3 Blind Method Debate Thread

[Silky]

I think learning BH is probably a decent idea for you. It is basically an intermediate method and should improve your ability to come up with comms on the fly using setup moves

@Tao Yu Can you explain how this works exactly (intermediate BH)? Are you just using L3C algs with setups? The BH youtube videos are no longer available, sadly.

 

[Tao Yu]

@Tao Yu Can you explain how this works exactly (intermediate BH)? Are you just using L3C algs with setups? The BH youtube videos are no longer available, sadly.

Okay, here's the crash course on BH for corners.

Disclaimer: Most of the people reading this would probably better off watching a 3-style youtube tutorial from NoahCubes, J perm, Jack Cai or Timothy Goh than learning this stuff. I'm just putting the information out there so you can make your own choice as to what you want to learn.

This assumes some familiary with commutators, J perm's tutorial is probably sufficient.

The premise of BH is this fact: if you get rid of mirrors, inverses, rotations, mirrored inverses etc there are only 15 unique corner cycles. If you learn how each of these 15 work in terms of commutators, you can do any 3-cycle on the the cube efficiently.

Here are the 15 cases and their HTM optimal solutions:

Pure commutators (8 htm)

These are a three move insert with a one move interchange. Everything other than the Per specials and Cyclic Shift are a setup to one of these cases so make sure you understand these well.

[R U' R', D]
[R' U' R, D]
[R U R', D2]
[R U' R', D2]
[R U' R', D']
[R U2 R', D']

Cyclic Shift (10 htm)

The commutator part of the cyclic shift is a sledgehammer insert with a D2 interchange. If you expand [R' F R F', D2], it reads as R' F R F' D2 F R' F' R D2. After adding the setup moves from the full alg, you get R F' D2 F R' F' R D2 R' F, which is just the alg, but with the first two moves copy pasted to the end. This is why it's called a cyclic shift.

[F' R: [R' F R F', D2]]

Columns (11 htm)

This case is a one move setup to an A9

[U' R2: [R U2 R', D]]

Orthogonals (10 htm)

These cases are a one move setup to a pure commutator, with no cancellations

[F': [R U2 R', D']]
[F: [R U2 R', D']]

Per Special: (12 htm)

The moves R' D2 L D2 R is simply the shortest way to insert UFL into DFR. The interchange is a simple D2

[R' D2 L D2 R, D2]

A9 (9 htm)

These are a one move setup to a pure commutator. Since it's possible to set up to many pure commutators, it takes some trial and error to figure out which setup yields a cancellation. Personally, I think it's easiest to just memorize the four cases here.

[R: [R U2 R', D2]]
[R2: [R' U2 R, D]]
[R2: [R U R', D2]]
[R2: [R U2 R', D]]

Keep in mind every 3-cycle case can be viewed in multiple ways, for example UBL-UFR-UBR is the same as BLU-FRU-RBU as well as LBU-RFU-BRU

To make it easier there are a number of simple rules you can use to tell what type of case you have:

Pure Commutator: two stickers are interchangeable by one move. The third is in a different layer and can be inserted into the other two in three moves.
Cyclic shift: all the stickers are on one layer, however it's impossible to interchange any sticker with the other in one move (htm)
Per special: all stickers lie on parallel planes and are on corners which are √2 distance away (ie diagonally apart) from each other on a unit cube.
Columns: two stickers are interchangeable by a 180 degree turn, and the third is on a different layer. However it's not possible to insert the third into the two interchangable pieces in 3 htm. (make sure it's not a per special first)
Orthogonals: all stickers are on corners which are √2 distance away (ie diagonally apart) from each other on a unit cube, but none are interchangeable in one move
A9: If it's none of the above.

So once you classify the case, you should know the type of setup, insertion and interchange required, and also the minimum number of moves required to solve it - this will allow you to solve the case in the optimal number of HTM moves.

For edges, I never learned BH so I will refer you to these pages: Link 1 Link 2 (there are 27 cases for edges). I've never heard of anyone who actually learned BH for edges though - usually I think people find it easier to find fast efficient algs intuitively for edges.

 

[eyeoh]

Ocrozco could work for a stepping stone to 3 style but really jump to 3 style and understand comms. If you want to learn Ocrozco don't learn the comps like algs. They're comms and you should understand them.

Use UF/UFR as buffers.

