A Hybrid of CFOP and Lars Petrus

This article assumes you are familiar with the CFOP method of solving Rubik’s Cube, but not a cube master, and you are interested in exploring some ways to cube that you may not yet have considered.

I recently have been studying Lars Petrus’ method for solving Rubik’s Cube (http://lar5.com/cube/index.html — I will refer to this as LP in this article). Actually, I have been looking at LP off and on for years, wondering when I would understand it. That day has finally arrived.

A revelation struck me as I finally started catching on: LP is an approach to F2L, but it is different than what I think of as the “standard” approach. By my admittedly coarse estimate, all the websites and videos that teach CFOP essentially do F2L the same way: Make a cross, then make and insert F2L pairs.

Not that the standard is bad. Learning F2L this way was an invaluable experience in my path to become a cube master (which I am not, yet–glad to clear that up). On that topic, and should this all seem trivial to you, I congratulate you on your higher understanding.

I can now appreciate the unique way LP does F2L. The main benefit I see comes from LP’s core concept of not messing up what you have already solved. This necessarily requires me to work within certain movement constraints. It can be a time saver because I manipulate the necessary bits with one hand most of the time, while holding a portion of the cube still with the other. Since LP forces me to make and solve F2L pairs from any angle, I get better at that.

However, I do not find all of LP’s ideas to be beneficial. It is difficult for me to find options on a noisy, scrambled cube as I build the first 2x2x2 block, and then extend that to a 3x2x2 block. In contrast, I find starting with the white cross à la “standard” CFOP (or, for the color-agnostic, whatever color cross) is more efficient because it anchors my next task during the F2L stage. Standard CFOP and LP approaches are different in this way. My revelation includes this candidate maxim: A master is not married to one solution.

As I was practicing LP, and after the 3x2x2 block was formed, I kept saying to myself, “this isn’t hard, this is just F2L with one hand”. Next I realized that in LP the formation of 2x2x2 and 3x2x2 blocks is difficult precisely because there are too many options.

There is a second aspect of LP that I think is useful, but perhaps this needs more testing to make a final decision about. After the 3x2x2 is built, LP does a step to resolve “bad edges”. In fact, this step requires breaking the holy 3x2x2 (as LP willingly admits), but it requires only three turns at a shot and therefore is low risk and very fast. I incorporate that step here, and I will speak to the potential benefits in detail in the instructions below.

I finally put the pieces together, so to speak. Drawing from the best of both worlds–standard CFOP and LP–my hybrid method is explained below. I do not provide algorithms or specific turn details here. The link to LP above and any of dozens of CFOP tutorials will help you with those should you need them. I should also mention this article is biased toward right-handed folks, but lefties should have no problem adapting.

Hybrid CFOP + LP Instructions

Step 1. Do 3/4 of the white cross (make a white triangle).
Step 2. Solve the two F2L pairs for the “middle” color of the triangle. This completes the 3x2x2 block found in LP.
Step 3. Resolve bad (flipped) edges per LP.
Step 3b. Complete the white cross.
Step 4. Complete F2L. Heed LP and do not break the 3x2x2 block.
Step 5. Complete OLL.
Step 6. Complete PLL.

Comments and Details:

Step 1 (White Triangle).

Of course, pick any color you prefer.

Step 2 (First Two F2L Pairs).

Commonly among cubing methods, early steps require the most explanation. This one is no exception.

First, a definition: The “middle” color is the one that does not have its opposite edge solved in the original triangle. As an example, suppose you made the white triangle with the white-blue, white-green, and white-red edges. Assuming blue and green are opposite faces of the cube, then red is the “middle” color. In this example the white-orange edge was not placed to make a white cross.

The two F2L pairs of interest here involve the corners with the middle and base colors of the triangle. Using the same example, these would be the white-red-blue and white-red-green corners.

