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New method for categorizing F2L cases

patricKING

Member
Joined
Apr 12, 2021
Messages
59
Location
Sweden
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
1621601378571.png
1621601107320.png
2 - Front left
1621601424719.png
1621601437726.png
3 - Back left
1621601466893.png
1621601488975.png
4 - Back right
1621601514783.png
1621601643549.png

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
1621601883346.png
1621602128576.png
2 - FL
1621602168223.png
1621602185751.png
3 - BL
1621602206928.png
1621602218910.png
4 - BR
1621602234636.png
1621602259465.png

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.
 

patricKING

Member
Joined
Apr 12, 2021
Messages
59
Location
Sweden
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
Joined
Sep 26, 2014
Messages
482
Location
U.K
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:
http://web.archive.org/web/20110621205048/http://cubefreak.net/speed/f2ladvanced/a0.html
 

patricKING

Member
Joined
Apr 12, 2021
Messages
59
Location
Sweden
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:
http://web.archive.org/web/20110621205048/http://cubefreak.net/speed/f2ladvanced/a0.html
How do you create a site like that? I'd like to know how to do it.
 

SenorJuan

Member
Joined
Sep 26, 2014
Messages
482
Location
U.K
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.
 

Attachments

patricKING

Member
Joined
Apr 12, 2021
Messages
59
Location
Sweden
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.
 
Joined
Aug 12, 2013
Messages
1,612
Location
Brazil
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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):


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
 
Last edited:

SenorJuan

Member
Joined
Sep 26, 2014
Messages
482
Location
U.K
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.
 
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Messages
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Visit Channel
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.
 
Joined
Dec 9, 2020
Messages
13
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
Joined
Apr 12, 2021
Messages
59
Location
Sweden
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

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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
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Sep 26, 2014
Messages
482
Location
U.K
"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.
 
Last edited:

patricKING

Member
Joined
Apr 12, 2021
Messages
59
Location
Sweden
"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

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Messages
482
Location
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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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