CFOP, aka. the Fridrich Method, is the wildly popular Rubik’s Cube solving method used by virtually all high- and mid-level speedcubers.  It gained popularity in the early 2000s because Jessica Fridrich’s website was the only thorough tutorial and algorithm library. Still, methods like Petrus, Roux, and ZZ have their merits too, so why has CFOP persisted? This article describes the numerous strengths of CFOP that most of us never pause to appreciate, especially the unique advantages that cement it as an accessible and effective speedcubing method.

Well, CFOP is straightforward enough: solve the 4 edges of one face (cross), slot in 4 corner-edge pairs to complete the first two layers (F2L), orient the 8 cubies on top (OLL), then permute them (PLL). At around 60 turns per solve, it’s fairly efficient, and there’s no method that’s vastly better than that. Personally, I have learned four methods: CFOP, Petrus, Roux, and ZZ. However, CFOP remains my weapon of choice, and the reason goes far beyond old habits and the community bandwagon.

 

ACCESSIBILITY

• It’s the most developed method
  Yes, it’s true, once something like this gains prominence, only an uprising can dethrone it. The number of tutorials is mind-boggling. There are countless OLL and PLL libraries. Subtle improvements and modifications to F2L have been developed and published. No matter how good other methods are, none are as thoroughly understood and studied as CFOP.
• The steps follow the same order as most beginner methods
  Prevalent beginner’s methods solve the cross in two steps, then 4 corners, then middle edges, then some 4-stage last layer. CFOP does the same and merely collapse each pair of steps into one.
• F2L is logically simple
  The bulk of the solve is repeatedly inserting 4 corner-edge pairs. Simple, clear, no nonsense. They even look pretty and orderly when they go in, establishing 2x2x2 blocks!
• LL has an easy learning curve
  2-look OLL (3 + 6 = 9 algs) and 2-look PLL (3 + 4 = 7 algs) solves the entirety of the last layer in a measly 16 algorithms, most of which are really easy to learn (e.g. 6-move T, Sune, U perm, A perm). It’s actually quite fast too.
  The next step is full PLL at 21 algorithms, which is still not that many. Many speedcubers stop here, as the payoff for learning the other 48 OLL is actually quite small.

FIRST TWO LAYERS

• The cross establishes the least visible pieces
  This is a remarkable boon, enabling the philosophy of “out of sight, out of mind”. In the heat of things, cube rotations are costly and disorienting, while inspection is the only time you get to freely handle the cube like a gyroscope and find whatever you need. Getting the relatively inaccessible 4 bottom edges solved quickly means you never have to peek at the bottom of the cube to find out what pieces are being hidden from your native vantage point.
• F2L is rotationally symmetric
  This is the big one, CFOP’s greatest boon. Following the cross, any of the four F2L pairs can be addressed first. It doesn’t matter which, just find any matching pair of non-yellow pieces and you’re good to go. You don’t even need to worry about where they are to be slotted, just align the first (no restrictions on which slot is used for setup) and find the right slot during that time.
• Solved pieces are pushed to less visible locations
  It’s a ubiquitous but under-appreciated feature. To realize what difference it makes, consider the beginners who solve with cross up. They constantly flick their wrist to look at the bottom of the cube. Moderate beginners who do the same execute triggers with their ring and pinky fingers. Seriously? Our eyes and our dexterous fingers are on top!
• Following every R with R’ is good for fingertricks
  The cross edges anchor us so that virtually every insertion alg has the format R U* R’ (or mirror or inverse), which is probably the most natural fingertrick. Flick wrist, trigger with index fingers, then flick wrist immediately back to resting position.

