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Thoughts about the BH method

Mike Hughey

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The purpose of this thread is to share thoughts about the BH method. Since a variant of BH was recently used to break the world record for 3x3x3 BLD, I suspect there will be more interest in it now. And since I just learned BH corners (I considered it learned earlier today when I managed to go through all of the algorithms successfully from memory), I thought now would be a good time for me to give my thoughts about it.

I hope that other people will add to this thread with their own thoughts – first Chris, Daniel, and Haiyan, and then hopefully others as well as they learn to use it. I’d also like to see anyone else who has learned it to post, if you would – are there others out there who know it already?

My comments will be focused on BH corners, since I still don’t know much of the BH edges, and I certainly don’t know the other pieces on bigger cubes. So I don’t know if some of what I have to say might not apply to edges.

Of course BH is a very efficient method to solve a cube blindfolded. It has a move count that’s very low – low enough that generally only a very advanced freestyle method can beat it. But it’s also fun to learn because you begin to really understand more about the cube. Being able to move any 3 pieces on the cube at will with maximum efficiency is really cool! I really believe it has helped me a bit with fewest moves solves in the past few weeks.

I’d like to echo what both Chris Hardwick and Daniel Beyer have said in the past about the method – learning BH is very much like learning intuitive Fridrich F2L. The parallels are actually quite amazing. For those who learned intuitive Fridrich F2L, try to think back to when you learned it. For most people, I think it usually starts with understanding some building blocks, in particular the two most common ways to insert a pair: constructing a corner edge pair and then inserting it, or constructing the pair as you insert it as is done with R U R’. For BH corners, a similar thing could be said about two types of algorithms: the basic 8-move commutator (like Niklas), or the basic 9-move setup to a commutator with a canceling move, like the A perm. Once you know these two basic moves and can see how to do them and why they work, you can then begin by yourself looking for ways to apply them to each case you want to solve. Many cases are similar – mirror images, inverses, or rotated somewhere else on the cube – so once you can see it in one case, you can usually see how to do the other cases as well.

I first started looking at BH corners last year, when Daniel sent me the list of commutators. But I had some other goals and put off learning them, although I did look at them occasionally just to get a feel for how to do some of them. Then early this year I played with them a little and learned all the cases for (UBL, URB, x), for each possible third sticker x. I think that took about a week. Then about 3 weeks ago I decided to go ahead and learn the whole thing. I was very surprised to discover it only took me about 3 weeks! It’s really not that hard. In fact, for an experienced cuber, I suspect it will take you about the same amount of effort as it originally took you to learn Fridrich F2L. Really! So I’m saying that I think it takes about as much effort for an experienced cuber to learn BH corners as it takes for a beginning cuber to learn Fridrich F2L!!! It’s just not all that hard. You get where you can turn around the cases in your head and see where each piece needs to go to solve a case, and so you don’t really memorize the algorithm – you simply remember where the pieces need to go for each step.

I used my images list to help me learn the BH algorithms. I found it was helpful to simply go through my image list alphabetically: BC, BD, BE, BF, etc. up to VW, VX, WX. First I would find the algorithm to solve the image, such as BC, and then it would be easy enough to invert it to solve the inverse case, CB. So I worked through the list that way. In order to learn it, it was best to construct the algorithm myself if possible; I only resorted to the list to “check my answer” or if I couldn’t figure it out myself. Once I had an algorithm that I thought was optimal, I would compare it with Daniel’s list. If my algorithm had more HTM than his, it was clearly worse, and so I would learn his instead and try to understand it. If it had the same HTM, I would compare QTM. Again, if mine had more QTM than his, I would learn his instead. But if not, then I knew my algorithm was as good as his was, so I usually wouldn’t even bother to look at his to compare (unless mine was really awkward somehow). After trying to “discover” the correct algorithm like this several times, you tend to simply learn it. And you find that very quickly you can perform it as fast as you can think of the letters you need to solve. It really works shockingly well.

I know that Chris and Daniel have worked very hard to think of the commutators in classes, according to what type they are. And I guess I wound up doing that myself even though I went through them alphabetically. So, for instance, I can tell you that, for my image list, GU, UG, MU, UM, RW, WR, LW, and WL are examples of the awful columns case that I hate so much. :) But perhaps other people will find it more helpful to group them like that to begin with, while learning. For me, the alphabetical approach worked well, though.