While you solve this step, treat the middle color as the long axis of the 3x2x2 block you are making per LP, even though that block is not solved yet. If you are solving right-handed, this means you should hold the cube firmly with your left hand to prevent movement in the block, except as needed. To be clear, you will need to disturb the block, but save disturbances for when they are actually required.

Now, being locked in to two specific F2L pairs at this step could be a bad thing. You probably cannot take advantage of easy non-middle color F2L pairs (e.g., involving either white-orange corner). The problem is the last piece of the white cross probably is not where you want it, and you may not be able to place it without ruining such an F2L pair.

However, there is an advantage. In standard CFOP, you have to be mindful to restore the cross whenever you turn a side. In this hybrid method, the R side of the cross is not solved, so you do not have to worry about it. R turns are frequent, and if anything it can be a challenge to stop reflexively “restoring” the R side of the non-existent cross. Although digging out target pieces may cost turns, the foregone requirement to restore the cross will save turns.

I find this helps me quickly find and solve F2L pairs, and from nearly any angle. Hunting for just four pieces seems more efficient than hunting for the best case among more options. I firmly hold the 3x2x2 block under-construction with my left hand, I work primarily with the right hand, and I do not change my grip. This tends to make moves fast and deliberate.

Step 3 (Flip Bad Edges).

Taking care of bad edges can be done quickly and sets you up for success because the U face edges will be correctly oriented even after you have worked through the complex turns needed to complete F2L, which is Step 4. I will explain why in a moment.

LP does a good job of explaining how to identify bad edges. I offer this additional explanation. Realize there are two faces to be concerned about. (They are U and R, assuming you have a hold of the 3x2x2 with your left hand. If you are following the same example as before, they are yellow and orange.) Now quite simply, any time the U color is on R, or the R color is on U, that is a bad edge. As LP points out, any time an edge is in the correct layer but the face color is not on that face’s surface, that is a bad edge. These are the only two things you need to know to identify bad edges.

In both CFOP and LP, working out the average number of turns required to resolve bad edges is a bit tricky. Both approaches invoke at most three repetitions of a sequence. Compared to CFOP, LP has an average lower turn cost per sequence (including the needed set-up turns in LP), but the probability of cases requiring zero to three sequences is not the same between the methods. Overall, I think LP comes out slightly ahead. For the record, I find the expected edge-flipping turn cost to be eight in CFOP and six in LP. I will post my analysis if there is interest.

When you are done with Step 3, you should be able to turn only U and R in such a way as to make crosses on the U and R faces. You do not actually have to do this, but it is a good way to check that you have done Step 3 correctly.

Step 3b (White Cross).

If you are thinking ahead you can try to put some of the remaining F2L pieces in a convenient place as you do this, especially if they are dwelling in the bottom two-thirds of R.

Step 4 (Final F2L Pairs).

It is important to not break up the original 3x2x2 block you created in step 2 (this is LP’s dictum). Working within this constraint forces you to work primarily with the U face, turning the R face 1/4 turn at a time to move pieces to U. LP says this can feel “claustrophobic”, but I find the techniques learned in standard F2L prepared me well for this. Just remember: use your right hand, do not reposition the cube in your hands, and do not break the original 3x2x2 you created in Step 2.

Step 5 (OLL).

This is normal OLL, but will not require any edge flipping if you have done steps 3, 3b and 4 correctly. Since edges are all oriented correctly, this will only require corner orientations. I think most methods, including LP and certainly myself, recommend permuting swapped corners first at this step. That is, unless you can do one-look OLL.

Step 6 (PLL).

This is business as usual from CFOP.

Concluding Remarks

CFOP is a widely documented method for solving Rubik’s Cube. F2L, the second phase of the method, has interesting alternatives documented by Lars Petrus. Along with a modified cross (the first phase), Lars’ method and standard CFOP creates a compelling hybrid method for solving the Cube.

I am very interested in feedback from cubers. Do you find this hybrid offers any advantage?

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