sigh
I probably won't be able to help much further. With shortcuts and the new 7.7 average one can probably average 14 moves total using your LSE method.

Place UL/UR: 2 (Results of an average - 0, 3, 1, 1, 2, 3, 2, 2, 3, 3, 1, 1)
Orient: 7.7
Permute: 1.5 (UL/UR) + 4 (M edge permutation has an average of 4 moves, you could talk about the chance of having the first move be a U2 but that doesn't remove anything from the average, either way there's going to be a U or U' after placing UL/UR in their correct slots)
Shortcuts: -1 possibly, really depends on what you choose to use.

I'll probably now work on describing the suitable optimizationss, unless you already see them.

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#### cubacca1972

##### Member
I probably won't be able to help much further. With shortcuts and the new 7.7 average one can probably average 14 moves total using your LSE method.

Place UL/UR: 2 (Results of an average - 0, 3, 1, 1, 2, 3, 2, 2, 3, 3, 1, 1)
Orient: 7.7
Permute: 1.5 (UL/UR) + 4 (M edge permutation has an average of 4 moves, you could talk about the chance of having the first move be a U2 but that doesn't remove anything from the average, either way there's going to be a U or U' after placing UL/UR in their correct slots)
Shortcuts: -1 possibly, really depends on what you choose to use.

I'll probably now work on describing the suitable optimizationss, unless you already see them.
Thanks for all the work you put in to this system. You definitely get major credit for finding all those optimizations.

The algorithm list as it stands now:

M' U2 M' U M U M' U' M' (9,10)
M U M' U2 M U M' (7,8)
M' U2 M' U2 M' U' M U2 M U2 M (11,15)
M U2 M' U M U M U2 M (9,11)
M U' M' U' M (5,5)
M' U2 M U' M' U' M' U2 M' (9,11)
M' U M U M' (5,5)
M' U' M' U M U' M (7,7)
M' U2 M' U2 M' (5,7)
M U M U M U M (7,7)
M' U M' U M U M' U2 M' U M (11,12)

I don't see any further optimizations yet, as I do not have enough experience yet with Roux. When you know a system cold, and you no longer have to concentrate on the actual solve, its way easier to let your eyes wander and notice new patterns.

For now, I will concentrate on algorithm crunching. On the upside, I don't think I will have to test drive all of the possible 7 move algorithms. If my logic isn't failing me, then:

When I start with a "solved state" for this system (UL and UR in D layer, all 6 oriented) the pattern is symmetrical.

If I search all algorithms that start with the move M, anything useful I find will have a mirror algorithm that starts with M'.

Therefore, there is no need to search the algorithms that start with M'.

If I complete the 7 move and 5 move search by brute force, then any remaining potential shortcuts for the 2 remaining 11 move algorithms will either be found, or be exactly 9 moves long.

If one or both are 9 moves long, I won't brute force search manually. I will try to write that program.

#### gogozerg

##### Member
This thread reminds me a lot talks I had with Josef Jelinek some time ago.

He was looking for a way to make the "last 6 edges" a 2-look process.That's why he decided to put UL and UR edges in U and D layers, a rather costless starting position requiring at most 1 move (rarely 2).

I had discarded the idea of considering UL and UR edges before orienting, except for special cases, because I thought a simple orientation is easy and fast to learn and anticipate. And while orienting, you have extra time to localize L and R stickers.

By the way, Josef had a small Java program made for optimizing "edges last" endings. Quite useful.

In your list of sequences, I would just drop the last 2 moves to make it look more simple, since the final M* is rather useless (chances for optimization with the next substep are 25%), and the U* before is just about aligning UL and UR.

There are a few possible ways of solving the edges rather efficiently (14-15 moves). The old standard "corners-first" strategy (solve UL or UR edge, then solve the other while orienting) is one of them.

By mixing techniques, you could average 12 moves.
(And of course, there are some other possible FM tricks)

The problem is, how to be fast? No need to learn a sequence that is 2 move shorter if you waste 2 seconds detecting when to use it.

I thought the best was to have an efficient basic method, and then use shortcuts for special cases that can be immediately detected (some orientations ending with non oriented centers, or the old standard strategy when an edge is already solved for instance).

The goal for this step is to consistently average sub-3.