One comment I will make about bigger cubes: I’m pretty sure I can see that every one of the corner algorithms can be used directly as slice moves to solve X centers on bigger cubes. It really surprised me when I discovered that. And it actually also messed me up on 4x4x4 and 5x5x5 solves for a little while – I would start to see the BH corners algorithms, and forget how I normally do them. But it would probably be a mistake to just use these algorithms for the X centers – I could clearly see that there were a bunch of cases where those algorithms are far from optimal, especially if you consider inner slice moves to be inferior to outer slice or wide moves, which I do. So I’m now fighting hard to ignore the BH corner algorithms when I solve center pieces on big cubes BLD.

I’m starting to get fast with it; I’ve had quite a few sub-30 2x2x2 BLD solves, and several sub-2 3x3x3 BLD solves. And it was really fun – I tried 3x3x3 OH BLD last night and right away was getting close to 3 minutes, which is close to my personal best.

Anyway, I hope this rambling of mine might help inspire some other people to try it. If I can learn it, almost anyone reading this can.
 
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tim

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Thanks for your post, Mike. It was really interesting to read your thoughts about BH. I considered learning BH myself, but the huge amount of algs couldn't motivate me ;). Your Fridrich F2L analogy makes a lot of sense and i guess i'll give it a try.
Just one question: I don't think i'll have any problems seeing the 8 moves optimal solution, but i find it quite hard to find the proper setup moves if it can't be solved in 8 moves. How hard is it to learn the setup moves for these 9/10 move cases? I'm kinda afraid, that i'll have to learn them by heart.

/edit: The algorithms look sooo scary once they are printed out o_O. 7 pages full of characters.
 
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Mike Hughey

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Thanks for your post, Mike. It was really interesting to read your thoughts about BH. I considered learning BH myself, but the huge amount of algs couldn't motivate me ;). Your Fridrich F2L analogy makes a lot of sense and i guess i'll give it a try.
Just one question: I don't think i'll have any problems seeing the 8 moves optimal solution, but i find it quite hard to find the proper setup moves if it can't be solved in 8 moves. How hard is it to learn the setup moves for these 9/10 move cases? I'm kinda afraid, that i'll have to learn them by heart.
Generally, I had to look at the first one or two of each basic named type (the types given names by Chris and Daniel - you'll notice there are only something like ten different named types, and several of those are the 8-movers, so it's not very many), and then I started to see most of them. Some of the big ones are kind of hard to see at first, and reading through Daniel's descriptions again once you hit them can help. But I'd guess I probably only really had to look up 20 or 30 of them total; the rest I figured out on my own.

And really, the cancelling setup moves start to all look the same after a while. As Chris mentioned, there are a handful of different sub-classes of the A9's. But each of those look exactly the same across a very large number of cases. An example is (URB FRU ULF). It's exactly the same (with mirrors, inverses, and translations) as:
(URB RUF ULF)
(URB LUB ULF)
(URB BLU ULF)
(URB BLU BRD)
(URB RUF RDB)
And there are a bunch of others that look similar to this one, but with single turns instead of double turns somewhere. So you knock out a whole bunch of cases by just knowing the first one.

Definitely don't try to learn them directly by heart. Just try to see the setup moves and how the commutators work. By doing so, you will automatically learn them by heart. At least, that's what's happened for me. I didn't really try - it just magically happened. BH seems almost magical that way.

Tim, with your memory and superior speedcubing skills, I'm betting you'll probably sail through these much faster than I did, once you get going. You can probably have all the corners learned in two weeks. :)
 

Mike Hughey

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Mike can you please send me the complete list of Algs as I will be completely free for about 2 months
The place to go is definitely Chris's website. He's only got the corners up there now, but he'll probably have the edges up soon, and that's all I have from Daniel anyway. I'm guessing he'll have the edges up before you finish learning the corners, so that shouldn't be a problem. :)
 

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Mike can you please send me the complete list of Algs as I will be completely free for about 2 months
The place to go is definitely Chris's website. He's only got the corners up there now, but he'll probably have the edges up soon, and that's all I have from Daniel anyway. I'm guessing he'll have the edges up before you finish learning the corners, so that shouldn't be a problem. :)
Well, I've been using a TuRBo/Freestyle variant, but I haven't practiced in at least a week in a half (not sure if that's important) possibly even two weeks. Is it worth it to try learning BH? I'm interested, I might just try it.

