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(FMC) A guide for finding DR's/Domino Reduction Guide

ottozing

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Recently, I posted a thread on what to do once you've found a DR, which you can find here. Before I start talking about actually finding DR's in the first place, I want to quickly gloss over the "good/bad corners" stuff since it's important for deciding whether or not you should even try to find a finish on a DR you've found. I also want to say that you can always learn this side of DR later on. As a beginner, just learning to find short (12 or less moves) DR's is a very good place to start. anyway, the boring good/bad corners stuff...

In short, the number of quarter turns needed to solve the DR + the move count length of your DR is generally the best indicator of what kind of final solution is possible with your DR. For example, if you find a 10 move DR that has 2 quarter turn corners, the expected value of this DR is a final solution of 23 without luck, or better than 23 if you get a little lucky. For more information on move count statistics, check out Rodney Kinney's spreadsheet here. It isn't perfect since it doesn't account for some corner cases being more likely to cancel with the DR via NISS, and also doesn't consider non DR moves even though tricks like R L F2 U2 R L' D (random example) are possible and not uncommon, but I personally speculate that the move count stats wouldn't change drastically with those things accounted for.

Alright, with that out of the way, on to the good stuff! Building a DR can be broken down into 3 primary steps; solving EO, doing some moves to give a desirable DR trigger, and then solving the DR trigger case. Getting better at these 3 steps is how you'll go from struggling to even find a DR, all the way to finding at least 3 or so promising DR's on every attempt. Let's start with EO.

EO

For solving EO, the biggest mistake you can possibly make during an attempt is not checking enough EO's. There's no set in stone rules on how many you should check, since on some scrambles it will make sense to check only a handful of very short EO's, whereas on other scrambles you'll want to check somewhere between 30 and 40 (or even more if necessary) 5 move EO's. With that said, here's what I recommend for improving your EO skills so that you can then adjust your strategy as needed.

On every scramble, you should be able to find every 4 move EO that doesn't involve NISS, and you also want to at least consider writing down NISS 4 move EO's that are a one move set up to 2-4 bad edges. There are other possible NISS 4 move EO's, such as one move setups to 6-8 bad edges, or 2 move setups to 4 bad edges, but these are much harder to find & less likely to work. Your time may be better spent going through a longer list of 5 move EO's that don't involve NISS.

Every possible 4 move EO case that doesn't involve NISS boils down to one of these ideas:

2 bad edges - Doing 1-2 moves to setup a 4 bad edge case. In the case of 2 bad edge cases which are solvable in 3 moves, there's a ton of ways you can insert a single redundant move to give a slightly different layout of pieces after the EO.

4 bad edges - Placing all of the edges on F or B and then doing an F or B quarter turn. Sometimes these solutions start with an F or B quarter turn to turn 4 bad edges into a different 4 bad edge case, such as F R D' F instead of D' B2 L2 F, or F/F'/F2 R' L F instead of R' L F. Inserting moves into 3 move EO's is also totally possible here (along with every other case, so I'll stop mentioning it now).

6 bad edges - This is where things get a little tricky. Most of the time, the only 4 move solutions will be either one immediate F or B turn into a 2-4 bad edge case. However, if you want to guarantee you never miss a 4 move EO on 6 bad, you'll need to consider that there are a handful of cases where you do a 1 move setup to something like F U2 B. There's also one specific case where the only way to solve the EO in 4 moves is by turning 6 bad into 8 bad by doing something like F R F B. I think it's a decent idea to learn these cases in an algorithmic fashion since they're a little counterintuitive and not the most obvious

8 bad edges - Similar to 6 bad, most of these will be an F or B turn followed by a 4 bad edge case. The other possible 4 movers are 1 move setups to F* U B, or 2 move setups to F B. For the F U B setups, I like to visualize placing the 4 oriented edges such that 3 are on the S slice & one is on F/B without "touching" more than one of the oriented S slice edges. Setting up to F B is pretty straight forward since you just need to put the 4 oriented edges on the S slice

~

As for the NISS 4 move EO's, they all boil down to the ideas I've already mentioned. As I said, you really only want to focus on the ones which are 1 move setups to 2-4 bad edges since they're the easiest to find. I'd also recommend learning to use NISS prediction when looking for these. To do this, look at the misoriented edges after your first move & take not of where those 4 edges *should* be on the cube. For example, if you have a misoriented edge currently in FR, but it belongs in BR, by NISSing from here, you'll find that the bad edge is now in BR. Getting consistent with this NISS tracing takes a bit of practice, but eventually you should be able to know whether or not your initial first turn can yield a 4 move EO or not.

