# New method for categorizing F2L cases

#### patricKING

##### Member
Recently I have been trying to do better in F2L, and I have come up with a new idea. I got some inspiration from when I learned BLD.
I used Speffs cubing notation: bit.ly/SpeffzNotation.

So every case has a name of this format: "X-YY" where X is a number and Y is a letter.

Number, or X

Let's take the number first. In my model the number one stands for the pair in the front right, no matter how the cube is turned.
Here is an idea of what it might look like (And just so you know, blue is Front and red is Right):

 Number​ Normal​ After y2 rotation​ 1 - Front right​ ​ ​ 2 - Front left​ ​ ​ 3 - Back left​ ​ ​ 4 - Back right​ ​ ​

If you would have another colour, for example, red as Front and green as Right, the table would look like this (red is Front and green is Right):

 Number​ Normal​ After y2 rotation​ 1 - FR​ ​ ​ 2 - FL​ ​ ​ 3 - BL​ ​ ​ 4 - BR​ ​ ​

You can remember it as the FR pair is number 1, and then it goes clockwise as seen from above.
In other words, the number tells you the orientation to hold your cube on. If it's 1, the pair is in the FR slot, and so on.

first letter, or Y (1)

The first letter stands for the edge. But first, look at the F and B colours. The edge has a sticker that corresponds to one of those colours. That sticker is called the heavy sticker, or the correct sticker. If you look at Speffz notation, you can see that each sticker has a number. Notice that it is each sticker and not each edge. This is important as it is two different cases if the edge is flipped.
To see which edge position you have, look at where the correct sticker is positioned. Then insert that letter into your equation.

second letter, or Y (2)

The second letter stands for where the corner is positioned. The correct or heavy corner piece is the bottom colour. For most people, it will be white.

The total possible cases will be 16 edge stickers in the top two layers, and 24 possible corner stickers in the whole cube, and that makes 384 cases, which is less than ZBLL. I will try and add examples during the weekend, and please tell me if you like this idea.

#### SenorJuan

##### Member
For this to be truly useful, would you not also require some notation to specify which slots are empty? Most competent cubers make good use of empty slots ( to reduce move-count & rotations ), and will know many hundreds of unique F2L situations.
"Bird" uses Speffz to describe all his F2l cases, for interest:
https://andydude.github.io/birdf2l/app/

#### patricKING

##### Member
For this to be truly useful, would you not also require some notation to specify which slots are empty? Most competent cubers make good use of empty slots ( to reduce move-count & rotations ), and will know many hundreds of unique F2L situations.
"Bird" uses Speffz to describe all his F2l cases, for interest:
https://andydude.github.io/birdf2l/app/
Lol I thought I had an original idea. But well, I'll use your link, it's great! Where did you find out about it? I mean, are there more sites like this that every body knows?

#### SenorJuan

##### Member
I've spent many hours tinkering with 'F2L' , coming up with original ideas, which nearly all seem to be 'reinvention of the wheel'. Macky's site is one of the oldest 'advanced F2L' sites on the net, containing some cool / weird stuff, many things I self-discovered turned out to be on there.
But the BirdF2L is fairly new to the web ( mid 2018 ? ), I saw a link to it on here in December last year. It's still little-known, I think, but then Macky's Cubefreak site is now a bit obscure ... losing it's original images doesn't help either. Thankfully, the web-archive has preserved most of it. Example page:

#### patricKING

##### Member
I've spent many hours tinkering with 'F2L' , coming up with original ideas, which nearly all seem to be 'reinvention of the wheel'. Macky's site is one of the oldest 'advanced F2L' sites on the net, containing some cool / weird stuff, many things I self-discovered turned out to be on there.
But the BirdF2L is fairly new to the web ( mid 2018 ? ), I saw a link to it on here in December last year. It's still little-known, I think, but then Macky's Cubefreak site is now a bit obscure ... losing it's original images doesn't help either. Thankfully, the web-archive has preserved most of it. Example page:
How do you create a site like that? I'd like to know how to do it.

