ottozing
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It's been a while since I've felt compelled to post an FMC related guide. Recently, a decent amount of progress has been made in the EO>DR department, so I feel like documenting the more current take on EO>DR stuff is worthy of my time
Intro
Traditionally, when trying to go from EO to DR, people would perform semi-random moves to produce an XCXE state of either 4C4E (solvable with conjugation to R), 4C2E (R U2 R), or 3C2E (R U R or R U' R)
While this family of DR triggers are a more than solid enough repertoire to get anyone averaging sub 25, other DR triggers do exist & are certainly beneficial to be aware of. Notably, there are 3 other XCXE cases which can be done in 3 or less moves once they've been conjugated properly. These are 8C8E (R L), 4C6E (R U2 L), and 7C8E (R U L or R U' L)
Outside of these 3 or less move cases, there also exists an entire family of cases known as JZP (stupid term I made up that caught on unfortunately), also known as AR or Axial Reduction (the term I prefer). These are special cases that can be solved using only the R L U2 D2 F2 B2 move group. Any case that has an even number of corners could also be AR, including those listed above
The scope of this post is intended to cover how I'm personally approaching all of these cases in my FMC attempts, though I should warn that I've only recently started implementing 7C8E and 8C8E meaning improvements on my methodology could be found due to how recent these developments are
Recognizing AR
Before going any further, it's worth going over how to do AR properly as familiarity with the technique is not only relevant in its own right, but also highly relevant for 8C8E specifically
Using FB EO solved and DR eventually ending with U and D oriented (white top green front orientation) for this & later example(s), the way you would recognize that you have AR is by:
1 - Having an even number of misoriented corners which all have the U/D sticker on the F/B faces
2 - Having the non placed E slice edges within the S slice
With these conditions met, the case will be solvable using the R L U2 D2 F2 B2 move group. More interestingly, if you have a case like this that's able to reach DR with this move group on one side of the scramble, by NISSing to the other side of the scramble, you'll be able to reach DR from that side with the U D R2 L2 F2 B2 move group! For this reason, even if the AR case you find doesn't look good, it's worth it to check the other side of the EO and count the number of corners and edges that are misoriented to see if it's still worth switching.
As a random example, if you happen to notice that this other axis has 8C8E misoriented, you're guaranteed to be 2 moves away from reaching a DR state! Of course, getting this case is quite unlikely (I've personally only had this once). It's also not the only way to viably approach 8C8E & I will have more to say on that DR subset soon. In any case, familiarizing yourself with good/bad AR subsets is very much worthwhile. In my experience, almost every case is good and potentially worth NISSing for in a similar number of moves to more traditional XCXE cases
One of the biggest benefits of DR's that are based on AR is the fact that you can often manipulate the sequence outside of the DR to solve a slice of edges. While solving nonDR slice isn't anything new, AR based DR's with nonDR leave slice on the correct nonDR axis tend to perform similarly well in terms of cancellations of moves, so don't sleep on this technique!
Learning XCXE stuff
Prominent FMCer Radomil Baran has been working on/maintaining a document for all sub 6 EO>DR cases, which you can find here
Due to the sheer number of algs for sub 6 EO>DR alone (as well as the complexity of some solutions like turning 4C4E into 7C8E then back to 4C4E), there are effectively two schools of thought when it comes to how to best make progress towards "full DR". One is to simply learn everything algorithmically, and the other is to learn only the best cases from the best sets and attempt to conjugate to those cases until you feel ready to learn more. I feel that the latter approach is more conducive to engaging in the discovery process, and also mitigating burnout
Using 4C4E as an example, before taking on the task of learning all the sub 6 solutions, even if you want to learn things algorithmically, it's best to start with smaller sets & learn to conjugate to those cases. For instance, you could learn the mini cases of R, F2 R, R2 U2 R, R2 F2 R, F2 U2 R, F2 B2 L etc etc (I CBF listing them all lol), and spend some time trying to conjugate other cases into these ways. This way you can naturally internalize some amount of the cases via the discovery process (something like F2 D F2 B2 R as a solution won't seem so counterintuitive if you've already learn F2 B2 R as a 3 mover, or even a more simple case like B2 U' F2 R)
The same logic can be applied to the other sets. For 3C2E for example, on top of learning R U R and R U' R, it's useful to be aware of the shape for L2 R U R, L2 R U' R, and F2 R U R. These additional mini cases give you more options to try and set up your DR
