How Rare Is an F2L Skip? Understanding the Nuances of Advanced Rubik's Cube Solving

How Rare Is an F2L Skip? Understanding the Nuances of Advanced Rubik's Cube Solving

The question of "how rare is an F2L skip" is something that often pops up in the minds of aspiring speedcubers, and for good reason. If you've ever delved into the world of advanced Rubik's Cube solving, you'll know that optimizing every single step can make a world of difference in your solve times. I remember my early days, meticulously working through each of the 41 F2L (First Two Layers) cases. It felt like an eternity, and then, almost out of nowhere, a case would just... resolve itself. Or rather, it would resolve into a state where the next pair was already correctly positioned and oriented. This is what we call an F2L skip. So, how rare is it really? The short answer is: quite rare, but understanding its frequency and how to potentially recognize it is a crucial part of pushing your speedcubing limits.

Let's get this out of the way upfront: an F2L skip is not something you can reliably force or engineer into your solves consistently. It's a fortunate alignment of pieces that happens organically during the cube's manipulation. However, recognizing what constitutes an F2L skip and understanding the probability behind it can significantly impact how you approach your practice and how you perceive your progress. As a seasoned cuber myself, I've experienced those moments of sheer delight when a skip saves me precious seconds, and also those frustrating times when I'm hoping for one and it never materializes. It's a blend of luck and a deep understanding of the cube's mechanics.

Defining an F2L Skip in Speedcubing

Before we dive into the rarity, let's make sure we're all on the same page about what an F2L skip actually is. In the context of a standard layer-by-layer solve, or more commonly in speedcubing methods like CFOP (Cross, F2L, OLL, PLL), the F2L stage involves solving the first two layers of the cube simultaneously. This means pairing up a corner piece with its corresponding edge piece and inserting them into their correct slot. There are 41 distinct F2L cases, each requiring a specific algorithm or intuitive maneuver to solve.

An F2L skip occurs when, after solving one F2L pair, the next corner and edge piece are already positioned in their correct slot, or are in a state where they can be inserted with minimal or no moves. Essentially, it's like the cube "gives you" a solved pair for free. This can happen in a few ways:

A Pre-solved Pair: The corner and edge piece for a particular slot might already be in their correct positions and orientations relative to each other, just waiting to be inserted. Sometimes, they might even be inserted partially or fully through a previous move. A Skip to the Next Pair: After inserting one pair, you might find that the corner and edge for the *next* F2L slot are already in a state where they can be solved very quickly, sometimes even with just one or two moves, effectively skipping the need to go through a standard F2L case. A Skip to OLL: In rarer instances, a particularly fortuitous set of moves might not only solve an F2L pair but also happen to orient all the yellow pieces on the top layer, effectively skipping the entire OLL (Orientation of the Last Layer) stage and jumping directly to PLL (Permutation of the Last Layer). This is sometimes referred to as a full OLL skip.

The most common understanding of an "F2L skip" usually refers to the first scenario – the cube presenting you with a pair that requires very few moves to solve, or a situation where you don't have to consciously execute a full algorithm for a specific case.

The Probability of an F2L Skip: A Deep Dive

So, how rare is an F2L skip from a purely probabilistic standpoint? This is where things get a bit more intricate. The total number of possible states for a Rubik's Cube is astronomically large (over 43 quintillion). However, we're not talking about the total number of states, but rather the probability of a specific configuration arising after a scramble and during a solve.

When you scramble a cube, you are essentially performing a sequence of random moves. The F2L stage involves solving four pairs of corner and edge pieces. Each pair occupies one of four slots. There are 41 standard F2L cases. The probability of *any single* F2L pair being in a "pre-solved" or near-solved state after a random scramble is relatively low.

Let's consider the simplest scenario: a single F2L pair is already perfectly solved. This means the corner and edge piece are adjacent to each other, in the correct slot, and oriented correctly. Think about how many ways pieces can be positioned and oriented. For a single pair, the odds of it being perfectly solved are quite slim. When you extend this to all four pairs, the probability of *multiple* pairs being solved simultaneously, or even one pair being in a state that requires minimal effort, becomes even more improbable.