#### SenorJuan

##### Member
I'm no web-guru, no doubt someone on here could give you advice on website creation.

Re: web archive of CubeFreak:
While the web-archive has saved the images, it seems to have slightly messed up the 'style' , and most of the menus at the top are hidden.

If you turn off 'page style' in your web browser, they all appear in full.
( in Firefox, View > Page Style > No Style will turn off the style-sheet )
Then hopefully you can successfully navigate through all his site.

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• Cubefreak1.jpg
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#### patricKING

##### Member
I'm no web-guru, no doubt someone on here could give you advice on website creation.

Re: web archive of CubeFreak:
While the web-archive has saved the images, it seems to have slightly messed up the 'style' , and most of the menus at the top are hidden.

If you turn off 'page style' in your web browser, they all appear in full.
( in Firefox, View > Page Style > No Style will turn off the style-sheet )
Then hopefully you can successfully navigate through all his site.
Thanks.

#### Filipe Teixeira

##### Member
Recently I have been trying to do better in F2L, and I have come up with a new idea. I got some inspiration from when I learned BLD.
I used Speffs cubing notation: bit.ly/SpeffzNotation.

So every case has a name of this format: "X-YY" where X is a number and Y is a letter.

Number, or X

Let's take the number first. In my model the number one stands for the pair in the front right, no matter how the cube is turned.
Here is an idea of what it might look like (And just so you know, blue is Front and red is Right):

 Number​ Normal​ After y2 rotation​ 1 - Front right​ 2 - Front left​ 3 - Back left​ 4 - Back right​

If you would have another colour, for example, red as Front and green as Right, the table would look like this (red is Front and green is Right):

 Number​ Normal​ After y2 rotation​ 1 - FR​ 2 - FL​ 3 - BL​ 4 - BR​

You can remember it as the FR pair is number 1, and then it goes clockwise as seen from above.
In other words, the number tells you the orientation to hold your cube on. If it's 1, the pair is in the FR slot, and so on.

first letter, or Y (1)

The first letter stands for the edge. But first, look at the F and B colours. The edge has a sticker that corresponds to one of those colours. That sticker is called the heavy sticker, or the correct sticker. If you look at Speffz notation, you can see that each sticker has a number. Notice that it is each sticker and not each edge. This is important as it is two different cases if the edge is flipped.
To see which edge position you have, look at where the correct sticker is positioned. Then insert that letter into your equation.

second letter, or Y (2)

The second letter stands for where the corner is positioned. The correct or heavy corner piece is the bottom colour. For most people, it will be white.

The total possible cases will be 16 edge stickers in the top two layers, and 24 possible corner stickers in the whole cube, and that makes 384 cases, which is less than ZBLL. I will try and add examples during the weekend, and please tell me if you like this idea.
I have my own f2l naming scheme based on the most logic order you should learn each case.
Each group receives a letter, each case receives a number, plus "a" (solution don't demand rotation) or "b" (solution demands rotation)
So each case is reduced to a previous case until the case is solved completely
Filipe's F2L cases

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#### SenorJuan

##### Member
Filipe:
Have you extended your notation to include all the F2L cases, or just the 42 'final slot' cases ?

This is what makes Patricks quest hard. With so many thousand unique cases, as a result of the 380- ish cubie locations, four possible y rotations and four U possibilities for most cases, there's a lot of complexity.

I can't offer up any notation of my own .... I learnt the 'make a pair' and 'insert a pair' seperately, and just gave an arbitrary number to each in my notes. I then learnt (most of) them, for all the orientation/AUF situations, without formally naming them.
Likewise when studying special cases, I've pages of notes and drawings, but no notation worth mentioning.

#### Filipe Teixeira

##### Member
Filipe:
Have you extended your notation to include all the F2L cases, or just the 42 'final slot' cases ?

This is what makes Patricks quest hard. With so many thousand unique cases, as a result of the 380- ish cubie locations, four possible y rotations and four U possibilities for most cases, there's a lot of complexity.