7C8E specific tips
One issue with learning "full DR" is the fact that there are so many patterns and many cases with large amounts of misoriented pieces, making the patterns less and less distinct. For this reason, I think it's worth it to touch on how I'm currently approaching both 7C8E and 8C8E as these are two of the most extreme examples of cases where efficient DR's are very much possible, but the recognition issues make it a hard sell
Taking a brief detour away from XCXE and back to EO, for as long as I can remember, I've always recognized 8 bad edge EO cases by not focusing on the misoriented edges, but instead focusing on the oriented edges. This slight manipulation may not seem so necessary in theory, but the quality of life improvement is very much real, especially when it comes to NISS EO's involving reductions & regressions to leave 8 bad edges
Only recently did it occur to me that something similar is possible with 7C8E! Notice how the cases R U' L and R U L both have the same pattern of oriented pieces on the U and D layers (a 1x2x2 + a line of edges). While I have successfully conjugated to R U/U' L in the past, I have no doubt I've missed dozens of potential DR's over the last year by not considering this approach to conjugating. At a high enough level, recognizing the whole case in advance will of course be demanded of you in order to find the best solution as sometimes it won't involve purely conjugating to the 3 mover. Still, I consider this approach of setting up the square+line pattern to be the best place to start for people trying to use 7C8E. Along with knowing the square+line pattern, it's also good to be aware of the cases that are 1 move away, possibly even 2 moves away
8C8E specific tips
Here I don't so much have "tips", but rather a framework that I've been using (and recently improving upon). Note that good AR knowledge is absolutely mandatory in order to take proper advantage of 8C8E situations. If you don't have sufficient knowledge of AR, read on at your own discretion. I am not liable if what I write makes no sense
anyway, for reasons unknown to me personally (but known to those in the FMC community who figured the technique out), once you have a DR state with U/D oriented, you can do either R L U D (R L U D) or F B U D (F B U D) from that position and produce a new DR on a different axis. While this is mostly wizardry to me, the fact that this phenomenon is true and consistent helps greatly in unlocking the secrets of finding 8C8E solutions using traditional conjugation
Let's say you do an EO of F R F B, and straight after the EO you notice that you have 8C8E on the white top axis. First, you need to confirm that it's the right 8C as you need an even distribution of cw/ccw corner twists. While rarer that the even split, it's possible to have 7 corners twisted in one direction and the remaining corner twisted in the other. The way you verify that you have "good" 8C8E is by doing R L U D, and then seeing if you've entered AR. If you have, you're ready for the next step, but if not you likely need to scrap one half of your EO immediately
For the next step, let's say you want to easily see what the optimal way to conjugate on the normal scramble is. The easy method is to do (R L U D) followed by your EO, and then solve the AR case as best you can. Let's say you get something like:
F R F B // EO
(R L U D) // AR
U F2 D R2 D // DR with R/L oriented in 13 moves
Now we can apply the wizardry:
F R F B // EO
U F2 D R2 U R L // DR in 11 moves!
While this approach isn't very time efficient, it greatly simplifies the recognition process if you have a background in AR. That said, there are many cases where the 8C8E case is reached in a high enough number of moves that you don't really want to waste time switching, but do at least want to attempt to solve it on that side of the scramble. This brings me to an alternative recognition system that's more difficult, but also more time efficient in this case (as well as others)
Take a cube with DR solved with U/D oriented, and do the moves R L U. Notice that the D layer pieces (all 4 corners and all 4 edges) are in AR, but all of the U layer pieces are not in AR. Take this cube state a step further by now doing R2 U and notice the relationship of AR and non AR pieces. If you have another solved cube handy, do U R2 U on that cube and compare the two states
Once you've verified that you have good 8C8E, instead of taking the premove path, you could instead identify one set of pieces (either all of the AR'd or all of the non AR'd, whichever set is smaller), and use that information to work out the shortest solution to R L (or just as importantly, quickly determine that there isn't a short solution and move on immediately)
Conclusion
That's all I have for now. Hopefully you the reader now have a framework to start improving your EO>DR game, whether you're a beginner who's just learning 4C4E for the first time, or an advanced solver looking to implement non standard triggers!
