CMLL Prediction

One goal among Roux solvers is to reduce or remove the pause for CMLL recognition. There have been conversations about predicting CMLL during the last pair of the second block. Some try to predict the U sticker orientation while finishing the last pair. However, there may be a better way. In a conversation with Zhouheng Sun, he suggested the idea that NMCMLL's order of recognizing non-U stickers first is likely better for CMLL prediction. During CMLL recognition, typically a Roux solver first checks the U sticker orientation then checks the pattern of non-U stickers. This pattern of non-U stickers is slightly more difficult and slightly slower to recognize compared to finding the U layer orientation. ATCRM and NMCMLL are the opposite in that first the orientation of the L/R or F/B stickers is found then just two stickers are checked to complete the case recognition. So if the solver can take care of predicting the difficult part first during the second block last pair, all that's left is a couple of easy stickers. ATCRM didn't yet exist when he brought up the idea. So with ATCRM's second step being just 2 stickers versus NMCMLL's 3, it now makes even more sense. That conversation got me thinking about how best to implement this and if there are even simpler ways to predict CMLL.

I have put together notes on ATCRM use in CMLL prediction, developed a new separate CMLL prediction and recognition method, and created some simple strategies for where to look during completion of the second block last pair.

These techniques were developed in July, 2022.

In ATCRM, you first find the orientation of the L/R stickers or the F/B stickers. Then you check just two pre-determined sticker positions to know the full case. So the goal is to predict the L/R or F/B orientation during the second block last pair. Then all you have left are two stickers. The two sticker step is as simple as checking if one, both, or neither are a U sticker or not. The L/R or F/B stickers form 23 different orientations with 1-4 cases per orientation, making 83 total patterns. It is still the same 42 algorithms that you already know, just each one associated with two different patterns.

With second block experience and the last pair becoming automatic, it shouldn't take too much effort to be able to see the L/R or F/B orientation while completing the last pair. A good starting point is to track either the two L stickers or the two R stickers of the corners. This will narrow down the type of orientation that will occur - with the LR stickers adjacent on L and R, adjacent on F and B, or diagonal.

To make this even better, it will be useful to learn multi-angle recognition. The L/R or F/B orientation will be in one of four AUFs after the second block is complete. Checking just two stickers after the orientation is already really simple. But it will be even easier if you learn the two-sticker recognition for other angles. There are only four orientations (or 16 cases) that can't be recognized from every angle. All others have the two stickers on the U layer.

During the last pair there needs to be a focus. Positions to track while solving the pair. The last four corners can be in many positions and orientations at each turn of solving the last pair. So where do we look to start tracking? It may be good to start by gaining an intuitive sense of what is going to happen to the corners during the last 2-3 moves of the last pair. Below is a link to a document that shows the orientation case that will be produced after finishing the most common last pair inserts. This orientation sticker targeting technique can be used for tracking and identifying any set of stickers (L/R, F/B, or U) and the document is developed to be neutral for that. So this can be used with ATCRM, NMCMLL, U sticker + pattern, and Hyperorientations.

View Orientation Cases

The pair inserts included are from specific AUF angles. In solves, the pairs will be created from various AUFs. So, depending on the AUF, other sticker targets can be watched. Or, tracking will be done at a different point. Taking the R' U2 R insert as an example, only the URF and UBR corners allow for knowing the targeted sticker orientation. ULB and DRB have only one visible sticker. The options are to watch the corners a move or two early when building the pair or to AUF and use the R' U R insert instead.

This orientation sticker targeting is based on the corners that have the most visibility at those points of solving the last pair. There are certain realizations that can further help make it natural to predict the orientation. Such as knowing that the UBR corner doesn't move during R U R', R U' R', or R U2 R'. Similarly, the UFR corner doesn't move during R' U' R, R' U R, or R' U2 R. Or knowing the simple ways in which the corners move during common combinations. For example, after R U2 R' the UBR corner stays in place and the UFL and UFR corners simply swap positions. An additional thing to consider may be the various ways in which the final pair can be solved. Some solutions provide more corner tracking opportunities than others. Such as M2 U M' r U r' versus R U' R' U R U R'. If a solution allows for easier corner tracking and is as fast as the solutions that don't, it may be better to use the tracking-friendly one.

It may be simpler to start by only tracking the two most visible corners and knowing the few possible orientations that they will lead to. The document mentions which two positions are the easiest to see, or primary, and the third position which is secondary. The secondary position can be checked during the final couple of turns to reveal the exact orientation case.

These solutions aren't exactly intended to be memorized and recalled, but can be learned that way if the user desired. The system is more like EOLR where you can learn it intuitively. Looking at the solutions, it is easy quickly gain an intuitive sense of what orientation case is produced after the final moves of the second block last pair. Someone with good lookahead may be good at tracking corners at a much earlier point. The earlier that you can start tracking, the better chance you have of seeing the last two stickers of ATCRM to know the full CMLL case. Or the final stickers of another recognition method. It is likely best to eventually develop the ability to globally track the corners and not rely on always starting to track during the final three turns of the last pair. Starting to watch from any convenient point is the long term goal. The document above can then serve as a starting point that helps your tracking ability from a few moves out.

