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2 step finish for Roux Edges

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I revisited an old solution method I came up with for corners first solves, which would work with the Roux method. After using cube explorer 5.0 to search out the algorithms, I found several shorter algorithms than the ones I found a few years ago.

First, solve up to step 3 in Roux (i.e., everything solved except the M slice edges, and UL and UR).

Step 1

Solve UL and place the UR cubie in UR, but flipped. This is relatively easy, but takes a bit of getting used to, as you have to resist the urge to solve UR.

Step 2

Use 1 of 24 algorithms to flip UR, and solve the M slice (9.583 moves on average). With UR flipped, one of two orientation patterns are forced in the M slice: 3 edges flipped, or 1 edge flipped. Park the odd edge (the single flipped edge, or the single oriented edge) at UF, and apply the appropriate algorithm. If you are solving corners first, this would be a handy place to align the L face with the R face.

Identify which edge is at UF and UD to determine which algorithm to use. There is no need to identify if it is a 3-cycle, double edge swap, etc. For a lot of the cases, you can deduce which edge is at DF without peeking at its D facelet.

Here are the algorithms. The first column shows which edge is at UF. The second shows which edge is at DF. The first 12 algorithms are the cases where there are 3 flipped edges in the M slice, and the last 12 are the cases where there is 1 flipped edge in the M slice.

UF Oriented, Remaining M Edges Flipped

UF-DF--M' U' M' U' M' U' M' U' (8s*)
UF-DB--M' U M U2 M' U M' U' M' U (10,11)
UF-UB--U' M' U2 M U' M U M U' (9s*)
DF-UF--U M U' M2 U2 M U' M' U' (9s*)
DF-DB--U' M' U M U2 M2 U M U (9s*)
DF-UB--U M U M U M U' M U2 (9s*)
DB-UF--M' U M U' M U' M U (8s*)
DB-DF--U' M' U M' U M' U' (7s*)
DB-UB--U' M' U M' U M' U' M2 U2 M U2 (11,14)
UB-UF--U' M' U M' U M' U M2 U2 (9s*)
UB-DF--U M U2 M' U' M' U M' U (9s*)
UB-DB--U' M' U M' U M' U M U2 (9s*)

UF Flipped, Remaining M Edges Oriented

UF-DF--F R' F' M2 F2 M' F' R F M F2 (11s*)
UF-DB--F R' F' M2 F2 M' F' R F M2 F2 (11s)
UF-UB--F R' F' M' F2 M2 F' R F M F2 (11s)
DF-UF--F R' F M2 F2 M F R F' (9f*)
DF-DB--M F' R' F M2 F2 M F R F (10f*)
DF-UB--F R' F M F2 M2 F R F' (9f*)
DB-UF--B2 M' B' R B' M' B2 M2 B' R' B' (11f*)
DB-DF--F R' F M2 F2 M F R F M F2 (11f*)
DB-UB--F R' F M F2 M2 F R F M F2 (11f*)
UB-UF--M' B' R B' M' B2 M2 B' R' B (10f*)
UB-DF--F R' F' M2 F2 M' F' R F' (9f*)
UB-DB--F R' F' M' F2 M2 F' R F' (9f*)

Align the M slice.

Special Cases

Occasionally, at the end of Step 3 in Roux, or the corners first equivalent, the UL and UR edges will be accidentally placed at UL and UF, in some configuration other than what we want for the method outlined as above. Here's how to handle these cases.

Case 1: UL is in the correct place but flipped, UR is solved.

Do y2 and proceed to Step 2 as above.

Case 2: UL and UR are in the correct place, but both are flipped.

2 M edges flipped, adjacent, and at UF and UB--U M2 F2 M' F2 U' (6f*)
2 M edges flipped diagonal, at DF and UB--U2 M' U F2 M F2 M2 U (8f*)
4 M edges flipped--R U' r' U' M' U2 M2 U' r U R' (11f*)
0 M edges flipped--U M2 U M' U M' U' M U M' U (11f*)

The M slice is now oriented, and can be solved with the usual algorithms.

Case 3: UL and UR are solved.

2 M edges flipped, adjacent, and at DB and UB--U2 F M F' U2 F M' F'
2 M edges flipped, diagonal, and at DB and UF--F M F' U2 F M' F' U2
4 M edges flipped--U M' U2 M' U' M U' M' U2 M' U

The M slice is now oriented, and can be solved with the usual algorithms.