I can't offer up any notation of my own .... I learnt the 'make a pair' and 'insert a pair' seperately, and just gave an arbitrary number to each in my notes. I then learnt (most of) them, for all the orientation/AUF situations, without formally naming them.
Likewise when studying special cases, I've pages of notes and drawings, but no notation worth mentioning.
oh.

#### BrightBlackHole

##### Member
Filipe:
Have you extended your notation to include all the F2L cases, or just the 42 'final slot' cases ?

This is what makes Patricks quest hard. With so many thousand unique cases, as a result of the 380- ish cubie locations, four possible y rotations and four U possibilities for most cases, there's a lot of complexity.

I can't offer up any notation of my own .... I learnt the 'make a pair' and 'insert a pair' seperately, and just gave an arbitrary number to each in my notes. I then learnt (most of) them, for all the orientation/AUF situations, without formally naming them.
Likewise when studying special cases, I've pages of notes and drawings, but no notation worth mentioning.
i don't think the AUF really matters since it doesn't affect the actual F2L slots that much, it just helps to set up to pairing the pieces

#### patricKING

##### Member
Some cases have different algorithms for different AUF's, but 'normal' solvers like us would never learn two algorithms for the same case. That's more Feliks Zemdegs stuff. But the general idea of naming every possible case, might be good. I'm not thinking to name every possible combination of 8 pieces, only every possible combination of 2 pieces. And besides that, is the slot's position. I don't think it would be that hard if people only knew how to do it. 384 cases isn't that much, considering that I have not excluded AUF's. But I'll try and get it done.

#### qwr

##### Member
I"m just waiting for birdf2l to be incorporated into speedcubedb.

I wish so much that the site would be open source, but I have asked Gil multiple times and while he is supportive he has never made it so.

#### SenorJuan

##### Member
"I don't think the AUF really matters since it doesn't affect the actual F2L slots that much, it just helps to set up to pairing the pieces."
It does matter. I have numerous cases where my solution differs depending on the AUF case.
As a trivial 'last F2L slot' example, do the following setup scramble ( on a cube with completed first two layers ):

R' U R U R' U2 R

From this AUF situation, I would use the reverse of the setup scramble.

But add a U2 to the setup, and my solution choice is:

R' U' R U2 R' U' R

which is obviously a shorter solution. And for different y orientations, my solutions differ again.

"... 'normal' solvers ... would never learn two algorithms for the same case."

Why not ? It's not that hard to build up your 'skill set' over time. If you only know one way, it does make decision-making easier, I admit, but once you become a more proficient cuber, you start to realise the limitations you're subjecting yourself to, by only knowing a very restricted choice/subset of possible solutions.
Learning a solution for the diagonally opposite case is one obvious choice. Performing a pointless, slow, clumsy y2 is not something I want to do during a one-handed solve if I can help it.

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#### patricKING

##### Member
"I don't think the AUF really matters since it doesn't affect the actual F2L slots that much, it just helps to set up to pairing the pieces."
It does matter. I have numerous cases where my solution differs depending on the AUF case.
As a trivial 'last F2L slot' example, do the following setup scramble ( on a cube with completed first two layers ):

R' U R U R' U2 R

From this AUF situation, I would use the reverse of the setup scramble.

But add a U2 to the setup, and my solution choice is:

R' U' R U2 R' U' R

which is obviously a shorter solution. And for different y orientations, my solutions differ again.

"... 'normal' solvers ... would never learn two algorithms for the same case."

Why not ? It's not that hard to build up your 'skill set' over time. If you only know one way, it does make decision-making easier, I admit, but once you become a more proficient cuber, you start to realise the limitations you're subjecting yourself to, by only knowing a very restricted choice/subset of possible solutions.
Learning a solution for the diagonally opposite case is one obvious choice. Performing a pointless, slow, clumsy y2 is not something I want to do during a one-handed solve if I can help it.
That's understandable, but I am only talking about different algorithms for different AUFs. That one you said is absolutely correct, and I must say you are right. But for most cases, I have one algorithm and then adjust the upper face. For different Y rotations, I always have several algorithms, unless I can solve them in the back efficiently.