Finally, with regards to 5 move EO's, there's quite a lot I could say about them, and maybe in the future I'll make a more advanced guide, but realistically you should be fine as long as you never miss a 4 move EO on a scramble (except the harder to see NISS ones).

If you're really curious about 5 move EO's, I'll say that there are only a handful of additional ideas you need to consider in order to not miss 5 move EO's when it's a case that's 5 optimal. For 4 bad, there's one case where one of the optimal solutions is 2 moves to 8 bad followed by U F B. For 6 bad and 8 bad, there are some rare instances where one of the optimal solutions will be an F or B quarter turn to give a different 6-8 bad case, similar to how you would turn 4 bad into a different 4 bad case. There's also a lot of cases within 6 bad that use an F or B quarter turn to give an 8 bad case which is solvable in 4 more moves, or even a one move setup to the previously mentioned F R F B case. Another common idea within 6 bad is doing 2 move setups to F U2 B, which isn't always easy to visualize. Every other 5 move EO is more or less straight forward. If you want to get super advanced at finding EO's, I recommend downloading NISSY and putting your scramble from an attempt into it to see what you may have missed.

TL;DR Don't miss 4 move EO's & don't check less than 20 EO's unless you find an insane DR very early in the attempt.

Turning your EO into a DR trigger

While there are a ton of possible DR triggers you could set up to and learn, there's really only 3 cases you want to think about; 4C4E, 4C2E, and 3C2E. Fancier triggers exist, and people have occasionally found really good DR solutions using triggers outside of the standard 3, but realistically you can get very very far with only these 3. You can always learn the other cases later, but just know that having no knowledge of other triggers probably isn't the reason you're having poor results from DR.

Of the 3 standard triggers, 4C4E is the most important one & the one you'll encounter the most often. On average, 4C4E takes around 7-8 moves to solve, and every solution is just a setup to an R turn. 4C2E is another one that takes around 7-8 moves on average, and usually gets solved by setting up to R U2 R/L F2 L. Finally, 3C2E takes around 6 moves on average & usually gets solved by setting up to R U/U' R'.

On an average scramble, you'll want to NISS for 4C4/2E in 5 or less, and 3C2E in 6 or less. If a scramble is either really good or really bad, you may want to increase or decrease this number by 1. It's also good practice to check one move above your threshold (without NISS) for the scramble to see if something lucky appears on the side of the scramble you're already checking, but performing NISS may be a waste of time. You may also want to forgo checking 4C4E in 6 with NISS even on a hard scramble if you happen to find a very promising DR super early in the attempt that you're unlikely to beat.

Generally speaking, I don't recommend NISSing immediately after an EO in most instances since this can be very time consuming. However, it's not a bad idea if the scramble has a small number of 3 move EO's with a lot of 4 movers, or a small amount of 4 move EO's with a lot of 5 movers. Switching after EO's that use one move followed by a NISS finish isn't a bad idea either since you'll have twice as many things to check when switching to the side of the scramble that only has one move. It's also a valid idea to NISS after EO's that may be nothing special in terms of move count, but happen to give either a lot of blocks or a lot of oriented edges and corners.

Another thing to consider is using NISS prediction to see if your DR trigger will be nicer after doing NISS, but I'm personally not convinced this is worth it since the prediction method is quite tricky. You can learn more about this concept here.

Some other things to consider:

Once you've found a DR trigger from your EO, you can try fishing for another DR trigger on the 2nd axis by adding another move on top. This way, when you NISS you'll have 2 things to check instead of 1. Similarly, if you find 4C4E in 5 off a 4 move EO, when you NISS to check, you can also check the other axis and see if there's a move on the other side of the scramble that gives a DR trigger. Adjust your strategy according to the scramble. You could always write down some double trigger 2 move setups early on, but if you find that a lot of your EO's are giving short enough DR triggers, you could decide that it's better to only check the original DR trigger and omit the following move to instead fish for another short DR trigger when you NISS.

During this process of checking EO's/DR triggers with NISS, there's often a lot of opportunities to check for more than the thing you were initially checking. For example, let's say you find a DR-4C4E in 5 by doing 3 moves on normal for EO, and then B L on inverse to give the trigger. When you switch back to normal, if the original DR trigger doesn't look great, you can still check quite a lot of stuff. For example, if you have other EO's on the U/D axis, the premoves B L may give a DR trigger in 1-2 additional moves on one of the axis. Another thing you could check with the premoves B L is whether or not the F/B or L/R axis have any EO's on them which are worth writing down. In this case, you would want to see if the L/R axis has 3 more moves to EO, and whether or not the F/B axis has 4 more moves to EO.