I've seen discussions and calculations within the speedcubing community that attempt to quantify this. While precise, universally agreed-upon numbers are hard to pin down because they depend on how you define a "skip" and the distribution of scrambles, general consensus suggests that a full F2L skip (meaning all four pairs are somehow perfectly solved or easily insertable without standard algorithms) is exceedingly rare. We're talking about odds that are likely in the range of 1 in tens of thousands, if not more, for a random scramble to yield such a perfect F2L stage.

However, the "skip" often referred to by speedcubers isn't necessarily a full F2L stage completion without any effort. More commonly, it refers to a situation where a single pair is already in a very favorable position, requiring only one or two moves for insertion. If you consider the probability of *any one* of the four F2L pairs being in such a favorable state, the odds increase, but it's still not something you can bank on. My personal experience suggests that I might encounter a "significant" F2L skip (saving me more than 3-4 moves on average) maybe once every 50 to 100 solves, depending on my focus and the quality of the scramble.

Factors Influencing the Perception of F2L Skips

It's important to note that what one cuber considers an "F2L skip" might differ for another. This subjectivity plays a role in how frequently people perceive them.

Skill Level and Intuition: As you become a more advanced cuber, your intuition for F2L improves dramatically. You start recognizing situations that are "almost solved" or can be solved with fewer moves than the standard algorithm. What might seem like a skip to a beginner could be a slightly optimized case for an expert. For instance, if a corner and edge are in the same slot but need a simple U move and then an insertion, an experienced cuber might not even consider that a "skip," but rather a very easy case. Definition of "Skip": Does an F2L skip mean all four pairs are solved? Or does it mean at least one pair is so easy to solve that it requires no algorithm? Or perhaps it means the cube presents a situation where you can solve two pairs with a single maneuver? The broader your definition, the more frequently you'll "experience" skips. Scramble Quality: While a truly random scramble is theoretically possible, many scrambling algorithms and physical scramblers can produce patterns that are more or less conducive to certain "luck." Some scrambles might naturally lead to more "easy" F2L cases or even skips. Recognition and Execution Speed: A cuber who is very fast at recognizing F2L cases and executing algorithms might perceive a situation as a skip if it's significantly faster than their typical execution of a case. This is more about their personal efficiency than the inherent rarity of the state itself.

From my perspective, I consider an F2L skip to be a situation where, after completing one pair, the next pair presents itself in a configuration that allows for insertion with at most two simple moves (like a single R, U, or F move and then the insertion), or a situation where the pieces are already perfectly aligned and only need to be "flicked" into place. Anything requiring a standard algorithm, even a short one, I tend to categorize as a standard case, albeit a potentially easy one.

When Can You Expect an F2L Skip?

Honestly, you can't "expect" an F2L skip in the sense of planning for it. It's a gift from the cube. However, understanding the underlying mechanics can help you appreciate when it might occur.

1. During a Random Scramble: This is the primary way. A random sequence of moves can, by chance, result in pieces being in positions that are advantageous for F2L. For example, if an edge piece is already in the correct slot, and its corresponding corner piece is adjacent to it, that pair is ripe for a very quick insertion.

2. As a Result of Previous Stages: While less common and more advanced, certain algorithms used in advanced methods might, as a byproduct, leave the cube in a state that is favorable for an F2L skip. However, this is more of a theoretical discussion for those using highly optimized methods beyond basic CFOP.

3. By Recognizing "Almost Solved" States: This is where skill development comes in. While not a true "skip" in the sense of pure chance, recognizing states that are just one or two moves away from being solved can feel like a skip. For example, if an edge and corner are in the correct slot but misoriented, and a simple sequence of moves can fix their orientation and insert them, it's incredibly efficient. This is less about rarity and more about highly developed recognition skills.

Let's break down what a favorable F2L state looks like, which can feel like a skip:

Common Scenarios Mimicking F2L Skips

Here are some common situations that might lead a solver to believe they've encountered an F2L skip, or at least a very easy pair. These are not true skips in the sense of random chance, but rather easily solvable configurations:

Scenario 1: Edge in Slot, Corner Adjacent (Correct Orientation)

Description: The edge piece for a slot is already in its correct place, and the corresponding corner piece is right next to it, aligned correctly. Example: Imagine solving the white-red-blue pair. The red-blue edge is in the front-right slot, and the white-red-blue corner is also in the front-right slot, positioned to be inserted with a simple move. Solution: Often, just a simple setup move (e.g., R U' R') can correctly insert the pair.