I know Orozco cops a bit of stick from several (most?) top 3blders for being "trash", but for me (as a slightly older cuber), I believe it accelerated my journey and commitment to learning 3-Style since I initially wasn't sure if it'd be worth the effort for me. Orozco corners did indeed introduce me to understanding commutators after previously being intimidated by comm notation and thinking it wasn't for me. It also gave me a taste of what 3-Style corners would be like, and I discovered I liked what I saw!

A quick background of my progress - my mindset has more or less been to not get too addicted/attached to any intermediate methods (especially Orozco corners) before trying something slightly more advanced as a challenge to see if I'm capable of learning it. Basically, there was not a chance in hell that I'd be one of those 3blders who can do OP/OP at sub-2 or even sub-1 pace:

• I'm not fast and my TPS isn't high, but I do enjoy learning good fingertricks (and love RUS U perms, both righty and lefty!) - I currently average sub-22 333 and sub-33 OH. I started cubing around July/August 2019 and got my first 3bld success (32:09!) around 3 months after 4 DNFs. In hindsight, I should have practised more sighted solves as well as separate corners and edges, but at the time, I thought "yolo".
• Started learning M2/OP sometime after my 3:56 single and 5:15 mo3 PBs (with OP/OP - most of these and the following times are from separate sessions)
• Started learning M2/Orozco sometime after 2:12 single and 2:39 mo3 (M2/OP)
• Started learning M2/3-Style after a 1:35 single, 2:24 mo3 and also rolled 3:08 ao25 (M2/Orozco)
• Finished learning 3-Style edges after a 2:16 mo3 and 2:48 ao25 (M2/3-Style)

In summary, I started Orozco corners roughly a year ago, 3-Style Corners about 7 or so months ago, and 3-Style Edges about 5.5 months ago (which I "completed" in Anki just over 3 months ago).

Full timed 3-Style solves commenced at the start of last month and there's no question about it being my most comfortable method now - the consistently faster execution times give me less pressure to memo quickly to still achieve similar times to what I had with M2/3-Style. This has been the same pattern with each new method I've moved on from.

I'm yet to set any new PBs with "full 3-Style" (without floating buffers; which I won't touch for the time being), but it's only been a month of solves and I know it'll just be a matter of time as the rust with memo is worked out.

While I sort of grok the anti-Orozco sentiment, I probably still mostly don't, because Orozco worked for me and is what I'd still recommend to past-me. Whether that means it's suitable for everyone else - maybe not, but it's probably suitable for at least some people who might be similar to me in mindset and experience. I don't really understand the "don't learn Orozco as algs" refrain, because I guess I'm not familiar with that since I must have mostly learned them as comms because that's the logical way to learn them. But then again, when does a comm become an alg given that with enough "muscle memory" and speed, a lot of comms end up a bit like algs anyway?

That said, for those who have a natural affinity to 3bld and have a much faster/stronger grasp of 333 than me, it seems reasonable that learning 3-Style right after M2/OP is "easy". But for everyone else, perhaps dipping one's toes in the water with Orozco corners isn't as bad as it's made out to be? I mean, it's either that, or "where do I even start with these 378 corner comms?".

 

[eyeoh]

If you follow any of my content ( which I encourage you to do ) it's fairly clear that I advocate for method variety. I was kind of just hoping there would be more method variety in blind.

This is very nice to know. Makes 3-Style seem much more accessible than making spreadsheets and learning hundred of algorithms. Will have to check out the guide.

However, given my goals, I think I'm going to grind out Ayam/Eka and see how far I can push it.

I suggest skipping the spreadsheet, unless you're just referencing an existing sheet to find which comm is the current one that a blder is using. Go straight to choosing algs from bldbase.net and enter them into Anki flashcards. Don't even bother making your own sheet since that'll just be double handling - getting the comms into Anki is more important. Also, learn all the common keyboard shortcuts for Anki - it's a lot more pleasant to navigate via keyboard.

(I notice this comment I'm replying to was posted some time ago now - was any progress found with Ayam/Eka?)

 

[Silky]

Okay, here's the crash course on BH for corners.

Disclaimer: Most of the people reading this would probably better off watching a 3-style youtube tutorial from NoahCubes, J perm, Jack Cai or Timothy Goh than learning this stuff. I'm just putting the information out there so you can make your own choice as to what you want to learn.

This assumes some familiary with commutators, J perm's tutorial is probably sufficient.

