ottozing
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(Alternative title; EO better smh)
I've previously covered this topic in my original thread on DR back in 2022. Since then, I've gotten a lot better at the event, and by extension have a better understanding of EO as a whole. Combined with one interesting discovery relating to "RLFB hackery" which I've also touched on in some previous guides, this thread should prove to be a useful framework for getting your EO skills up to scratch as a DR solver
While the entirety of this guide is intended for DR, a lot of what I'm about to cover will also be useful for non DR solvers who like doing EO starts, namely all of the stuff relating to tricky sub 5 move NISS EO's
EO's that I consider to be important to find on every scramble
As fun as it is to just indiscriminately spam 5 movers and gamble, if you're a DR solver, you would be wise to at least start out with the "best" EO's before going to the 5 mover casino. What are these EO's? In my humble opinion...
1. Any sub 5 move linear EO
2. Any sub 5 move NISS EO that's one move to 2-8 bad and switch (often referred to as a 1+3 EO)
3. Any sub 5 move NISS EO that's two moves to 4 bad and switch (note that this includes something like F B on normal, switch, U F, these are known as 2+2 EO's)
4. F B (F B) (this case is very rare, but when it comes up you absolutely want to find it)
5. Any 5 move linear EO that ends with some U F B type finish (only possible on 6-8 bad typically, but also possible on some rare 4 bad cases)
6. Any 5 move NISS EO that ends with some U F B type finish (both the 1+4 and 2+3 type, though you actually don't need to check both to find both... more on this later)
7. Any 5 move NISS EO that starts with F B followed by switch and 3 more moves to EO
The reasoning for valuing <=4 move EO's over everything else should make sense to anyone, but why am I rating 5 movers with U F B style finishes so highly? Through some simulation research done by a few top solvers, its been shown that these U F B finishes tend to perform a move better on average in the context of DR>Solved,. More speculatively (but likely true), in the DRM>DR context I believe this U F B state could lead to move count averages for many DRM's being a move better than it otherwise would be
Note that I only feel this way about U F B and not just F B without a quarter turn preceding it. Statistically speaking it's unclear how much better F B is as an EO finish compared to U F B or just F. I'm guessing it's somewhere in the middle but could plausibly see it going either way. This is why the F B switch 2+3's are at the bottom of the totem pole
How to find all linear 4 move EO's
One resource that I would highly recommend is Shota's EO doc which you can find here. It contains all 180ish EO cases and all of the optimal solutions within the relevant move count constraints of what DR solvers typically do. In order to never miss linear 4 move EO's, my recommendation is to first make sure you know all of your linear 3 move EO cases cold. From there, it's just a matter of trying all 18 first moves and seeing if it gives a 3 move case or not. This alone is enough in theory, but I think it's useful to quickly go over important themes for linear EO in 4 based on how many bad edges there are...
2 bad - It's all just 1-2 moves to 4 bad then solve the case
4 bad - Sometimes you do an F or B to make 4 bad into a different 4 bad but that's really it
8 bad - Same as 2 bad for the most part, but also sometimes it's a one move setup to U F B (these 4 movers are good to know cold for the same reason standard linear 3 movers are good to know)
6 bad - Definitely the hardest in terms of linear EO in 4. One move to 2-4 bad is most common, but one move setups to the F R2 B case exist as well. There's also the weirdo case that's solved with F U F B which is one you'll really want to memorize for the same reasons as the U F B 8 bad 4 movers. I like to think of this case as "arrow+offset edge with the F/B faces + 2 adjacent S slice edges that occupy an outer layer with only 2 bad edges on it". It isn't exactly catchy but hopefully it makes some sense, lol
How to find all 1+3 NISS 4 move EO's
To do this, you'll need to check 1 move to 2-8 bad and NISS trace where the bad edges go (or the good edges in the case of 8 bad) and see if it's a 3 move case or not. Purely tracing in this way is sufficient for 2/4/8 bad without learning/memorizing special patterns, so if you're someone who already does this for 2/4 bad, try it with 8 bad for a few attempts and you should find it's actually not all that bad!
For one move to 6 bad however, this is where purely tracing can become a problem. As far as 4 movers go, since the only possible case here is something like F (F R2 B), you could do some mental checklist like this;
1. See if there's a bad "S slice" edge. If there is, it's not the case. Otherwise...
2. See if the 6 edges separate between F and B in a 3+3 fashion rather than a 4+2 fashion. If they don't, it's not the case. If they do...