LAST LAYER

• OLL is extraordinarily easy to recognize
  There are yellow stickers everywhere! Which way are yellow stickers facing? It’s so easy that it’s almost natural even for non-cubers.
  Anyone who has tried to learn COLL can attest that OLL is comparatively easy to recognize, and not just from more practice. For example, depending on whether it’s the Sune group or T group, you have to look at different side stickers and match patterns depending on whether two colors are on the same or opposite sides. Ugh.
• PLL is reasonably easy to recognize ahead of time
  Staring at the 12 side stickers is straightforward and natural while executing OLL. There’s no need to pay attention to the ubiquitous and confusing yellow stickers and which way they’ll end up pointing.
• OLL -> PLL is an intelligent ordering and grouping
  Consider some alternatives:
  The opposite, permuting pieces then orienting them, is an unabashedly terrible idea, as algorithms that orient cubies but retain permutation are abysmal.
  Another possibility is to solve the edges then solve the corners. In fact, that’s more similar the beginner’s method I teach, which orients edges (6-move T), permutes edges (sune), permutes corners (niklas), then orients corners (sexy move). However, all the algorithms I know that solve the corners while leaving the edges untouched are either just a PLL+OLL or horribly long. It’s just part of the cube’s nature how it’s difficult to affect the corners without moving edges too.
  Solving the corners first with CLL then edges with commutators is plausible (it’s what Roux does). I prefer memorizing and practicing algorithms to dynamically generated commutators, however.
• It balances ease of memorization and efficiency
  57+21= 78 algorithms to solve the entirety of the last layer is a fortuitously reasonable number. Not too many, not too few. Consider two extremes:
  Beginner’s methods have as few as 4 algorithms, so they’re easy to learn, but not efficient enough. The fewer things you memorize the more time you have to spend reducing things into the few cases you do recognize.
  ZBLL has a whopping 493 algorithms, so it’s difficult to learn, but certainly efficient. However, it’s not faster because of several reasons: some of the algorithms are inevitably awkward, it’s implausible to train the muscle memory for every algorithm, and recognition is a nightmare. Analyzing the positions of all 16 relevant stickers? No thanks!

WEAKNESSES, to be fair:

• CFOP doesn’t utilize the 15 seconds of inspection time
  Except at the highest level, CFOP users plan out the 4 cross edges, and that’s it. Solving 4 pieces is quite enough, but as it only takes about 5 seconds of planning for most people, one wonders how we could better spend those precious free seconds. Advanced cubers might plan or track the first pair for a smoother transition into F2L, but that’s about it.
• It’s not all that efficient
  Yes, it’s true, the average turn count of ZZ, Roux, and Petrus are all lower. Still, it loses efficiency in the F2L pairs and lack of effort to influence the last layer beforehand. Still, I feel like these inefficiencies are intelligently allocated to enable blind thoughtless bursts of turns.

Yes, I know I’m overthinking it. After all, as speedcubing adheres to the KISS principle: “Keep it simple. stupid”. Speed comes with instinct, not its cumbersome cousin, thought. It shows, too; at around 14 seconds, I’m quite slow by speedcuber standards, but I excel at One-Handed cubing, where the inherently slower turn speed allows other skills to compensate.

 

A few notes on the other methods:

• ZZ I like. The EOLine is immensely difficult, but it properly uses all 15 seconds of inspection. Reducing the F2L to just {L, U, R} is just about the best thing ever for one-handed cubing. Pre-orienting the LL edges enables me to use COLL leading to EPLL, the fastest PLL cases for OH.
• Roux seems like a fantastic method, and the Roux experts are mind-blowingly quick. The first block uses inspection well and reduces the second block to just {M, R, r, U}, which flows well ergonomically with no regrips. CLL is a good alg set, and L6E can be murderously fast to execute when learned thoroughly. I just don’t use it because the M slice is not good for OH.
• Petrus really doesn’t feel that good. It does have a lower turn count and in theory the best lookahead, as it sets the 4 invisible pieces in the 2x2x2 DBL block, but the blockbuilding is somewhat cumbersome. Unless you have fantastic color-neutral recognition, the non-structure is too unstructured for proper lookahead.

 

-Peter Hung, Sept 2013