Often times you'll encounter EO's or DR solutions which have "HTR equivalents", meaning you can do the moves in a different but related way while preserving HTR if you were to apply the inverse of one solution with the other normal solution. In the case of EO's, something like B U D F is HTR equivalent to B' U D F, and F U2 B is equivalent to B L2 F. If you were to NISS for one and find a DR-x using some moves, when you switch back you'll have the same DR-x on both of the HTR equivalent EO's. As for DR's, things like R U2 R' and L F2 L' are HTR equivalent, so if you find a DR in this way you really have 2 DR's. Another way to get two DR's is by finding an EO with HTR equivalents, switching, and then solving the rest of the DR on that side of the scramble.

TL;DR NISS for 4C4/2E in 5 or less, NISS for 3C2E in 6 or less, be careful with how much you NISS & try to make the most of every NISS you perform. You should always have at least 2 things you can check with every NISS you do, if not more.

Solving DR Triggers

For 4C4E, the main things you'll want to try are setting up a 1x1x3 bar & continuing from there, or setting up two 1x1x2's & continuing from there. Most of the 4 move 4C4E cases use one of these 2 ideas, but it's also possible to shift your 4C4E to a different 4C4E and get a 4 move solution with R F2 U2 R type stuff. There's also a good chunk of 5 move 4C4E cases which do this by turning 4C4E into either a different 4C4E, a 4C2E, a 4C6E, or even a 7C8E (R U' L'/L U R). These are the cases you want to focus on getting comfortable with. As I said earlier, 4C4E is by far the most important case to get comfortable with.

For 4C2E, you pretty much exclusively want to try and set up to R U2 R'/L F2 L', but I'm aware of at least one 4C2E 5 mover that goes R' F2 D/D' F2 R, essentially turning a 4C2E into a 4C4E case. There might be other weird 5 movers that exist, but this is the only one I know personally

3C2E is very straight forward. Just set up to R U'/U R' as efficiently as possible. If you happen to set up to R U' R' specifically, you could try adding a B2/Bw2 beforehand to see if it makes the corners better. Similar things are possible with other cases, but this is the most common way you'll see corners influenced by taking the less efficient route

Other interesting DR triggers that you may or may not want to be loosely aware of

2C - R U' L2 U R' works. If you get DR-2C in something insane like 6 or less moves, it's probably a better idea to just try inserting a bunch of random corner commutators to see if one of them gives a DR with good corners. You could then solve the DR from here, remove the commutator afterwards, and then do a 3C skeleton insertion. I once found a 16 moves to 3C skeleton by doing this, and IMO it's a better way to deal with 2C than other approaches, especially when you consider that there are 12 possible corner comms you could insert.

4E - R U2 D2 L is a thing. If you happen to come across it, it's pretty easy to use NISS prediction to see whether or not the 4 edges will be placed nicely or not. It's also easy to see whether or not you'll have good corners, so it doesn't take that much time to check. This case also has 3 HTR equal variations which is desirable if the DR is short enough and has good corners. There's a similar 2E trick using L U2 F2 U2 L but since it's a 5 mover it's a lot less likely to work & really only worth knowing for solving HTR after the DR.

4C6E - R U2 L is probably the best non conventional DR trigger to know since it's pretty easy to recognize due to the blocks. Not really worth NISSing for in most instances since the odds of the blocks being in a nice place is extremely low, but if you have a hard scramble that has a ton of 5 move EO's with awful edge placements, it's something you may need to fish for if DR-4C4/2E in 6 isn't going anywhere. This case also has an HTR equal the same way R U2 R does.

3C6E - R U/U' D2 L is a fun one, but similar to 4C6E it's very rare that the pieces line up in a way that's efficient to solve. Not worth NISSing for, but similarly to before, may be necessary to note down on harder scrambles where the EO's are long and the edge placements are painful

TL;DR Getting good at 4C4E is the best bang for your buck, followed by 4C2E and 3C2E. Everything else is mostly for swag points.

~

Just like last time, let me know if you want anything added or clarified in the guide. This covers pretty much everything I do for DR FMC that I would consider useful :)
 
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