3. Compare the "missing" edge for each group of 3. If the non F/B colors for these two edges match or are opposite, it's not the case. If they're adjacent, then tada!
How to find all 2+2 NISS 4 move EO's
Here the possibilities are a lot more limited than with the 1+3's. Each side of the 2+2 is either going to be something like U/U2 F or F B. With the exception of F B (F B), all of these cases could be considered two moves to 4 bad followed by switching
For the ones that reduce to 4 bad by starting with F B (possible on everything except 0 and 2 bad), I'd also recommend seeing if there's a 2+3 instead of a 2+2. I'll also say that cases where you can do F B to give 2 bad followed by a 3 mover are pretty damn easy to trace, so I may as well include that in this section rather than the final 2+3 section (these are possible on 4 6 and 8 bad but not 2 10 12)
For the stupid rare F B (F B) case, You'll need to see whether or not F B gives 8 bad. For RLFB hackery reasons, if this EO exists on one axis, it'll exist on all 3 (meaning R L (R L) and U D (U D) will also exist). The tracing for the 4 good edges is pretty obvious, really the hardest part of this EO is remembering to account for it
Finally, the most common 2+2's where you do 2 moves to 4 bad on both sides in a conventional way. My biggest tip for these would be to delay checking them until you've seen an EO axis on both normal and inverse. Since you don't need to check both sides of the EO for these 4 movers, you can use this information to only check the side that has more restricted options. For example, if you have an 8 bad case on normal where one move to 4 bad is possible, but on inverse your good edges are in a 2/1/1 fashion across F/S/B, the inverse side will be a lot easier to check as there's at most 3 ways to reduce to 4 bad in 2 moves
Aside from that, standard NISS tracing is probably good enough for most people. Really all you have to remember is that you're looking for 3/4 of the same F/B color and for the other edge to contain the "missing" color from the 3 previous edges
How to find all linear 5 move EO's ending in U F B (stuff that's useful for non-DR solvers ends here)
Here I once again highly recommend Shota's EO doc from earlier since these case benefit from a bit of route memorization. If you've reached this point in the guide, while somewhat optional, I'd highly recommend learning all of the linear 4 movers cold the same way I previously recommended knowing the 3 movers cold. This will not only help for the remainder of the guide, but also just for finding more random 5 move linear EO's as a whole
In terms of "themes", these U F B linear EO's only exist on;
1. 2 unique 4 bad cases (F B U F B and F' B U F B)
2. A lot of 8 bad cases (sometimes even doing 1 move to a different 8 bad similar to what you see in linear 4 bad 4 movers sometimes)
3. A surprising amount of 6 bad cases (most of these are going to be one move F U F B, but sometimes for 3/2/1 and 2/3/1 cases you can just do 1 move to 8 bad and get an 8 bad 4 mover ending with U F B)
For memorizing these, I would recommend focusing on 3-4 optimal 6/8 bad cases initially and learning which ones have these EO's available (the only 3 optimal that has this is the F U B case with two possible non-HTR-equivalent 5 movers ending in U F B)
How to find all NISS 5 move 1+4 EO's ending in U F B (and how to use them to find all of the 2+3's with the same theme!)
Now for the fun stuff! Most of these 1+4's will arise from one move to 8 bad, but of course we have to consider that 1 move to 6 bad followed by F U F B is a thing. Thankfully, unlike the F (F R2 B) 6 bad NISS case, something like F (F U F B) is actually quite common, so if you're serious about getting good with DR I would highly recommend learning the recognition system for this case (either the one I'm about to outline or something that makes the most sense to you)
The 8 bad ones I once again feel are perfectly suited to standard NISS tracing. For the goofy goober 6 bad case, here's how I personally tackle it;
1. See if there's exactly 2 bad edges belonging on S in an adjacent fashion and NOTE THE COMMON COLOR OF THESE EDGES (caps because I find mentally latching onto this color makes the following steps a lot easier)
2. See if the remaining 4 bad edges arrange themselves in a 3+1 fashion across F/B
3. Make sure none of these 4 edges contain the common color of the S slice edges from step 1 while also making sure the 1 edge from the 3+1 doesn't contain the opposite color of the S slice edges from step 1
With that covered, let's quickly go over how to derive the 3+2's ending with U F B from the 4+1's
RLFB hackery dictates that if you have EO solved, performing U D F B (U D F B) or similar will also result in EO being solved. Here's how we use that info to find the 3+2's;
Lets say you find F (U2 R F B) as an EO on a scramble. What happens if we do the UDFBx2 trick while trying to cancel the most amount of moves? Well, we get something like this...