#### cubacca1972

##### Member
In your list of sequences, I would just drop the last 2 moves to make it look more simple, since the final M* is rather useless (chances for optimization with the next substep are 25%), and the U* before is just about aligning UL and UR.
I hadn't considered that. Once I definitively find the optimal algorithms for all of the cases, I will try both ways- original, and original minus the last 2 moves, and perhaps minus the last M move only. I am not very speedy though. I get most of my kicks by exploring different solving methods.

There are a few possible ways of solving the edges rather efficiently (14-15 moves). The old standard "corners-first" strategy (solve UL or UR edge, then solve the other while orienting) is one of them.
The hallmark of my preferred solving methods is my aversion to learning a lot of algorithms. This is why I like corners first, permuting all U and D corners in one algorithm (vs. Direct solving D corners, then 41 algorithms to solve the U corners).

I am approaching this particular orientation phase from a corners first mindset. If you solve UR, then solve UL + orient the M slice, you need 21 algorithms down cold:

LU edge is at DF: 8 cases, plus their mirrors = 16 algorithms
LU is in place but flipped: 2 cases = 2 algorithms
LU is "accidentally" solved when RU is solved: 2 adjacent M edges flipped, 2 diagonal flipped, all 4 flipped= 3 algorithms.

This doesn't include special cases where 2 or 4 M edges are flipped in place.

This method is very good, but already starts to grate on my own personal "number of algorithms to know cold" tolerance.

By mixing techniques, you could average 12 moves.
(And of course, there are some other possible FM tricks)

The problem is, how to be fast? No need to learn a sequence that is 2 move shorter if you waste 2 seconds detecting when to use it.

I thought the best was to have an efficient basic method, and then use shortcuts for special cases that can be immediately detected (some orientations ending with non oriented centers, or the old standard strategy when an edge is already solved for instance).
I agree that there is always room for improvement on speed by adding special cases algorithms to you repetoire. I made a point in the hijacked thread that the more special cases you add, the more the system shifts away from the speed end of the spectrum to the FMC end.

I don't know how it is for you, but if I step away from the cube for a few months, or weeks, or even days sometimes, I forget certain algorithms. For corners, I end up having to do multiple sunes to orient the U layer corners for example.

On the other hand, if you are immersed in speed solving, you obviously retain more through constant practice, and would therefore know your base algorithms cold, and would therefore have a much higher special case algorithm tolerance.

#### Athefre

##### Member
In your list of sequences, I would just drop the last 2 moves to make it look more simple, since the final M* is rather useless (chances for optimization with the next substep are 25%), and the U* before is just about aligning UL and UR.
I hadn't considered that. Once I definitively find the optimal algorithms for all of the cases, I will try both ways- original, and original minus the last 2 moves, and perhaps minus the last M move only. I am not very speedy though. I get most of my kicks by exploring different solving methods.

There are a few possible ways of solving the edges rather efficiently (14-15 moves). The old standard "corners-first" strategy (solve UL or UR edge, then solve the other while orienting) is one of them.
The hallmark of my preferred solving methods is my aversion to learning a lot of algorithms. This is why I like corners first, permuting all U and D corners in one algorithm (vs. Direct solving D corners, then 41 algorithms to solve the U corners).

I am approaching this particular orientation phase from a corners first mindset. If you solve UR, then solve UL + orient the M slice, you need 21 algorithms down cold:

LU edge is at DF: 8 cases, plus their mirrors = 16 algorithms
LU is in place but flipped: 2 cases = 2 algorithms
LU is "accidentally" solved when RU is solved: 2 adjacent M edges flipped, 2 diagonal flipped, all 4 flipped= 3 algorithms.

This doesn't include special cases where 2 or 4 M edges are flipped in place.

This method is very good, but already starts to grate on my own personal "number of algorithms to know cold" tolerance.

By mixing techniques, you could average 12 moves.
(And of course, there are some other possible FM tricks)

The problem is, how to be fast? No need to learn a sequence that is 2 move shorter if you waste 2 seconds detecting when to use it.

I thought the best was to have an efficient basic method, and then use shortcuts for special cases that can be immediately detected (some orientations ending with non oriented centers, or the old standard strategy when an edge is already solved for instance).
I agree that there is always room for improvement on speed by adding special cases algorithms to you repetoire. I made a point in the hijacked thread that the more special cases you add, the more the system shifts away from the speed end of the spectrum to the FMC end.