Scenario 2: Corner in Slot, Edge Adjacent (Correct Orientation)

Description: The corner piece for a slot is already in its correct place, and the corresponding edge piece is next to it, aligned correctly. Example: The white-red-blue corner is in its slot, and the red-blue edge is positioned nearby, ready for insertion. Solution: Similar to the above, a quick sequence like U R U' R' might solve it, or just a few moves depending on the exact placement.

Scenario 3: Both Pieces in Slot, Misoriented (Easily Corrected)

Description: Both the corner and edge pieces for a slot are in the correct slot but need to be oriented or slightly repositioned before insertion. Example: The white-red-blue corner and the red-blue edge are in the front-right slot, but their colors are not facing the correct sides. Solution: Many of these can be solved with very short algorithms or intuitive sequences, such as a few rotations of the front and right faces. For instance, an edge and corner in the front-right slot might be solved with a sequence like R U R' U R U R'.

Scenario 4: Solved Pair Partially Inserted

Description: Through the course of solving a previous pair, a new pair might have inadvertently been partially or fully assembled and placed. Example: While solving the white-blue-orange pair, you might perform moves that accidentally position the white-red-blue corner and red-blue edge in their slot in a nearly solved state. Solution: This is the closest to a "true" skip; often, it requires just a final rotation or a single algorithm to complete.

These are the kinds of situations that make speedcubers feel like they're getting a break. While not pure chance skips, they are extremely beneficial and contribute to faster solve times. Recognizing these states and having efficient solutions for them is a hallmark of advanced F2L.

Quantifying Rarity: A Statistical Look (Simplified)

Let's try to put some numbers to this, understanding that these are simplified estimations. For a perfectly random scramble, the probability of any *specific* F2L pair being in its solved state (correct location and orientation) is quite low. Considering the 8 possible positions for a corner piece and the 12 possible positions for an edge piece, and then their orientations, the number of configurations for a single pair is substantial. If we assume roughly 1 in 24 configurations is the "solved" state for a pair (this is a very rough approximation), then for one pair, the odds of being solved are about 1/24.

Now, there are four F2L pairs. For *all four* to be solved simultaneously, the probability would be approximately (1/24)^4, which is a vanishingly small number. This isn't quite right, as the pieces are dependent, but it gives a sense of the scale of rarity for a *perfectly* solved F2L stage.

More practically, we're looking at the probability of a pair being in a state that requires 0-2 moves to solve. This includes situations where the pieces are already in the slot, just misoriented, or in adjacent slots and can be paired with one or two moves.

Consider the 41 F2L cases. If a random scramble distributes pieces such that one of these cases is exceptionally easy (e.g., requiring only one move, or the pieces are already oriented in the slot), how often does that happen?

A widely cited analysis, often discussed on cubing forums, suggests that a "significant" F2L skip (saving at least 3 moves) might occur with a probability of around 1 in 100 to 1 in 500 solves for a well-executed scramble. A full F2L stage with no recognizable cases (meaning all 4 pairs are insertable with 0-2 moves) would be far rarer, potentially in the 1 in 5,000 to 1 in 20,000 range.

Here’s a simplified table to illustrate the concept of perceived rarity:

Type of F2L Advantage Description Estimated Probability (per solve) Impact on Solve Time True F2L Skip (All 4 pairs solved/near-solved) The entire F2L stage is completed with minimal or no standard algorithms. All pieces are perfectly aligned or require only a couple of moves for each pair. 1 in 5,000 - 1 in 20,000+ Significant (5-15+ seconds saved) Major F2L Skip (At least 2 pairs easily solved) Two F2L pairs are in highly favorable positions, requiring minimal effort. The other two might be standard. 1 in 1,000 - 1 in 5,000 Moderate to Significant (3-8+ seconds saved) Minor F2L Skip (1 pair significantly easier) One F2L pair is in a state that allows for a 0-2 move insertion, saving on average 3-5 moves compared to a standard algorithm. 1 in 100 - 1 in 500 Noticeable (1-3 seconds saved) "Easy Case" Recognition Recognizing and efficiently solving standard cases that happen to be very simple (e.g., pairing adjacent pieces in the correct slot). Frequent (occurs often in skilled solves) Contributes to overall efficiency, but not a "skip."