Intro
Traditionally, when trying to go from EO to DR, people would perform semi-random moves to produce an XCXE state of either 4C4E (solvable with conjugation to R), 4C2E (R U2 R), or 3C2E (R U R or R U' R)
While this family of DR triggers are a more than solid enough repertoire to get anyone averaging sub 25, other DR triggers do exist & are certainly beneficial to be aware of. Notably, there are 3 other XCXE cases which can be done in 3 or less moves once they've been conjugated properly. These are 8C8E (R L), 4C6E (R U2 L), and 7C8E (R U L or R U' L)
Outside of these 3 or less move cases, there also exists an entire family of cases known as JZP (stupid term I made up that caught on unfortunately), also known as AR or Axial Reduction (the term I prefer). These are special cases that can be solved using only the R L U2 D2 F2 B2 move group. Any case that has an even number of corners could also be AR, including those listed above
The scope of this post is intended to cover how I'm personally approaching all of these cases in my FMC attempts, though I should warn that I've only recently started implementing 7C8E and 8C8E meaning improvements on my methodology could be found due to how recent these developments are
Recognizing AR
Before going any further, it's worth going over how to do AR properly as familiarity with the technique is not only relevant in its own right, but also highly relevant for 8C8E specifically
Using FB EO solved and DR eventually ending with U and D oriented (white top green front orientation) for this & later example(s), the way you would recognize that you have AR is by:
1 - Having an even number of misoriented corners which all have the U/D sticker on the F/B faces
2 - Having the non placed E slice edges within the S slice
With these conditions met, the case will be solvable using the R L U2 D2 F2 B2 move group. More interestingly, if you have a case like this that's able to reach DR with this move group on one side of the scramble, by NISSing to the other side of the scramble, you'll be able to reach DR from that side with the U D R2 L2 F2 B2 move group! For this reason, even if the AR case you find doesn't look good, it's worth it to check the other side of the EO and count the number of corners and edges that are misoriented to see if it's still worth switching.
As a random example, if you happen to notice that this other axis has 8C8E misoriented, you're guaranteed to be 2 moves away from reaching a DR state! Of course, getting this case is quite unlikely (I've personally only had this once). It's also not the only way to viably approach 8C8E & I will have more to say on that DR subset soon. In any case, familiarizing yourself with good/bad AR subsets is very much worthwhile. In my experience, almost every case is good and potentially worth NISSing for in a similar number of moves to more traditional XCXE cases
One of the biggest benefits of DR's that are based on AR is the fact that you can often manipulate the sequence outside of the DR to solve a slice of edges. While solving nonDR slice isn't anything new, AR based DR's with nonDR leave slice on the correct nonDR axis tend to perform similarly well in terms of cancellations of moves, so don't sleep on this technique!
Learning XCXE stuff
Prominent FMCer Radomil Baran has been working on/maintaining a document for all sub 6 EO>DR cases, which you can find here
Due to the sheer number of algs for sub 6 EO>DR alone (as well as the complexity of some solutions like turning 4C4E into 7C8E then back to 4C4E), there are effectively two schools of thought when it comes to how to best make progress towards "full DR". One is to simply learn everything algorithmically, and the other is to learn only the best cases from the best sets and attempt to conjugate to those cases until you feel ready to learn more. I feel that the latter approach is more conducive to engaging in the discovery process, and also mitigating burnout
Using 4C4E as an example, before taking on the task of learning all the sub 6 solutions, even if you want to learn things algorithmically, it's best to start with smaller sets & learn to conjugate to those cases. For instance, you could learn the mini cases of R, F2 R, R2 U2 R, R2 F2 R, F2 U2 R, F2 B2 L etc etc (I CBF listing them all lol), and spend some time trying to conjugate other cases into these ways. This way you can naturally internalize some amount of the cases via the discovery process (something like F2 D F2 B2 R as a solution won't seem so counterintuitive if you've already learn F2 B2 R as a 3 mover, or even a more simple case like B2 U' F2 R)
The same logic can be applied to the other sets. For 3C2E for example, on top of learning R U R and R U' R, it's useful to be aware of the shape for L2 R U R, L2 R U' R, and F2 R U R. These additional mini cases give you more options to try and set up your DR
7C8E specific tips