EDIT: Wow, 378 algs, and Mike, you learned them all? I don't think I can do this...
 
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Mike Hughey

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I suspect that a person who's really good at freestyle (like Ville) really won't get much out of BH. Freestyle implies that you already essentially know how to solve every possible combination. But you only qualify as being "really good at freestyle" if you tend not to have very many setup moves. If you use very many setup moves, then BH could really help, since you've prelearned all the setup moves that you use, and you know you're at minimum movecount for each algorithm.

I really suspect that Ville wouldn't get much out of BH - he'd probably just get slower. Then again, I also suspect that Ville uses a lot of BH already - I bet most of his algorithms are already optimal. (Looking at the sample solves he's published here, it certainly appears that they are.) The ones that aren't movecount-optimal are probably even better - they're probably speed-optimal. (Like doing the standard 11-move U perm instead of the more move-optimal commutator.)

BH is particularly useful for me, since I'm relatively slow - movecount matters more to me than raw speed. But Haiyan has shown you can go almost as fast as Ville with BH, so the algorithms can still be pretty fast.
 
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I have been really interested in getting faster in BLD recently, and I think BH may be the way to go for me. I really enjoy learning and incorporating commutators instead of spamming algorithms as well! I think I will give this a good look after I'm done with school exams and related things. Thanks for your thoughts, Mike!
 
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I use BH for big blind, but not for corners and edges.

Mike is right, learning BH is like F2L. You have some basics cases and variations.

I'm currently learning this method for corners. I still use a customized M2 method for edges, because I find this more finger friendly. I use commutators when on piece is in the M slice, so I avoid all crapy cases and UF/DB slot swapping.

Anyway, the way I use M2 can be seen as commutators, but with non optimal move count.

BH is really easy to learn for wing and center of big cubes. It's harder for corner because you moce half of the stickers in each move so set-up with cancelling move are harder to find. But it's really easier than it seems !
 
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I finally learned to create commutators of my own since I was thinking of learning BH. After learning commutators I start to wonder:

1. Is BH basically doing commutators but with a fixed buffer?
2. What happens if there is 2 2-cycle of edges?(I'm guessing more commutators)
3. If freestyle just doing optimal commutators?(So far all I know is that freestyle is basically doing permutations while orientating)

Sorry if these questions don't seem to fit here but to me these questions will sorta help me decide on what to do next.
 
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1. Is BH basically doing commutators but with a fixed buffer?
yes

2. What happens if there is 2 2-cycle of edges?(I'm guessing more commutators)
You break into new cycle. For exemple if you have to solve AB and CD (where ABC and D are things to solves, edges or whatever you want) then you can pack the whole thing into ABCDC.

Finaly you do ABC then ADC.

3. If freestyle just doing optimal commutators?(So far all I know is that freestyle is basically doing permutations while orientating)
Freestyle is freestyle. You do whatever you want :D

You can consider that BH is a freestyle method.
 