I don't know how this compares to other finishes as far as move count goes, but it does guarantee a 2 look finish every time (there is a slim chance of a skip in special cases 2 and 3), and there are fewer algorithms to know compared to solving DF and DB, then O and P of the LL edges.
 
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jms_gears1

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#4
oh hell naw. Did you really just put an F in roux's LSE? D:<
AND B? D:<

Im not sure about this idea tho. Its not 2 step really its just another way to do 2.5 look, and IMO 2.5 look has nicer algs.
 
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Wait, what do you propose doing if the centers are an M2 away at the end? You can either (a) propose a specific M slice orientation (so, not setup the one odd edge but just deal with it wherever it is) and then have 4*12 algs plus mirrors, or (b) deal with it later in half of the cases (yuck). Or maybe you have another idea.

Also, if you can't get the UF edge to be bad with just M2's, you would put it on UB and mirror the algorithm, right? Otherwise you'll end up with an edge 2-cycle and a center 4-cycle. I imagine anything with F's would not be so good mirrored.
 
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All algs you have for UF flipped are terrible btw.
I am assuming that you applied x or x' as appropriate to convert the F and B moves into U moves, thereby converting the algorithms into U M R algorithms.

If you want exclusive U M algorithms, the penalty is added moves. But then again, optimal isn't always the same as fastest. Most of the cases had very short but ugly algorithms with S and E moves.
 
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Wait, what do you propose doing if the centers are an M2 away at the end? You can either (a) propose a specific M slice orientation (so, not setup the one odd edge but just deal with it wherever it is) and then have 4*12 algs plus mirrors, or (b) deal with it later in half of the cases (yuck). Or maybe you have another idea.
The centers would be an M2 away 25% of the time after applying the correct algorithm from the list. They would be M away 25% of the time, and M' away 25% of the time. Its not clear to me why this is an issue. The M slice will be solved as will UR. You just need to apply an M move 75% of the time to finish.

Also, if you can't get the UF edge to be bad with just M2's, you would put it on UB and mirror the algorithm, right? Otherwise you'll end up with an edge 2-cycle and a center 4-cycle. I imagine anything with F's would not be so good mirrored.
I am not following what you mean by just M2s. I am proposing that at the stage where the last 6 edges are unsolved, just solve UL and UR, with the exception that UR is flipped. Use whatever M moves you need. For this method, you don't need to track or align your centers so that either the U or D center are pointing up at any point. You don't need to worry about identifying cycles or swaps unless you are doing special cases 2 or 3.

Does this address your concerns, or am I not understanding what you are getting at?
 
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oh hell naw. Did you really just put an F in roux's LSE? D:<
AND B? D:<
Just do x or x' to convert the F moves or B moves into U moves. Once you finish the algorithm, do an M move to align the layers, and you are done, so you don't have to worry about doing an inverse of the starting x move.


Im not sure about this idea tho. Its not 2 step really its just another way to do 2.5 look, and IMO 2.5 look has nicer algs.
Orthodox Roux:

0.5 Step 4a - Edges orientation

1 Step 4b - Finish L/R-sides

2 Step 4c - Permute M-edges

2.5 looks

The alternate I posted:

1 Finish L/R sides but with UR flipped

2 Solve M slice and UR with 1 algorithm

2 looks

I am just posting a different way to solve the last 6 edges, whether they were arrived at by corners first or Roux.
 

jms_gears1

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#9
oh hell naw. Did you really just put an F in roux's LSE? D:<
AND B? D:<
Just do x or x' to convert the F moves or B moves into U moves. Once you finish the algorithm, do an M move to align the layers, and you are done, so you don't have to worry about doing an inverse of the starting x move.


Im not sure about this idea tho. Its not 2 step really its just another way to do 2.5 look, and IMO 2.5 look has nicer algs.
Orthodox Roux:

0.5 Step 4a - Edges orientation

1 Step 4b - Finish L/R-sides

2 Step 4c - Permute M-edges

2.5 looks

The alternate I posted:

1 Finish L/R sides but with UR flipped

2 Solve M slice and UR with 1 algorithm

2 looks

I am just posting a different way to solve the last 6 edges, whether they were arrived at by corners first or Roux.
2.5 look is:
place UL/UR in DF/DB (irrespective of centers)
EO alg
Placed UL/UR
4c
 
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#11
Solve UL and place the UR cubie in UR, but flipped. This is relatively easy, but takes a bit of getting used to, as you have to resist the urge to solve UR.
Isn't it easier to pair it up correctly and then do whichever alg is necessary for solving the M-slice?
 