#### SenorJuan

##### Member
Another example: a very common situation, with numerous ways of achieving a solution ... but choosing the best one can save a turn or two.

Start with a solved cross and BL slot. Setup:

L U' L2 U' L

It's the first slot, and solving it on the back is generally considered beneficial:

The best solution is L' U L L U L' executed as L' U L2 U L'

other longer options include R U' R' U L U L' or R' U' R U L U L'

But add U' to the setup and L U L' U L U L' is my choice, as it's 2-gen. But U + L' U L2 U L' is fine, it's 7 turns QTM, but has a half-turn, but isn't 2-gen ... personal preference plays a part.

Add U2 and the best choices are L U' L' U' L U' L' or L' U' L U' L U' L'

a poor choice is R' U R U2 L U' L' as the pairing still leaves the corner-cubie half a turn away from where you want it.

And adding U to the setup: I tend to use:

U' + L' U L2 U L'

though R U R' U' L U' L is also OK, it's also 7 turns QTM.

And the other 3 y-orientations have their own best solutions for the 4 AUF situations. Avoiding having the corner-cubie U2 away from where it's wanted is one aim.

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#### Andrew Robbins

##### Member
I am also very interested in making all F2L cases easy to understand. That is why I wrote BirdF2L! If you would like it to be updated or merged with another open-source web app, I would be happy to do so. Also, it comes to my attention that the inspiration for BirdF2L (Birdflu) has gone into 404 land, and is not working. Is there a place that would host such useful cubing web apps, that would perhaps be more long-term than many other short-lived sites? The reason why I chose GitHub Pages was that it was free for static content, and so I wrote it as a preprocessor that would create all the static pages for all F2L cases, and link to SpeedSolving web apps for the dynamic stuff.

Regards,
Andrew Robbins

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#### Andrew Robbins

##### Member
Since @qwr said that speedcubedb is not open-source, it seems more appropriate to merge its good parts into my app. One difference that I see immediately is that BirdF2L algorithms are "unhanded" (or canonicalized), whereas speedcubedb algorithms are "handed" (expressed for human hands to do them). For example, take pattern "Ct" (what speedcubedb calls "AF2L_22"):
• Alg "S R2 S'" (from speedcubedb) is listed in a short curated list.
• Alg "U' B F' U2 B' F" (from BirdF2L) is the same algorithm (with a different AUF), in a much bigger uncurated list, but is the first result when sorting by STM.
I've tried to add a spice of curating by using the Notes field, which is also used for RUF, RU, and named algorithms. I had hoped that the algorithms with notes would stand out, and perhaps would indicate that those algorithms were somehow preferred, or something.

A feature I was working on circa 2018 was an automatic unhanding procedure, which I used to convince myself that I had indeed performed an exhaustive search of the problem space (F2L). I initially used a dumb search of the space, but then went back with other databases, just to check if their algorithms were instances of the canonical versions. Although it took a lot of work, I think I got it working for F2L algorithms. I don't think I ever tested it for other cases. Canonicalization was probably the hardest part, and in some steps the code relies on a CSV table with commonly found algorithms that reduce to the null algorithm, and can safely be removed, but they are most probably not complete. I'm sure there are null algorithms I didn't include in it.

Another feature that I think would be incredibly useful that I haven't seen in too many other cubing databases was annotation. I believe I documented this in the Readme, but I'm not sure if anyone ever used it because I didn't make it accessible from the website. I would suspect it would have to be reimplemented in JavaScript (or TypeScript) if it were to be useful to other people making cubing websites. The idea behind it was a giant search bar (perhaps the only way to use the site, in the future) in which you enter a cubing algorithm, and it would spit out pages and pages of knowledge about that algorithm. Think what would happen if wolframalpha.com and birdflu.lar5.com had a child. Perhaps if it were combined with reconstructions of popular tournaments it would show who used the algorithm in the past!

#### qwr

##### Member
I'm more interested in algs for speed solving using a voting system like scdb rather than exhaustively finding algs. It would take much more human involvement to curate