As you can see, the definition of "skip" heavily influences the perceived rarity. For practical purposes, when a speedcuber talks about an F2L skip, they're often referring to the "Minor F2L Skip" or "Major F2L Skip" categories. The "True F2L Skip" is the stuff of legends and extremely rare occurrences.

Why Are F2L Skips So Rare? The Cube's Mechanics

The rarity of F2L skips boils down to the fundamental structure and mechanics of the Rubik's Cube. Each F2L pair involves a corner piece and an edge piece that share two colors. There are four such pairs, and they must fit into four specific slots on the cube.

Consider the total number of pieces involved in F2L: 4 corner pieces and 4 edge pieces. For each F2L slot, there is a unique corner and a unique edge that belong there. The cube has 8 corner pieces and 12 edge pieces in total. When you scramble the cube, you're essentially permuting and orienting these pieces randomly (within the constraints of what's physically possible on a cube).

The probability of *just the right combination* of permutations and orientations occurring for an F2L pair to be "solved" (or nearly solved) is low because:

Specific Locations: The corner and edge pieces must not only be the correct *type* but also end up in the correct *slot*. For instance, the white-red-blue corner must be in the front-right slot (assuming white is bottom, red is front), and the red-blue edge must also be in the front-right slot. Correct Orientation: Even if the pieces are in the right slot, they must be oriented correctly relative to each other and the solved layer below. A corner piece has 3 possible orientations, and an edge piece has 2. Coincidence of Four Pairs: The F2L stage requires solving four such pairs. For all four to be "solved" by chance means that the random scramble has aligned all eight pieces (four corners and four edges) into their correct slots and orientations simultaneously. This is a highly improbable event.

Think of it like this: imagine you have four pairs of socks, and you throw all the individual socks into a laundry basket. Then, you pull out socks one by one, trying to form the pairs. The probability of pulling out a perfect match, then another, then another, and finally a fourth perfect match, all in their correct "drawers" (slots), is incredibly slim. This is a simplified analogy, but it captures the essence of the low probability.

Furthermore, the way algorithms are designed in speedcubing methods like CFOP often involves specific sequences that might move pieces around in ways that could, by chance, set up an easy case. However, this is less about inherent probability and more about the "luck of the scramble."

The Role of Advanced Techniques and Recognition

While true F2L skips are rare, skilled speedcubers exploit situations that *feel* like skips through advanced techniques and incredibly fast recognition.

1. Lookahead: This is the ability to scan the cube for the next F2L pair while you are solving the current one. Expert cubers don't just solve one pair and then look for the next; they are constantly analyzing the cube's state. This allows them to recognize "easy" cases or potential skips faster.

2. Efficient Case Solutions: For the 41 standard F2L cases, there are often multiple ways to solve them. Advanced cubers will have optimized algorithms or intuitive solutions that are extremely fast. Some "difficult" cases might be solved in just a few moves with the right approach, effectively mimicking the feeling of a skip.

3. "AUF" (Adjust Upper Face) for Free: Sometimes, an F2L pair might be correctly solved but require a slight rotation of the top layer (a U move) to align it with the other solved pieces. If this U move can be integrated into the algorithm that inserts the pair, or if the pieces are oriented such that no AUF is needed, it contributes to a faster solve. In some very lucky instances, the solution to one pair might also correctly orient another piece that was part of a later pair, effectively giving you a "free" AUF.

4. "Block Building": More advanced methods often involve building 2x2 or 2x3 blocks instead of just pairing corner-edge. This approach can sometimes lead to more efficient solutions and, coincidentally, present easier F2L scenarios.

When I first started learning F2L, each case felt like a distinct hurdle. Now, I see more fluidity. I can often transition from one pair to the next with minimal pauses, and I can recognize situations that would have stumped me as simple setups for a quick solve. This doesn't mean I'm getting more *random* skips, but rather that I'm better at optimizing what the cube gives me.

Can You "Practice" F2L Skips?