One issue with learning "full DR" is the fact that there are so many patterns and many cases with large amounts of misoriented pieces, making the patterns less and less distinct. For this reason, I think it's worth it to touch on how I'm currently approaching both 7C8E and 8C8E as these are two of the most extreme examples of cases where efficient DR's are very much possible, but the recognition issues make it a hard sell
Taking a brief detour away from XCXE and back to EO, for as long as I can remember, I've always recognized 8 bad edge EO cases by not focusing on the misoriented edges, but instead focusing on the oriented edges. This slight manipulation may not seem so necessary in theory, but the quality of life improvement is very much real, especially when it comes to NISS EO's involving reductions & regressions to leave 8 bad edges
Only recently did it occur to me that something similar is possible with 7C8E! Notice how the cases R U' L and R U L both have the same pattern of oriented pieces on the U and D layers (a 1x2x2 + a line of edges). While I have successfully conjugated to R U/U' L in the past, I have no doubt I've missed dozens of potential DR's over the last year by not considering this approach to conjugating. At a high enough level, recognizing the whole case in advance will of course be demanded of you in order to find the best solution as sometimes it won't involve purely conjugating to the 3 mover. Still, I consider this approach of setting up the square+line pattern to be the best place to start for people trying to use 7C8E. Along with knowing the square+line pattern, it's also good to be aware of the cases that are 1 move away, possibly even 2 moves away
8C8E specific tips
Here I don't so much have "tips", but rather a framework that I've been using (and recently improving upon). Note that good AR knowledge is absolutely mandatory in order to take proper advantage of 8C8E situations. If you don't have sufficient knowledge of AR, read on at your own discretion. I am not liable if what I write makes no sense
anyway, for reasons unknown to me personally (but known to those in the FMC community who figured the technique out), once you have a DR state with U/D oriented, you can do either R L U D (R L U D) or F B U D (F B U D) from that position and produce a new DR on a different axis. While this is mostly wizardry to me, the fact that this phenomenon is true and consistent helps greatly in unlocking the secrets of finding 8C8E solutions using traditional conjugation
Let's say you do an EO of F R F B, and straight after the EO you notice that you have 8C8E on the white top axis. First, you need to confirm that it's the right 8C as you need an even distribution of cw/ccw corner twists. While rarer that the even split, it's possible to have 7 corners twisted in one direction and the remaining corner twisted in the other. The way you verify that you have "good" 8C8E is by doing R L U D, and then seeing if you've entered AR. If you have, you're ready for the next step, but if not you likely need to scrap one half of your EO immediately
For the next step, let's say you want to easily see what the optimal way to conjugate on the normal scramble is. The easy method is to do (R L U D) followed by your EO, and then solve the AR case as best you can. Let's say you get something like:
F R F B // EO
(R L U D) // AR
U F2 D R2 D // DR with R/L oriented in 13 moves
Now we can apply the wizardry:
F R F B // EO
U F2 D R2 U R L // DR in 11 moves!
While this approach isn't very time efficient, it greatly simplifies the recognition process if you have a background in AR. That said, there are many cases where the 8C8E case is reached in a high enough number of moves that you don't really want to waste time switching, but do at least want to attempt to solve it on that side of the scramble. This brings me to an alternative recognition system that's more difficult, but also more time efficient in this case (as well as others)
Take a cube with DR solved with U/D oriented, and do the moves R L U. Notice that the D layer pieces (all 4 corners and all 4 edges) are in AR, but all of the U layer pieces are not in AR. Take this cube state a step further by now doing R2 U and notice the relationship of AR and non AR pieces. If you have another solved cube handy, do U R2 U on that cube and compare the two states
Once you've verified that you have good 8C8E, instead of taking the premove path, you could instead identify one set of pieces (either all of the AR'd or all of the non AR'd, whichever set is smaller), and use that information to work out the shortest solution to R L (or just as importantly, quickly determine that there isn't a short solution and move on immediately)
Conclusion
That's all I have for now. Hopefully you the reader now have a framework to start improving your EO>DR game, whether you're a beginner who's just learning 4C4E for the first time, or an advanced solver looking to implement non standard triggers!
