Comparison of 2x2x2 methods

On this page I will share my thoughts about which 2x2x2 methods I think are the most viable and show the most promise. Please note, I am by no means a record-setting speedsolver. I just find 2x2x2 methods interesting. This is all just an opinion.

More information about these methods can be found on the speedsolving.com wiki.


Beginner Methods

Layer by Layer (LBL)

This is the beginner method that most people start with. Solve the first layer intuitively, then orient the top layer using 7 OLL algorithms (or just 1, for the most basic version of this method), and finally permute the last layer using 2 algorithms.

This is the method that you use just to prove that you can solve the cube. It should be learned just as a stepping stone towards the Ortega method.

Ortega

This is the most well-known 2x2x2 solving method, due to its effectiveness and ease of learning. It is similar to the LBL method, but starts out with simply making a face of one color, rather than solving the first layer in its entirity. The OLL step is the same as the LBL method. Finally, both layers are permuted at the same time using PBL algorithms. Once you have learned the LBL method in full, this just adds 4 new algorithms. For this reason, I consider this a beginner method as well. This is a 3-look method, which means it will generally be slower than more advanced methods, which usually reduce the solution to 2 looks or less. Despite that, this is a method that every cuber needs to know. Even if you intend to ultimately learn a different method, almost everything else builds off of this.


Intermediate Methods

Guimond

This is the first method that I would consider to be an "intermediate" method. It's a little difficult to explain succinctly, so I would just point you to my tutorial for how it works. While this might initially seem to have more steps than Ortega, it can actually be a faster method. That is because the first "step" is usually solved right from the beginning or just requires 1 setup move. Then the OLL step is short enough that advanced solvers can predict the separation step during the inspection time. So when the method is fully utilized, it is a 2-look solution.

This method requires learning about 20 new algorithms on top of what are already used in Ortega, and most of those algorithms are very short, being just 3 or 4 moves long. This is not a very popular method, but sub-3 second times have been demonstrated with this.

CLL

This method starts off like the LBL method, by solving the first layer. Then you solve both the orientation and permutation of the top layer using a single CLL algorithm. This requires learning 42 algorithms. This is a tried and true method, and can lead to sub-3 second times with enough practice.

SOAP

The steps for this method as as follows: First, separate two opposite colours into opposite layers and build half a face on the bottom. Next, orient all pieces using one of 53 algorithms. Finally, permute both layers. (PBL).

The first step is generally just 1-2 moves, so its quite easy to plan the 2nd step during inspection. If you learn 2-gen algorithms for the orientation step, it actually becomes feasible to predict the PBL case during the inspection time. As a 2-look method, I think this is probably not worth it, as other 2-look methods seem just as good or better. As a potential 1-look method, I think this shows some promise, but this method is largely unproven. I don't believe anyone has learned this method in full yet. One potential issue is that some of the 2-gen algorithms require up to 11 moves, and 2-gen algorithms may be more difficult to memorize than normal algorithms.

HD

The HD method begins by solving 3/4 of a face (the "V"), then use 16 algorithms to orient the remaining 5 pieces (but a corner may end up in the wrong layer), then use 36 algorithms to both separate and permute. This has some ideas in common with the Guimond and SS methods. There are 52 algorithms all together, which is more than CLL, but this could be a bit easier to 1-look than CLL.


Advanced Methods

HD-G

This is a variation on the HD method that I am only just starting to learn about, but it seems to show a lot of potential. This could be thought of as an add-on to Guimond. It basically involves semi-intuitively modifying the Guimond OLL algs to force a V on the bottom layer, and then combine the separation and PBL steps to finish the solve using 36 algorithms. You could theoretically plan the entire solve during inspection. I don't know enough about this method yet to determine how practical it might be.

SS

Solve 3/4 of a face, then use one of 109 orientation algorithms to orient both the top and bottom, then finish with PBL. The first step is about 1 move on average, so this is a 2-look method. With the number of algorithms required, I think you may as well just learn EG. The case recognition is pretty easy though, and about half of the algorithms are reflections, so it might be a bit easier to learn than some other methods.

OFOTA

Make a full face using opposite colors (like Guimond, but you do a full face instead of 3/4 of a face), then orient and separate using one of 87 algorithms, and finally do PBL. Again, if you are going to learn this many algs, I think EG is the better option.

EG

Make a full face (like with Ortega), then solve the rest of the cube in one step using 128 algorithms. This is generally considered to be the "best" method for solving the 2x2x2, and sub-2 second world record averages have been set with this. One third of the cases are just the CLL cases. Some people never bother to learn the last third of the algorithms (known as the EG-2 subset) because they can be solved by just cancelling the last moves of your face into R2 F2 R2, and then performing a normal CLL algorithm. The best solvers with this method can usually 1-look the solves, but this is very difficult to do.

These days, some cubers are learning some additional algorithm sets to add on to EG. LEG-1 is basically the EG-1 set from a different angle, and TCLL is a version of CLL that allows one corner of the layer to be twisted. Altogether, these additional sets will basically double the number of algorithms, but make it slightly easier to 1-look and reduce the movecount.


Progression Trees

The following are some paths through different methods that would make sense as you progress from beginner to advanced.


First Step Move Count

The first step is a critical component of most methods, because if it's easy enough it allows you to look ahead into the next step during your inspection time. Also, the more moves you have to do, the more difficult it is to do them optimally. So for example with Ortega, most people probably don't usually solve with the optimal number of moves. All of the statistics below were calculated by cuBerBruce from the speedsolving.com forums.

Guimond + OLL (Either 3/4 or a full face of opposite colors)
distance positions Cumulative total
0 3223440 87.73%
1 445536 99.86%
2 5184 100%
Average distance = 0.12
Guimond (3/4 of a face of opposite colors)
distance positions Cumulative total
0 3097152 84.30%
1 569088 99.78%
2 7776 99.99%
3 144 100%
Average distance = 0.16
SS (3/4 of a face)
distance positions Cumulative total
0 1075254 29.27%
1 2149200 87.76%
2 447630 99.94%
3 2076 100%
Average distance = 0.83
OFOTA (a face of opposite colors)
distance positions Cumulative total
0 699984 19.05%
1 2189088 78.63%
2 762048 99.37%
3 23040 100%
Average distance = 1.03
SOAP (a face but 2 adjacent pieces of the face can be unoriented)
distance positions Cumulative total
0 460696 12.54%
1 1900278 64.26%
2 1302058 99.70%
3 11124 99.99%
4 4 100%
Average distance = 1.24
Ortega/EG (a face)
distance positions Cumulative total
0 22654 0.62%
1 132828 4.23%
2 626354 21.28%
3 2057908 77.29%
4 832588 99.95%
5 1828 100%
Average distance = 3.78
LBL/CLL (a layer)
I don't have stats for this, but I believe it should have an Average distance of about 5