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Merits of CFOP

ravenguild08

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I've been inactive in the forums for a long time, but I recently wrote this article and thought I would share. I hope you find it informative!

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CFOP, aka. the Fridrich Method, is the wildly popular Rubik's Cube solving method used by virtually all high- and mid-level speedcubers. Still, methods like Petrus, Roux, and ZZ have their merits too, so why has CFOP persisted? 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. 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.


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.
 

TDM

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I don't know how many people use Petrus now, but it isn't really a very fast method compared to CFOP/Roux/ZZ. I think Roux is best for 2H, ZZ is best for OH but CFOP gives a nice balance and although those other two methods are great for one event, CFOP is good (not as good, but definitely far from bad) in both. CFOP is also good for reduction on big cubes where you don't have any inspection time. However, there's a few things I disagree with you with: firstly, the number of algorithms. You've only compared it with the extremes, and not with Roux/ZZ. CMLL/COLL is half the number of algs (~40) as OLL+PLL (~80). Then there's "Solved pieces are pushed to less visible locations" is true for CFOP, but it can be done with ZZ too. Also, ZZ/Roux have no rotations and CFOP does have rotations. And you said "Solving the corners first with CLL then edges with commutators is plausible". You don't have to use commutators: you can use ELL instead of commutators; CFCE is another method similar to CFOP that does this.
 

ravenguild08

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You've only compared it with the extremes, and not with Roux/ZZ. CMLL/COLL is half the number of algs (~40) as OLL+PLL (~80). Then there's "Solved pieces are pushed to less visible locations" is true for CFOP, but it can be done with ZZ too. Also, ZZ/Roux have no rotations and CFOP does have rotations. And you said "Solving the corners first with CLL then edges with commutators is plausible". You don't have to use commutators: you can use ELL instead of commutators; CFCE is another method similar to CFOP that does this.
You're totally right about ELL. My bad.
While COLL at 40 is better than OLL+PLL's 78, it's still not bad on an absolute scale. Several of these aspects are not unique to CFOP, nor is CFOP the class leader in those aspects!

In fact, despite praising CFOP here, I have been contemplating switching to ZZ for OH because, as you also note, ZZ is pretty much perfect for OH. Even after just limited practice, I'm already averaging 24 with ZZ compared to 18 with CFOP. I know most of COLL and some CLS, so... working on it.
 

Dapianokid

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Petrus is (arguably) the most efficient method of them all, simply because it was designed to be that way. But since we aren't computers that can focus solely on the cube and know exactly what to do all the time (No matter how much we practice with it!), we can't be as fast as the method inherently presents itself to be capable of. It says "hey look! 40 turns average? Super easy look-ahead? I'd say so, bud!" but it really means "Okay, here are 12000 cases, wayy too many to just instantly recognize or even know what to do with right away. Just intuitively solve each step and hope you got lucky. Oh, look at that, you can't make sub-20 with it? Sorry about that."

Petrus is REALLY easy to understand for being so efficient, but in practice as a speedsolving method, it just doesn't work.

Roux and ZZ speak for themselves. The benefits outweigh the disadvantages. They are both plausibly (and proven!) just as much world-class methods as CFOP, if you set your mind to it.

Petrus just takes so much work that it takes the fun out of it, I think. I have become tired of it and switched to CFOP. I do see many people who know CFOP, Roux, and ZZ all pretty well and I'm starting to see method neutrality in some folks. These methods are all engineered to work really well with our brains and our fingers. Petrus works well mathmatically and logically. Other than that... *sigh* Erik J will just have to show us what we'll never amount to.
 
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Could be a case of didn't read the OP.
Yeah, I was thinking that...Or he just has a strong urge to defend Roux? Lol I have the same feeling especially when people who are slower than most Rouxers out there, criticize the method as "slow" and "not as good as CFOP", but I try to control it :D
 

rj

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And your point? The OP already acknowledged exactly how "mind blowingly fast" Roux experts are.
[URL="http://www.speedsolving.com/forum/member.php?10749-ravenguild08" said:
ravenguild08[/URL]

]
CFOP, aka. the Fridrich Method, is the wildly popular Rubik's Cube solving method used by virtually all high- and mid-level speedcubers.
That's the point
 

Tim Major

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  • 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.
I disagree with both cons. People only using 5 seconds inspection is nothing to do with the method, and in terms of efficiency, it is generally more efficient than ZZ. If you solve ZZ slowly, then sure, but the fastest ZZ solvers average similar to CFOP movecounts.

For me the pros of CFOP are;
-lots of information on the web, algs, etc
-lookahead and case recognition
-spammy <RU> <RUF> and <RUD> algs.
-very low intuition needed, which leads to less pauses/slow TPS.

cons;
-movecount
-rotations

Edit: during F2L, you see a case and apart from preserving other pairs and effecting LL edge orientation, you don't think much. Whilst you do your first pair you can look ahead to your next couple of pairs, because you solve pairs the same 70% of the time. In Roux, there aren't "2nd block" cases, so whilst you can plan out your first block, and fast Roux solvers can plan some of their second block, there is slightly more intuition which slows the solve down. Generally, the more brain dead a method is, the faster it is, as you can just turn.
 
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