I don't know how it is for you, but if I step away from the cube for a few months, or weeks, or even days sometimes, I forget certain algorithms. For corners, I end up having to do multiple sunes to orient the U layer corners for example.

On the other hand, if you are immersed in speed solving, you obviously retain more through constant practice, and would therefore know your base algorithms cold, and would therefore have a much higher special case algorithm tolerance.

I had saw his reply earlier but didn't have time to make my own reply, but you said just about everything I was planning on saying

gogozerg said:
This thread reminds me a lot talks I had with Josef Jelinek some time ago.

Finally, I was hoping you would come here to help. You are the true master of this method. I wonder why

gogozerg said:
In your list of sequences, I would just drop the last 2 moves to make it look more simple, since the final M* is rather useless (chances for optimization with the next substep are 25%), and the U* before is just about aligning UL and UR.

I thought that was obvious so I didn't tell him about that, I figured he already noticed that it was one of the simpler shortcuts and was already using it.

Also, do you see any way to shorten any of cubacca's sequences? It's easy to find lots of faster alternatives that have the same amount of moves (M'U2M'U2M'UM'U2M'U2M' is faster than the original).

gogozerg said:
The goal for this step is to consistently average sub-3.

Do you average sub-3 in Step 4 yet? What besides what is on your page do you use? The best average of 12 I've been able to do is 3.01 seconds, sub-3 doesn't look that far away but it feels like I will never get there.

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#### blah

##### brah
That's why he decided to put UL and UR edges in U and D layers, a rather costless starting position requiring at most 1 move (rarely 2).
Sorry if I'm dumb or missing something, but I don't see how this requires at most 1 move?!

#### gogozerg

##### Member
The hallmark of my preferred solving methods is my aversion to learning a lot of algorithms.
...
I agree that there is always room for improvement on speed by adding special cases algorithms to you repetoire. I made a point in the hijacked thread that the more special cases you add, the more the system shifts away from the speed end of the spectrum to the FMC end.
...
On the other hand, if you are immersed in speed solving, you obviously retain more through constant practice, and would therefore know your base algorithms cold, and would therefore have a much higher special case algorithm tolerance.
I agree with you, 100%. Except what I personnaly don't like is the number of stupid sequences to learn, not algorithms which I love. ;-)
That's why at first I decided to use an easy orientation substep you can figure out in a few minutes. I wish I had find how to deal with corners at some point in a more elegant way...
That's why when learning the old "corners-first" method, I tried to see how it was working in order to learn as few as possible (http://web.archive.org/web/20050111065826/grrroux.free.fr/method/Step_4.html).
In Josef's first phase, I agree there's a lot to learn, and your way makes it much more simple. Try to see now how good it is for speed.

Finally, I was hoping you would come here to help.
Since you arrived before, I fear there's nothing left for me!

Off-topic:

Do you average sub-3 in Step 4 yet? What besides what is on your page do you use? The best average of 12 I've been able to do is 3.01 seconds, sub-3 doesn't look that far away but it feels like I will never get there.
I think you're faster than me. Never been sub-3.
By the way, timing conditions are important and controversial. In order to make it look more representative of a speed solve I try not to analyze the situation in details and stop the timer with hands flat. I think I naturally use optimizations 1a 3a 6e 9a, and 2a 2b 4d when possible.
With bionic fingers real speed cubers have, I think sub-3 is possible, and sub-5 for steps 3 and 4 is achievable.

Sorry if I'm dumb or missing something, but I don't see how this requires at most 1 move?!
http://rubikscube.info/lastsix2look.php

#### cubacca1972

##### Member
Originally Posted by gogozerg
In your list of sequences, I would just drop the last 2 moves to make it look more simple, since the final M* is rather useless (chances for optimization with the next substep are 25%), and the U* before is just about aligning UL and UR.
I thought that was obvious so I didn't tell him about that, I figured he already noticed that it was one of the simpler shortcuts and was already using it.
I am not seeing the shortcuts yet, or even test driving the method in solves right now. I am still obsessing about searching for shorter algorithms for the last 2 cases with 11 moves (maybe shorter ones for the 9 move algorithms).

As far as speed goes, (stealing a term from a Futurama episode) I have what the speedcubing community would refer to as "stupid fingers".

