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

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.

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.

Last edited: Jan 3, 2010