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BH is a freestyle method that can be compiled to a finite number of cases.
You have broader control factors than most methods.
Pochmann -- Solving one piece at a time. Hence only 21 cases to optimally learn. You can squeeze by with one algorithm, and use a lot of setups. You could learn three algorithms to cycle a corner to its polar opposite. To reduce the number of setup moves to 1 move max per cycle.
3OP -- You orient first, so that only U/D stickers are cycled. You are looking at 42 possible cycles starting from any corner.
This takes extra moves, and there is more to memorize. It also brings into play the 12-move cases are more frequenct, as are the 11-move cases.
I do not believe that any case can be optimally solved in 10 moves, when you oriented all corners to the U/D layer.
You normally freestyle these setups, and hate when you run into a 12-move case. Most would actually solve these cases with far greater moves anyway (Though quick triggers are involved.)
Cancelations are lost, and setups are added.
Turbo -- Your control is setting up everything to the U layer as efficiently as possible, and doing a really fast algorithm.
BH -- Finally. You have center safe algs (always no matter what). They can be applied to big cubes blind. You are no longer controling the situation. You are able to look at each problem and solve it optimally and quickly, by dealving deeper into what the case really is. You notice more patterns. Rather than solving the cube layer by layer, and doing a 4LLL (or more), you move to CFOP. This is the greatest understanding of optimally solving the cube. Your have fewer reservations about what you control.
BH's goal: Directly and efficiently solve any cycle.
Breaking into cycles, rather than freestyling.
No setups to the U layer. No orient first methods.
-- By limiting the cycles to always involving one piece, the buffer. There is still a finite number of cases, because you are limiting yourself by cycling 3 pieces at a time. I mean certainly, you could learn all 9072 cases. By picking three random stickers from three separate cubies. (24x21x18)
By restricting yourself to a buffer and only cycling three pieces at a time. BH correlates to letter pair memory systems. Since you always cycle from a buffer, you just need to know what the next two pieces are -- the next letter pair image!

It's an amazing concept.
More to come. I'm glad that the interest has peaked.

Later,
DB
 
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There are classifications, that allow you to truly understand the method. Using it more like an F2L approach. You aren't learning algorithms, you are recognizing relations between the 3 pieces in space. I have described in detail these cases on corners. Edges, centers, and wings will come. It's an amazing method. I trust that you will all be quite pleased.
In the last 2 years, I have worked with Chris. His world Records have been cut into a third of what it was back then. Our memory techniques, execution methods, and theory for cutting time and delays have made him a great cuber. Its time that everybody else reap in our knowlege on the theory of blindfolded cubing as a whole.
 
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Hey, can someone explain to me about the orientation of inactive corners? Perhaps a few example solves. I've been playing around with BH and just improvised on the corners but I'm not sure if its right.

Oh, and can someone help me with recognizing the cases? I understand the commutators used, although I jumble up their names(yeah, I use the names to assign to a type of case), I still get what commutators to use for the cases(half of the time non-optimal). But at most times, I take a monstrous amount of time trying to recognize the case or think of the commutator to use. Help?
 

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Hey, can someone explain to me about the orientation of inactive corners? Perhaps a few example solves. I've been playing around with BH and just improvised on the corners but I'm not sure if its right.

Oh, and can someone help me with recognizing the cases? I understand the commutators used, although I jumble up their names(yeah, I use the names to assign to a type of case), I still get what commutators to use for the cases(half of the time non-optimal). But at most times, I take a monstrous amount of time trying to recognize the case or think of the commutator to use. Help?
Glad to see that you're interested in the BH method! I'm obviously a little biased in my opinion here, but I think it is a great way to solve the 3x3x3 BLD, and definitely one of the easiest ways to solve bigger cubes BLD.

For permuted but disoriented corners I use double sune algs and setups to twist them. Algs like R' U2 R U R' U R L U2 L' U' L U' L' and its inverse. Daniel sometimes cycles to the corners and then places them back into their locations, or he might use orienting algs as well. He is a bit more versatile than I am when it comes to handling those corners.

As for easy ways to recognize the cycles, you must learn what we call viewpoint shifting. I use viewpoint shifting nearly every solve, sometimes more than once on a single solve.

Hope this helps! Also check out Brian's BH resources thread, there's a lot of good information there.

Chris
 

Mike Hughey

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As for easy ways to recognize the cycles, you must learn what we call viewpoint shifting. I use viewpoint shifting nearly every solve, sometimes more than once on a single solve.
I have to admit that I don't do viewpoint shifting for BH corners. Very occasionally, if I get completely stuck (meaning I've taken 15 to 30 seconds, meaning my BH recall was a complete failure on that particular solve), I might do viewpoint shifting, but generally I don't. I know how to do it (although I'm slow at it), but it seems to me like I should be able to see the algorithm instantly without a viewpoint shift for every case in BH corners anyway, so I don't really see the point in practicing viewpoint shifting. Maybe that's holding me back, but I have yet to be convinced it will help.
 
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