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#13
Wait, what do you propose doing if the centers are an M2 away at the end? You can either (a) propose a specific M slice orientation (so, not setup the one odd edge but just deal with it wherever it is) and then have 4*12 algs plus mirrors, or (b) deal with it later in half of the cases (yuck). Or maybe you have another idea.
The centers would be an M2 away 25% of the time after applying the correct algorithm from the list. They would be M away 25% of the time, and M' away 25% of the time. Its not clear to me why this is an issue. The M slice will be solved as will UR. You just need to apply an M move 75% of the time to finish.
Lemme show you why I'm skeptical.

Setup: M' (F U' F') M2 F2 M' (F' U F')
OK, here you have UR and UB flipped. So by your approach we would start with M, that puts UB in the UF slot. So now the edges in UF and DF are UF and DF. I remember one edge in M was flipped, so we should use F R' F' M2 F2 M' F' R F M F2. It's not solved, but it's only U2 M U2 off, so that's not too bad.

Fair enough; maybe we made a mistake and should've said that all but UF were flipped, since we did an M move and that is known to flip all four edges. So now we do an M and then we should use M' U' M' U' M' U' M' U'. And that's even worse.
 
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Wait, what do you propose doing if the centers are an M2 away at the end? You can either (a) propose a specific M slice orientation (so, not setup the one odd edge but just deal with it wherever it is) and then have 4*12 algs plus mirrors, or (b) deal with it later in half of the cases (yuck). Or maybe you have another idea.
The centers would be an M2 away 25% of the time after applying the correct algorithm from the list. They would be M away 25% of the time, and M' away 25% of the time. Its not clear to me why this is an issue. The M slice will be solved as will UR. You just need to apply an M move 75% of the time to finish.
Lemme show you why I'm skeptical.

Setup: M' (F U' F') M2 F2 M' (F' U F')
OK, here you have UR and UB flipped. So by your approach we would start with M, that puts UB in the UF slot. So now the edges in UF and DF are UF and DF. I remember one edge in M was flipped, so we should use F R' F' M2 F2 M' F' R F M F2. It's not solved, but it's only U2 M U2 off, so that's not too bad.

Fair enough; maybe we made a mistake and should've said that all but UF were flipped, since we did an M move and that is known to flip all four edges. So now we do an M and then we should use M' U' M' U' M' U' M' U'. And that's even worse.
I did the scramble as described.

I did M to move the odd M edge to the UF position.

Now take a look at the colors of the U center and the F center. Note that the cubie at UF has facelets that match the F center and the D center. The cubie at UF is therefore the DF cubie. The Cubie at DF is the DB cubie.

The algorithm for this case is M F' R' F M2 F2 M F R F.

After this you need to do M' and you're done.

So to clarify ( I didn't catch this in the OP), after step 1 is done, and you've placed the odd M edge at UF, you need to identify which cubies are at UF and DF, relative to which center is at U at this stage.
 
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All algs you have for UF flipped are terrible btw.
I am assuming that you applied x or x' as appropriate to convert the F and B moves into U moves, thereby converting the algorithms into U M R algorithms.

I love <R,U,M> algorithms. I don't like regrips.
Hey, who doesn't like RUM?

I submitted them as is, since they are optimal, and only 1 regrip is required. To avoid the regrip, one would have to add moves. So it would really come down to picking your poison.
 
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Solve UL and place the UR cubie in UR, but flipped. This is relatively easy, but takes a bit of getting used to, as you have to resist the urge to solve UR.
Isn't it easier to pair it up correctly and then do whichever alg is necessary for solving the M-slice?
I am not too sure about this.

If you solve UL and UR, you are left with 4 orientation patterns:

All 4 Medges oriented:

2 3-cycles, 1 double adjacent edge swap, 1 diagonals swap.