#### cubacca1972

##### Member
The current algorithm list:

M' U2 M' U M U M' U' M' (9,10)
M' U M U2 M' U M (7,8)
M' U2 M' U2 M' U M' U2 M' U2 M' (11,15)
M U2 M' U M U M U2 M (9,11)
M U' M' U' M (5,5)
M' U2 M U' M' U' M' U2 M' (9,11)
M' U M U M' (5,5)
M' U' M' U M U' M (7,7)
M' U2 M' U2 M' (5,7)
M' U M' U M' U M' (7,7)
M' U M' U M U M' U2 M' U M (11,12)

Algorithms 2, 3 and 10 have been revised to be a bit more finger friendly. Patterns 2 and 10 now have UB and UL flipped, instead of UF and UR.

#### gogozerg

##### Member
I think you won't find shorter sequences for cases 3 and 11.

(Just in case you're interested in additional tricks:
These cases are not as bad as they look, since with the right initial U adjustment, you can directly orient all edges and solve UL+UR)

#### Athefre

##### Member
I think you won't find shorter sequences for cases 3 and 11.

I figured that, but I hoped there could at least be something shorter for number 3. I tried Cube Solver and it gives 9 move solutions, but they have lots of F2 and M2, not worth it.

#### Emblem62

##### Member
hey i need some help with roux. i hav a pretty good understanding of the cube and can grasp most concepts. however i dont understand the edge orientation part of roux. i know what it means for a cubie to be oriented and i know how to find which cubies are oriented and which arent. my only problem is fixing the bad edges using only M and U slices.

#### cubacca1972

##### Member
hey i need some help with roux. i hav a pretty good understanding of the cube and can grasp most concepts. however i dont understand the edge orientation part of roux. i know what it means for a cubie to be oriented and i know how to find which cubies are oriented and which arent. my only problem is fixing the bad edges using only M and U slices.
I am a newbie with the Roux method as well. I did play with it for a while, and can give you a beginner's perspective on it.

Basically, note which cubies are flipped, according to Roux's definitions on this page:

http://grrroux.free.fr/method/Step_4.html

Next, turn the U layer so that the flipped edges form one of the 9 patterns on that page.

Do the move associated with that pattern.

If there are still flipped edges, repeat the process:

Turn U until the pattern matches one of the nine patterns listed.

Do the move associated with that pattern.

Repeat until all six edges are oriented. Because the LU and RU edges behave slightly differently than the M edges, you won't get the exact same pattern every time you do do one of these iterations.

The first and fifth pattern associated with the M'UM' move have mirror images from front to back. Just do the mirror algorithm MU"M for those.

You should be able to orient all six edges with a maximum of 3 iterations.

#### cubacca1972

##### Member
I am now attempting to write a program to search algorithms.

Its a painful process so far, but much less painful than testing all possible algorithms of 7 moves or 9 moves. I managed to explore all 7 move algorithms that start with M, but just don't have the heart to do all of the M2 group. The 9 move set is just way too many to do manually.

#### cubacca1972

##### Member
The current algorithm list:

M' U2 M' U M U M' U' M' (9,10)
M' U M U2 M' U M (7,8)
M' U2 M' U2 M' U M' U2 M' U2 M' (11,15)
M U2 M' U M U M U2 M (9,11)
M U' M' U' M (5,5)
M' U2 M U' M' U' M' U2 M' (9,11)
M' U M U M' (5,5)
M' U' M' U M U' M (7,7)
M' U2 M' U2 M' (5,7)
M' U M' U M' U M' (7,7)
M' U M' U M U M' U2 M' U M (11,12)

Algorithms 2, 3 and 10 have been revised to be a bit more finger friendly. Patterns 2 and 10 now have UB and UL flipped, instead of UF and UR.
I have just confirmed (the hard way) that these are the optimal algorithm lengths for all 11 cases. What I did was use Ron's cube solver program to "solve" with the whole U layer blanked out, and with DF and DB set as flipped, oriented, or just one flipped. The program checked for all cases without checking centers. Then I manually checked each one in the 7 or 9 move range for the five patterns with 9 or 11 moves. While I didn't find any shorter algorithms, I was able to practice the optimal solutions whenever I reset my cube to try the next algorithm on the list.

Nothing left to do now except get them memorized. Once again, thank you to Athefre for finding the optimal cases for this system.

#### gogozerg

##### Member
M' U2 M' U2 M' U M' U2 M' U2 M' (11,15)
M'UMU2MUM'U2MU'M (or symmetrical friend) in only 13-SQTM long.