(U2 R F B) F
(U2 R F B - F' B' R' L') F - F' B R L = (U2 L) B R L
The exact same logic applies to the other case types with this structure
How to find the rest of the 2+3 NISS 4 move EO's where the 2 side is F B
We've already covered how to do this for 2/4 bad, but what about the 6 and 8 bad 3 movers? Let's go through them one by one. RLFB hackery is very much relevant here including some more obscure applications of it
For F B (U F B), you may be wondering why it wasn't mentioned in the previous section given that it fits the structure. My reason for including it here is mostly that it's easily derived from a NISS 3 mover on the scramble (in this case, F B (U F B) would mean that U D (D) is an EO on the scramble, and IMO it's easier to just find this 3 mover first and then gen the 5 movers from it)
For F B (F U B), this case is a unique one in the sense that it's the only F B switch 2+3 that implies the existence of another F B switch 2+3 on the same side of the scramble. Here's how it breaks down for this case;
F B (F U B)
F B - F' B' R L (F U B - B' F R L) = R L (F U F R L)
But wait, remember that previous section on how the 3 mover F U B has linear 5 movers ending with U F B? Well, it turns out that the (F U F R L) portion could just be solved with R/R' U' L!!!
Lastly, for F B (F U2 B), while you could NISS trace this directly from the axis where F B gives 6 bad, I have a preferred method that avoids needing to do this, at least initially. If you append this EO RLFB style both ways, you'll find that it gives the 8 bad case with 3 good edges in S (same as the F U B case) but the 4th good edge isn't quite in the correct spot. Using this information, I can actually limit which scenarios I need to consider F B switch to only 3 cases; F B gives 2 bad, F B gives 4 bad, or F B gives 8 bad
Obviously I'll need to trace the 6 bad later anyway, but at least by taking the indirect approach I can be sure it's the case rather than spending 20+ seconds realizing that it's not the 3 move case but actually the 5 mover
I've previously covered this topic in my original thread on DR back in 2022. Since then, I've gotten a lot better at the event, and by extension have a better understanding of EO as a whole. Combined with one interesting discovery relating to "RLFB hackery" which I've also touched on in some previous guides, this thread should prove to be a useful framework for getting your EO skills up to scratch as a DR solver
While the entirety of this guide is intended for DR, a lot of what I'm about to cover will also be useful for non DR solvers who like doing EO starts, namely all of the stuff relating to tricky sub 5 move NISS EO's
EO's that I consider to be important to find on every scramble
As fun as it is to just indiscriminately spam 5 movers and gamble, if you're a DR solver, you would be wise to at least start out with the "best" EO's before going to the 5 mover casino. What are these EO's? In my humble opinion...
1. Any sub 5 move linear EO
2. Any sub 5 move NISS EO that's one move to 2-8 bad and switch (often referred to as a 1+3 EO)
3. Any sub 5 move NISS EO that's two moves to 4 bad and switch (note that this includes something like F B on normal, switch, U F, these are known as 2+2 EO's)
4. F B (F B) (this case is very rare, but when it comes up you absolutely want to find it)
5. Any 5 move linear EO that ends with some U F B type finish (only possible on 6-8 bad typically, but also possible on some rare 4 bad cases)
6. Any 5 move NISS EO that ends with some U F B type finish (both the 1+4 and 2+3 type, though you actually don't need to check both to find both... more on this later)
7. Any 5 move NISS EO that starts with F B followed by switch and 3 more moves to EO
The reasoning for valuing <=4 move EO's over everything else should make sense to anyone, but why am I rating 5 movers with U F B style finishes so highly? Through some simulation research done by a few top solvers, its been shown that these U F B finishes tend to perform a move better on average in the context of DR>Solved,. More speculatively (but likely true), in the DRM>DR context I believe this U F B state could lead to move count averages for many DRM's being a move better than it otherwise would be
Note that I only feel this way about U F B and not just F B without a quarter turn preceding it. Statistically speaking it's unclear how much better F B is as an EO finish compared to U F B or just F. I'm guessing it's somewhere in the middle but could plausibly see it going either way. This is why the F B switch 2+3's are at the bottom of the totem pole
How to find all linear 4 move EO's
One resource that I would highly recommend is Shota's EO doc which you can find here. It contains all 180ish EO cases and all of the optimal solutions within the relevant move count constraints of what DR solvers typically do. In order to never miss linear 4 move EO's, my recommendation is to first make sure you know all of your linear 3 move EO cases cold. From there, it's just a matter of trying all 18 first moves and seeing if it gives a 3 move case or not. This alone is enough in theory, but I think it's useful to quickly go over important themes for linear EO in 4 based on how many bad edges there are...