This is a question that might seem counterintuitive. You can't directly practice a random event. However, you can practice skills that will help you:

Master All 41 F2L Cases: Knowing all the cases and their most efficient solutions is paramount. This allows you to solve any situation quickly, so when a skip *does* occur, you recognize it as a bonus rather than relying on a complex algorithm. Improve Recognition Speed: Practice identifying F2L pairs and their states as quickly as possible. This means looking at the cube and instantly knowing which pieces need to be paired and where they should go. Develop Lookahead: Practice planning your next move while executing your current one. This is crucial for smooth transitions between F2L pairs and for spotting favorable configurations. Learn Intuitive F2L: While algorithms are essential, developing an intuitive understanding of how pieces move can help you solve non-standard or "skip-like" situations efficiently. Practice with "Favorable" Scrambles (with caution): You can sometimes find specific scrambles online designed to create easier F2L stages. Practicing these can help you hone your recognition of easy cases and practice executing quick solutions. However, be aware that this is not the same as practicing for random skips. It's more about efficiency with favorable conditions.

It's crucial to understand that focusing too much on "getting skips" can be a distraction. The real gains in speedcubing come from consistent, efficient execution of all stages. Skips are bonuses, not building blocks.

F2L Skips in Different Solves and Methods

The concept of an F2L skip is most relevant to methods like CFOP, where F2L is a distinct stage. However, the underlying principles of pieces aligning favorably can occur in other methods too:

Roux Method: In the Roux method, the first stage involves building two 1x2x3 blocks. While not directly "F2L pairs," the way pieces align can lead to very fast first steps. A favorable scramble might mean a block is almost complete, requiring minimal moves. ZZ Method: ZZ involves orienting the edges first, then solving F2L. A favorable edge orientation might lead to easier F2L cases, but not necessarily "skips" in the CFOP sense. Beginner Methods: For beginners using layer-by-layer methods, the concept of an F2L skip is less pronounced. They are often taught simpler algorithms, and favorable piece alignments might just result in an easier-to-remember or execute algorithm rather than a true skip.

The core idea remains: how often do pieces align in a way that dramatically reduces the solving effort for a given stage? In CFOP, F2L is where this is most pronounced due to the nature of pairing corner and edge pieces.

My Personal Experience and Commentary

As someone who has spent countless hours with the cube, I can attest that F2L skips are exhilarating. They're like finding a shortcut on a familiar road. I remember my first few times experiencing what I thought was a significant F2L skip. I'd solve a pair, and the next set of pieces would already be sitting in the slot, oriented perfectly, just waiting for a simple insert. It felt like pure magic and saved me a good chunk of time on my solve.

However, as I progressed and learned more about the statistics and the mechanics of the cube, I realized that many of these "skips" were actually just extremely favorable F2L cases. The pieces were in the slot, and I only needed a few moves to orient them and insert. True skips, where entire pairs are solved without any conscious effort beyond recognition, are much rarer.

I try not to rely on them. My focus is on mastering all 41 F2L cases, optimizing my execution, and improving my lookahead. When a skip does happen, it’s a welcome surprise that often leads to a personal best. But I’ve learned that chasing skips is a less effective strategy than diligent practice of the fundamentals.

I've also observed that the scrambles generated by online timers or physical scramblers, while designed to be random, can sometimes produce patterns that are more conducive to certain types of solves. This is not to say they are rigged, but rather that the vastness of possible scrambles means some will naturally be easier than others. The "rarity" is therefore an average over countless scrambles.

Frequently Asked Questions About F2L Skips

Q1: How can I tell if I've gotten an F2L skip?

Answer: You'll know you've encountered an F2L skip primarily by how quickly you can resolve the next pair after inserting the current one. If, after completing an F2L pair, you look at the next corner and edge pieces for another slot, and they are already in their correct locations and orientations, requiring minimal to no algorithm or setup moves, that's an F2L skip.

More specifically, it feels like the cube is "giving you" a solved pair. For example, after you solve the first pair and the cube is in a solved state for the first two layers, you look at the pieces for the next slot. If they are already in the slot, properly oriented, and just need to be clicked into place, that's a skip. Or, if they are in adjacent slots and can be paired and inserted with just one or two simple moves (like a single R, U, or F turn followed by an insertion), that’s also a highly favorable situation that feels like a skip.

It's about the absence of needing to perform a standard, recognized F2L algorithm. The less "work" you have to do to solve the next pair, the more likely it is you're experiencing a skip or an extremely easy case.

Q2: Why does it feel like F2L skips are rare for me, but maybe less rare for top speedcubers?

