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.

I have put together notes on various corner recognition methods for 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 starting in July, 2022.

In Straughan recognition, just four stickers are checked to determine a case. Because of this low sticker count, it should be the easiest out of all recognition methods for CMLL prediction.

Two of the stickers are on one corner and the other two stickers match that corner. So for a solver with good look ahead abilities, it should be possible to find the four stickers while solving the final pair of the second block. An orientation prediction guide is provided below to enhance your ability to determine where the stickers will end up. A potentially useful way of thinking about the recognition, as pointed out by Liam Highducheck, is that only one sticker on the two sticker corner needs to be tracked. Know the location of the two sticker corner and one of its two involved stickers and you will know where the other involved sticker is located on that corner. This leaves just two other stickers to track, making this a pseudo three sticker tracking system.

Straughan recognition uses all of the same algorithms of course, with four patterns per algorithm. Many of the patterns are mirrors of each other with the same algorithm, so associating the patterns to the algorithms isn't difficult.

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. 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 is the opposite of U sticker recognition 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 of using NMCMLL. So with ATCRM's second step being just 2 stickers versus NMCMLL's 3, it now makes even more sense.

OCLL can be predicted, or even influenced, during the last pair. A document is provided below to show what happens to each corner orientation when inserting the final pair.

View Orientation Cases

This is an alternate CMLL prediction and recognition method. It allows for the continued use of checking the U layer sticker orientation. 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.

It may be difficult to process the initial three stickers + two U stickers step versus finding the specific stickers of other recognition systems. 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, Straughan recognition at 4 stickers is likely the easiest for tracking during the final second block pair or during inspection if solvers are ever able to plan that far. ATCRM also contains a low number of stickers at 5. 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 has well developed look ahead abilities, it is a huge advantage to only need to track four stickers in Straughan recognition. 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 still has to then check 3 additional stickers afterward. 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 to simply finding the location of the four stickers in Straughan recognition.

Straughan recognition, as well as ATCRM, use for CMLL prediction requires learning additional patterns, but the benefits outweigh the effort. 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 Straughan, 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.