2 Adjacent Medges oriented:

8 3-cycles, 2 double adjacent edge swap, 1 diagonals swap

2 Diagonal Medges oriented:

4 3-cycles, 2 double adjacent edge swaps, 1 diagonals swap

All Medges flipped:

2 3-cycles, 1 double adjacent edge swap, 1 diagonals swap

Everything would hang on how easy it would be to identify each case (the diagonal medges oriented cases might be especially tricky), and how good the algorithms are. I am not sure, but I think Minh Thai might have solved this way. Anyone out there have a copy of the Winning Solution to confirm this?
 
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So to clarify ( I didn't catch this in the OP), after step 1 is done, and you've placed the odd M edge at UF, you need to identify which cubies are at UF and DF, relative to which center is at U at this stage.
Aha. This is a pretty important point; thanks for clarifying it. Wouldn't the recognition for this be somewhat difficult, though? You not only have either one or three edges flipped, but also the M slice can be in any of 4 orientations and you have to look at where two edges go (one of which you can't see in full without rotating the cube) relative to that slice. I'd need some input from actual Roux users, but I think I would find this difficult.
 

jms_gears1

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So to clarify ( I didn't catch this in the OP), after step 1 is done, and you've placed the odd M edge at UF, you need to identify which cubies are at UF and DF, relative to which center is at U at this stage.
Aha. This is a pretty important point; thanks for clarifying it. Wouldn't the recognition for this be somewhat difficult, though? You not only have either one or three edges flipped, but also the M slice can be in any of 4 orientations and you have to look at where two edges go (one of which you can't see in full without rotating the cube) relative to that slice. I'd need some input from actual Roux users, but I think I would find this difficult.
in the few seconds of attempting to reply to this ive changed my mind several times. However i think that recog would not be that hard The edge at BD could be seen while inserting L/R edges. And if the misoriented edge is at UB then youll be able to the BD while AUMing.

EDIT: I changed my mind again >.>
Basically i think that once one got used to using it the recog would be really easy, however since the UF DF piece placement is relative to the M slice orientation it could be difficult at first.
 
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So to clarify ( I didn't catch this in the OP), after step 1 is done, and you've placed the odd M edge at UF, you need to identify which cubies are at UF and DF, relative to which center is at U at this stage.
Aha. This is a pretty important point; thanks for clarifying it. Wouldn't the recognition for this be somewhat difficult, though? You not only have either one or three edges flipped, but also the M slice can be in any of 4 orientations and you have to look at where two edges go (one of which you can't see in full without rotating the cube) relative to that slice. I'd need some input from actual Roux users, but I think I would find this difficult.
My fault for being my own editor. I caught another error in my special cases algorithms as well, which I will fix shortly.

Regarding recognition, identifying the odd cubie at UF is straightforward, but being color neutral as far as seeing the M slice goes is critical.

If the F facelet of the DF cubie matches one of the UF facelets, you don't need to see the D facelet to identify the cubie. I haven't looked at the list closely enough to see which cases don't require peeking at the D facelet. There might also be information derived from looking at the U facelet of the UB cubie as well. I think a detailed case by case study would be required to see if there is any value in learning a recognition system based on looking at only U and F facelets.
 
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So to clarify ( I didn't catch this in the OP), after step 1 is done, and you've placed the odd M edge at UF, you need to identify which cubies are at UF and DF, relative to which center is at U at this stage.
Aha. This is a pretty important point; thanks for clarifying it. Wouldn't the recognition for this be somewhat difficult, though? You not only have either one or three edges flipped, but also the M slice can be in any of 4 orientations and you have to look at where two edges go (one of which you can't see in full without rotating the cube) relative to that slice. I'd need some input from actual Roux users, but I think I would find this difficult.
in the few seconds of attempting to reply to this ive changed my mind several times. However i think that recog would not be that hard The edge at BD could be seen while inserting L/R edges. And if the misoriented edge is at UB then youll be able to the BD while AUMing.

EDIT: I changed my mind again >.>
Basically i think that once one got used to using it the recog would be really easy, however since the UF DF piece placement is relative to the M slice orientation it could be difficult at first.
It is a bit of a mind bender to change how to perceive cubie patterns and take on an alien style. I have done most of my cubing using corners first, and have always found it difficult to transition to a different style. Think of all the F2L solvers trying to build blocks, when all they see is crosses and CE pairs.
 
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