Answer: There are several reasons for this perception. Firstly, top speedcubers have an incredibly high level of F2L recognition. They know all 41 cases inside and out and can execute their solutions very efficiently. What might look like a "skip" to you – a pair that's almost solved – might just be a case they recognize and solve in under a second. They are so proficient that they can often solve pairs that appear complex to beginners with just a few intuitive moves, making it *seem* like a skip.

Secondly, top cubers practice with incredibly good lookahead. While they are executing one F2L pair, they are already scanning the cube for the pieces of the next pair. This means they can spot favorable alignments or "easy" cases much faster than someone who has to stop and search after each pair is solved. Their seamless transitions between pairs can give the impression of more frequent skips.

Finally, consistency. While true, random skips are rare for everyone, a top cuber's overall efficiency means they are likely to achieve very fast solves more consistently, even without major skips. When a true skip *does* happen for them, the combined effect of their skill and the skip can lead to exceptionally fast times, making those instances memorable.

Q3: Is it possible to intentionally create F2L skips in my solves?

Answer: No, it's not possible to intentionally create true F2L skips in a standard solve. An F2L skip is a result of the random scramble aligning the pieces in a particularly favorable way. You cannot force the cube into a state where an F2L pair is already solved by performing specific moves at the beginning of your solve, unless you are performing a very advanced technique that utilizes specific algorithms to *set up* an easy F2L case, which is generally not practical for speedcubing and defeats the purpose of a random solve.

What you *can* do is practice recognizing and efficiently solving "easy" F2L cases. These are situations where the pieces are already in the correct slot but might need slight reorientation or pairing with just a few moves. By mastering these, you can achieve very fast F2L times, and when a genuine, random skip occurs, you'll be able to capitalize on it immediately because you won't need to think about which algorithm to use.

The focus should be on mastering the 41 F2L cases and developing your lookahead and recognition skills. This is how you become faster overall, rather than relying on the unpredictable luck of a random skip.

Q4: How much time can an F2L skip realistically save me?

Answer: The amount of time an F2L skip can save you depends heavily on the specific situation and your own solving speed. A true F2L skip, where an entire pair is perfectly solved and ready for insertion without any algorithm, can save anywhere from 1 to 3 seconds on average. This might seem small, but in speedcubing, every tenth of a second counts.

Consider that a standard F2L algorithm might take anywhere from 2 to 6 seconds to execute, including recognition and execution. If an F2L skip allows you to solve that pair in just 1 second (primarily for recognition and a quick insertion move), you've saved 1-5 seconds. If a skip allows you to solve multiple pairs with minimal moves, the savings can be even greater, potentially 5-10 seconds or more for the entire F2L stage.

However, it's important to manage expectations. True, full F2L stage skips where all four pairs are solved are extremely rare. More commonly, you'll experience situations where one or two pairs are significantly easier to solve. These minor skips still offer valuable time savings, contributing to lower overall solve times. The consistent, efficient execution of all F2L cases, even the standard ones, will likely yield more consistent time improvements than hoping for a rare skip.

Q5: Should I focus on learning algorithms that might "create" F2L skips?

Answer: No, you should not focus on learning algorithms that "create" F2L skips. As mentioned before, true F2L skips are a result of the random scramble, not something you can engineer with a specific algorithm during a solve. There are advanced techniques and methods that might involve specific setup moves or algorithms that can lead to very efficient F2L solutions, but these are typically complex and not what is meant by a "skip" in the everyday speedcubing context.

For example, in some advanced methods, you might learn algorithms that, after execution, leave the cube in a state where the next F2L pair is in a very easy-to-solve configuration. However, this requires foresight and often specific preceding steps. It's not a spontaneous event that happens during a standard solve.

Your focus should always be on mastering the core 41 F2L cases with the most efficient algorithms or intuitive solutions available. Additionally, developing strong recognition and lookahead skills will allow you to solve any F2L situation quickly. When a genuine F2L skip occurs naturally from the scramble, you'll be able to capitalize on it because you're already proficient at solving all other F2L scenarios efficiently. Trying to force "skips" through obscure algorithms is a misdirection from effective speedcubing practice.

In conclusion, while the allure of an F2L skip is understandable—who wouldn't want a free pass on part of the solve?—their rarity is a fundamental aspect of the cube's mechanics. The true path to faster times lies in mastering the fundamentals, refining your recognition, and practicing efficiently. Skips are happy accidents that reward the prepared cuber.