The premise of BH is this fact: if you get rid of mirrors, inverses, rotations, mirrored inverses etc there are only 15 unique corner cycles. If you learn how each of these 15 work in terms of commutators, you can do any 3-cycle on the the cube efficiently.

Here are the 15 cases and their HTM optimal solutions:

Pure commutators (8 htm)

These are a three move insert with a one move interchange. Everything other than the Per specials and Cyclic Shift are a setup to one of these cases so make sure you understand these well.

[R U' R', D]
[R' U' R, D]
[R U R', D2]
[R U' R', D2]
[R U' R', D']
[R U2 R', D']

Cyclic Shift (10 htm)

The commutator part of the cyclic shift is a sledgehammer insert with a D2 interchange. If you expand [R' F R F', D2], it reads as R' F R F' D2 F R' F' R D2. After adding the setup moves from the full alg, you get R F' D2 F R' F' R D2 R' F, which is just the alg, but with the first two moves copy pasted to the end. This is why it's called a cyclic shift.

[F' R: [R' F R F', D2]]

Columns (11 htm)

This case is a one move setup to an A9

[U' R2: [R U2 R', D]]

Orthogonals (10 htm)

These cases are a one move setup to a pure commutator, with no cancellations

[F': [R U2 R', D']]
[F: [R U2 R', D']]

Per Special: (12 htm)

The moves R' D2 L D2 R is simply the shortest way to insert UFL into DFR. The interchange is a simple D2

[R' D2 L D2 R, D2]

A9 (9 htm)

These are a one move setup to a pure commutator. Since it's possible to set up to many pure commutators, it takes some trial and error to figure out which setup yields a cancellation. Personally, I think it's easiest to just memorize the four cases here.

[R: [R U2 R', D2]]
[R2: [R' U2 R, D]]
[R2: [R U R', D2]]
[R2: [R U2 R', D]]

Keep in mind every 3-cycle case can be viewed in multiple ways, for example UBL-UFR-UBR is the same as BLU-FRU-RBU as well as LBU-RFU-BRU

To make it easier there are a number of simple rules you can use to tell what type of case you have:

Pure Commutator: two stickers are interchangeable by one move. The third is in a different layer and can be inserted into the other two in three moves.
Cyclic shift: all the stickers are on one layer, however it's impossible to interchange any sticker with the other in one move (htm)
Per special: all stickers lie on parallel planes and are on corners which are √2 distance away (ie diagonally apart) from each other on a unit cube.
Columns: two stickers are interchangeable by a 180 degree turn, and the third is on a different layer. However it's not possible to insert the third into the two interchangable pieces in 3 htm. (make sure it's not a per special first)
Orthogonals: all stickers are on corners which are √2 distance away (ie diagonally apart) from each other on a unit cube, but none are interchangeable in one move
A9: If it's none of the above.

So once you classify the case, you should know the type of setup, insertion and interchange required, and also the minimum number of moves required to solve it - this will allow you to solve the case in the optimal number of HTM moves.

For edges, I never learned BH so I will refer you to these pages: Link 1 Link 2 (there are 27 cases for edges). I've never heard of anyone who actually learned BH for edges though - usually I think people find it easier to find fast efficient algs intuitively for edges.

So I ended up finding this thread which essentially outlines 3EF. This seems to be what I'm looking for, if I'm not correct. You memorize a comm for each of 18 cases URB->LFD->x. Then from here it's just set up into one of these 18 cases? Is this the idea that you're outlining?

 

[Tao Yu]

So I ended up finding this thread which essentially outlines 3EF. This seems to be what I'm looking for, if I'm not correct. You memorize a comm for each of 18 cases URB->LFD->x. Then from here it's just set up into one of these 18 cases? Is this the idea that you're outlining?

I've never heard of 3EF, but that sounds exactly the same as eka just with a URB buffer. It's a perfectly reasonable way to transition to 3-style, although UFR is usually considered to be a slightly better buffer than UBR

It has nothing to do with BH however.

To try and state it more clearly, here is how BH works:

You (intuitively) learn exactly 15 3-cycles (not 18). Then, to solve any 3-cycle, you figure out what rotation, inversion or mirror transformation (i.e. these are transformations don't add extra moves - they are not setup moves) required to turn it into one of those 15 cases. You do not do any setup moves in order to change the case into one of those 15 cases (the setup moves are already in the 15 cases themselves).