This is an alternate CMLL prediction and recognition method. It allows for the continued use of checking the U layer sticker orientation. It also has the benefit of not requiring the solver to learn the additional patterns of ATCRM. The method is similar to the old style NMCMLL recognition method, but with a focus on determining the CP location. So you are associating your CMLL algorithms with which two corners need to be swapped.

During the second block last pair, find either three L/R stickers or three F/B stickers. Of these three stickers, check any two that are opposite colors and find the relative position of the U stickers. Then complete the case determination by finding any single U sticker on another corner.

There are two types of L/R or F/B sticker positions in this system. The stickers from each side will be either next to each other or diagonal.

Diagonal always means that there is an adjacent corner swap. When they are next to each other, it can be any type of corner permutation. The relative U sticker positions will determine the corner swap location. + and - symbols are used to show the relative positions of the U stickers. Meaning if they are a clockwise or counter-clockwise position from the L/R or F/B sticker. In the image below, the last two cases in the Adjacent Orientation set say "Swap Left" and Swap Right". Swap Left means that the corners that need swapped are the two corners to the left, clockwise, of the ones you are checking with the U stickers. Swap Right means to swap the two corners that are to the right, clockwise, of them. The Opposite Orientation cases mean just as you would think. That you have a front, left, back, or right swap case.

To make this system faster, if you used the L/R stickers as your initial three stickers, in the two opposite colored stickers step you can check the F/B stickers on those corners instead of the U stickers. The relative sticker position rules are then inverted. The same goes for if you used the F/B stickers as your initial three stickers where, during the two opposite colored stickers step, you can check the two L/R stickers instead of the U stickers. During the fast turning of the last pair of the second block, it would likely be useful to know these additional rules to be able to take advantage of the corner sticker positions that are easiest to see in the current moment. With experience, additional versatility may come from being able to spot the third and final required U sticker early.

This system requires a little more effort upfront with the need to check one additional sticker compared to ATCRM and requires the same number of stickers as the other CMLL recognition methods. It may be difficult to process the initial three stickers + two U stickers step versus finding the L/R or FB orientation in ATCRM. If a solver can become good at checking the three L/R or FB stickers and the initial two U stickers, it could be competitive.

I developed this system based on how I used to recognize CMLL. In 2006 when I started using Roux, there weren't a lot of guides online. Mostly just Gilles Roux's website. I didn't know about the U sticker + pattern recognition system at first, so I developed my own way. That way was based on the natural order of the corners when in their correctly permuted state. After finding the U sticker orientation (taking yellow for example), if you see two blue stickers next to each other, then what follows counter-clockwise must be two red stickers for it to be a correct permutation. Rules based on this provide an intuitive way of recognizing CMLL and knowing where the corner swaps are.

Looking for the order of F/B and L/R stickers in this way as the first step could be another way of predicting CMLL and I may explore and add that to the page. However, for the relative CP system above, I decided that focusing on a single color group (L/R only or F/B only) may be easier on the solver's mental capacity during the second block last pair.

If we go by the minimum number of stickers required to recognize a CMLL case, ATCRM is a 5 sticker method. 3 stickers to find the L/R or F/B orientation and 2 stickers for the final step. U sticker + pattern and Hyperorientations are both 6 sticker methods. 3 stickers to find the U orientation and 3 stickers for the final step.

Solvers are continually pushing the limits and showing that we are capable of more than we thought. If a solver puts in the effort and can determine the L/R or F/B orientation early, it is a huge advantage to have just two stickers left to check and to already know exactly where they are. These two stickers are also easy to compare as being either "U" or "Not U". This is in contrast to the U sticker + pattern or Hyperorientations recognition methods which require the user to first find the U sticker orientation. If this orientation is determined during the second block last pair, the user then has to check 3 stickers. In the typical U sticker + pattern recognition, a relationship among these stickers has to be determined. In Hyperorientations, an orientation has to be determined. Both of which may be slower process compared with the two sticker "U" or "Not U" of ATCRM.

ATCRM use for CMLL prediction requires learning additional patterns, but has the easiest and fastest second step once at the CMLL step. U sticker + pattern and Hyperorientatations have fewer orientations to determine during the last pair, but have the most time consuming part of CMLL recognition left once the solver gets to CMLL.

If you are using a U sticker first recognition method for CMLL, it may seem like a lot of effort to switch to a different recognition method if the goal is to use ATCRM or NMCMLL. For those that don't want to switch, other techniques have been provided on the page - such as orientation sticker targeting which works for all of the current recognition methods.