2 bad - It's all just 1-2 moves to 4 bad then solve the case
4 bad - Sometimes you do an F or B to make 4 bad into a different 4 bad but that's really it
8 bad - Same as 2 bad for the most part, but also sometimes it's a one move setup to U F B (these 4 movers are good to know cold for the same reason standard linear 3 movers are good to know)
6 bad - Definitely the hardest in terms of linear EO in 4. One move to 2-4 bad is most common, but one move setups to the F R2 B case exist as well. There's also the weirdo case that's solved with F U F B which is one you'll really want to memorize for the same reasons as the U F B 8 bad 4 movers. I like to think of this case as "arrow+offset edge with the F/B faces + 2 adjacent S slice edges that occupy an outer layer with only 2 bad edges on it". It isn't exactly catchy but hopefully it makes some sense, lol
How to find all 1+3 NISS 4 move EO's
To do this, you'll need to check 1 move to 2-8 bad and NISS trace where the bad edges go (or the good edges in the case of 8 bad) and see if it's a 3 move case or not. Purely tracing in this way is sufficient for 2/4/8 bad without learning/memorizing special patterns, so if you're someone who already does this for 2/4 bad, try it with 8 bad for a few attempts and you should find it's actually not all that bad!
For one move to 6 bad however, this is where purely tracing can become a problem. As far as 4 movers go, since the only possible case here is something like F (F R2 B), you could do some mental checklist like this;
1. See if there's a bad "S slice" edge. If there is, it's not the case. Otherwise...
2. See if the 6 edges separate between F and B in a 3+3 fashion rather than a 4+2 fashion. If they don't, it's not the case. If they do...
3. Compare the "missing" edge for each group of 3. If the non F/B colors for these two edges match or are opposite, it's not the case. If they're adjacent, then tada!
How to find all 2+2 NISS 4 move EO's
Here the possibilities are a lot more limited than with the 1+3's. Each side of the 2+2 is either going to be something like U/U2 F or F B. With the exception of F B (F B), all of these cases could be considered two moves to 4 bad followed by switching
For the ones that reduce to 4 bad by starting with F B (possible on everything except 0 and 2 bad), I'd also recommend seeing if there's a 2+3 instead of a 2+2. I'll also say that cases where you can do F B to give 2 bad followed by a 3 mover are pretty damn easy to trace, so I may as well include that in this section rather than the final 2+3 section (these are possible on 4 6 and 8 bad but not 2 10 12)
For the stupid rare F B (F B) case, You'll need to see whether or not F B gives 8 bad. For RLFB hackery reasons, if this EO exists on one axis, it'll exist on all 3 (meaning R L (R L) and U D (U D) will also exist). The tracing for the 4 good edges is pretty obvious, really the hardest part of this EO is remembering to account for it
Finally, the most common 2+2's where you do 2 moves to 4 bad on both sides in a conventional way. My biggest tip for these would be to delay checking them until you've seen an EO axis on both normal and inverse. Since you don't need to check both sides of the EO for these 4 movers, you can use this information to only check the side that has more restricted options. For example, if you have an 8 bad case on normal where one move to 4 bad is possible, but on inverse your good edges are in a 2/1/1 fashion across F/S/B, the inverse side will be a lot easier to check as there's at most 3 ways to reduce to 4 bad in 2 moves
Aside from that, standard NISS tracing is probably good enough for most people. Really all you have to remember is that you're looking for 3/4 of the same F/B color and for the other edge to contain the "missing" color from the 3 previous edges
How to find all linear 5 move EO's ending in U F B (stuff that's useful for non-DR solvers ends here)
Here I once again highly recommend Shota's EO doc from earlier since these case benefit from a bit of route memorization. If you've reached this point in the guide, while somewhat optional, I'd highly recommend learning all of the linear 4 movers cold the same way I previously recommended knowing the 3 movers cold. This will not only help for the remainder of the guide, but also just for finding more random 5 move linear EO's as a whole
In terms of "themes", these U F B linear EO's only exist on;
1. 2 unique 4 bad cases (F B U F B and F' B U F B)
2. A lot of 8 bad cases (sometimes even doing 1 move to a different 8 bad similar to what you see in linear 4 bad 4 movers sometimes)
3. A surprising amount of 6 bad cases (most of these are going to be one move F U F B, but sometimes for 3/2/1 and 2/3/1 cases you can just do 1 move to 8 bad and get an 8 bad 4 mover ending with U F B)
For memorizing these, I would recommend focusing on 3-4 optimal 6/8 bad cases initially and learning which ones have these EO's available (the only 3 optimal that has this is the F U B case with two possible non-HTR-equivalent 5 movers ending in U F B)
How to find all NISS 5 move 1+4 EO's ending in U F B (and how to use them to find all of the 2+3's with the same theme!)