The 15 cases being the ones listed in my comment:

[R U' R', D]
[R' U' R, D]
[R U R', D2]
[R U' R', D2]
[R U' R', D']
[R U2 R', D']
[F' R: [R' F R F', D2]]
[U' R2: [R U2 R', D]]
[F': [R U2 R', D']]
[F: [R U2 R', D']]
[R' D2 L D2 R, D2]
[R: [R U2 R', D2]]
[R2: [R' U2 R, D]]
[R2: [R U R', D2]]
[R2: [R U2 R', D]]

Quick example solve:

Scramble: R B' L B R B' L B D2 B R2 B' U2 L2 B U2 L2 F

Solution:
[B :[L2, BR2B']] //UFR->LUF->UBL -transformation of [R: [R U2 R', D2]] - 11th on the list
[B2:[BL2B', R]] // UFR->FLD->BLD - transformation of [R2: [R U2 R', D]] - 15th on the list
[U', R D R'] // UFR->UBR->RDB - transformation of [R' U' R, D] - 2nd on the list
[B'D:[R2, D'BDB']] //UFR->DFR->RUB - transformation of [F' R: [R' F R F', D2]] - 7th on the list

alg.cubing

 

[Silky]

I've never heard of 3EF, but that sounds exactly the same as eka just with a URB buffer. It's a perfectly reasonable way to transition to 3-style, although UFR is usually considered to be a slightly better buffer than UBR

It has nothing to do with BH however.

To try and state it more clearly, here is how BH works:

You (intuitively) learn exactly 15 3-cycles (not 18). Then, to solve any 3-cycle, you figure out what rotation, inversion or mirror transformation (i.e. these are transformations don't add extra moves - they are not setup moves) required to turn it into one of those 15 cases. You do not do any setup moves in order to change the case into one of those 15 cases (the setup moves are already in the 15 cases themselves).

The 15 cases being the ones listed in my comment:

[R U' R', D]
[R' U' R, D]
[R U R', D2]
[R U' R', D2]
[R U' R', D']
[R U2 R', D']
[F' R: [R' F R F', D2]]
[U' R2: [R U2 R', D]]
[F': [R U2 R', D']]
[F: [R U2 R', D']]
[R' D2 L D2 R, D2]
[R: [R U2 R', D2]]
[R2: [R' U2 R, D]]
[R2: [R U R', D2]]
[R2: [R U2 R', D]]

Quick example solve:

Scramble: R B' L B R B' L B D2 B R2 B' U2 L2 B U2 L2 F

Solution:
[B :[L2, BR2B']] //UFR->LUF->UBL -transformation of [R: [R U2 R', D2]] - 11th on the list
[B2:[BL2B', R]] // UFR->FLD->BLD - transformation of [R2: [R U2 R', D]] - 15th on the list
[U', R D R'] // UFR->UBR->RDB - transformation of [R' U' R, D] - 2nd on the list
[B'D:[R2, D'BDB']] //UFR->DFR->RUB - transformation of [F' R: [R' F R F', D2]] - 7th on the list

alg.cubing

Been al long time since my last reply but I wanted to thank you for this breakdown of BH. After a month of experimentation, I can say I have a MUCH better understanding of how commutators work which has been very very exciting.

I also did a breakdown of 10 solves comparing 3-style and Eka for both corners and edges. Here are the numbers:

3-Style Corners Movecount: 41.6
3-Style Edge Movecount: 54.8
Parity Movecount: 7
Total: 103.4

Eka Corners Movecount: 48.3
Eka Edges Movecount: 64.2
Parity Movecount: 7
Total: 119.5

Notes:
For 3-Style I ended up just using blddb.net to come up with the algs. This means, most likely, the algs aren't entirely optimized, especially for edges. Even so, only needing to learn 38 compared to 409 ( not including inverses ) algs and having a differential of ~20 moves is super nice and I think worth it in terms of learning an intermediate method ( that is with no plans to end up transitioning to 3-style ). Another note, I ended up using reflections fairly often while solving Eka Edges. For edges, I found reflections to be much easier than for corners and, for the later, almost never used them ( except for an easy lefty A-Perm ).

I think, if you plan to transition to 3-style, the best approach ( at least the one I would use ) would be to memorize the Cyclic Shift, Columns, Orthogonals, and Per Special cases, since there ends up only being 27 ( not including inverses ). The leaves only learning Pure Comms and A9 which I find are far easier to do intuitively. This, obviously, only applies to 3-Style for corners.. but I still think is generally pretty good. I haven't looked into such an approach for edges but I'll update if I end up exploring that.