Now for the fun stuff! Most of these 1+4's will arise from one move to 8 bad, but of course we have to consider that 1 move to 6 bad followed by F U F B is a thing. Thankfully, unlike the F (F R2 B) 6 bad NISS case, something like F (F U F B) is actually quite common, so if you're serious about getting good with DR I would highly recommend learning the recognition system for this case (either the one I'm about to outline or something that makes the most sense to you)
The 8 bad ones I once again feel are perfectly suited to standard NISS tracing. For the goofy goober 6 bad case, here's how I personally tackle it;
1. See if there's exactly 2 bad edges belonging on S in an adjacent fashion and NOTE THE COMMON COLOR OF THESE EDGES (caps because I find mentally latching onto this color makes the following steps a lot easier)
2. See if the remaining 4 bad edges arrange themselves in a 3+1 fashion across F/B
3. Make sure none of these 4 edges contain the common color of the S slice edges from step 1 while also making sure the 1 edge from the 3+1 doesn't contain the opposite color of the S slice edges from step 1
With that covered, let's quickly go over how to derive the 3+2's ending with U F B from the 4+1's
RLFB hackery dictates that if you have EO solved, performing U D F B (U D F B) or similar will also result in EO being solved. Here's how we use that info to find the 3+2's;
Lets say you find F (U2 R F B) as an EO on a scramble. What happens if we do the UDFBx2 trick while trying to cancel the most amount of moves? Well, we get something like this...
(U2 R F B) F
(U2 R F B - F' B' R' L') F - F' B R L = (U2 L) B R L
The exact same logic applies to the other case types with this structure
How to find the rest of the 2+3 NISS 4 move EO's where the 2 side is F B
We've already covered how to do this for 2/4 bad, but what about the 6 and 8 bad 3 movers? Let's go through them one by one. RLFB hackery is very much relevant here including some more obscure applications of it
For F B (U F B), you may be wondering why it wasn't mentioned in the previous section given that it fits the structure. My reason for including it here is mostly that it's easily derived from a NISS 3 mover on the scramble (in this case, F B (U F B) would mean that U D (D) is an EO on the scramble, and IMO it's easier to just find this 3 mover first and then gen the 5 movers from it)
For F B (F U B), this case is a unique one in the sense that it's the only F B switch 2+3 that implies the existence of another F B switch 2+3 on the same side of the scramble. Here's how it breaks down for this case;
F B (F U B)
F B - F' B' R L (F U B - B' F R L) = R L (F U F R L)
But wait, remember that previous section on how the 3 mover F U B has linear 5 movers ending with U F B? Well, it turns out that the (F U F R L) portion could just be solved with R/R' U' L!!!
Lastly, for F B (F U2 B), while you could NISS trace this directly from the axis where F B gives 6 bad, I have a preferred method that avoids needing to do this, at least initially. If you append this EO RLFB style both ways, you'll find that it gives the 8 bad case with 3 good edges in S (same as the F U B case) but the 4th good edge isn't quite in the correct spot. Using this information, I can actually limit which scenarios I need to consider F B switch to only 3 cases; F B gives 2 bad, F B gives 4 bad, or F B gives 8 bad
Obviously I'll need to trace the 6 bad later anyway, but at least by taking the indirect approach I can be sure it's the case rather than spending 20+ seconds realizing that it's not the 3 move case but actually the 5 mover
