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BOPE/Higgs

Thermex

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Hello everyone,
This is a thread for a method I recently proposed on the new method/substep thread called "BOPE" or Higgs. BOPE is the first method ever to have a potential movecount of 40 or less moves, making it one of the most efficient methods ever proposed. Despite being so few moves, BOPE doesn't have a rediculous amount of algorithms, totalling nearly a fourth of the algs of other top methods such as LMCF and ZBLL (about 160 algorithms in its current state). The name BOPE comes from the initials of the steps of the method, which are:

1. Blocks: Solve two 1×2×2 blocks next to each other on the left side of the cube, in other words a 2×2×3 block minus the DL edge (~10 moves on average)
2. Orientation: Orient the six remaining corners on the cube, this step is known as "OSC" (~50 algorithms that each average 4-5 moves)
3. Permutation: Permute the six remaining corners, this step is known as "PSC" (~50 algorithms that are about 8 moves on average)
4. Edges: There are several approaches to the last 8 edges, most being around 19 moves. The most simple version of this step is:
a.) Solve either the FL and FR edges or the UL and UR edges
b.) Solve the last six edges with Roux LSE

The more efficient algorithmic approach used in eric fattah's LMCF method can also be used here and goes as follows:

a.) In one algorithm, solve any two edges of the right and left layers
b.) Orient all 6 remaining edges while solving the rest of the edges that go in the right or left layer
c.) Permute the midges

To learn more about this approach, check out efattah's LMCF pdf here: (ttps://drive.google.com/open?id=0B2QnZ3uD6I8kNkpHSURSbzluc2s)

With these estimates, BOPE would average in the ballpark of around 40 moves. Algorithms are currently being made for the OSC and PSC steps, so this method is not quite ready to be published. There is also potentially a more efficient way to solve the last 8 edges than solving ULUR and then doing LSE, so any ideas for that are appreciated. The method is currently being worked on by me, @Spencer131, @Neuro, @crafto22 and should be completed soon. Any questions, ideas or constructive criticisms are encouraged.
 
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mDiPalma

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bope.png


This is for fixed blocks, but optimal everything. After adding 2 moves for human LSE, 2 moves for human blocks, some moves for AUFs using your algorithms, I think this method loses out to petrus/zz with zzll on by several moves for a similar alg count.

Also your estimate for the 6-7 move P-stage is certainly a bit low if the 6-gen optimal solution is 8.45 moves, AUFs included.

That being said, it's certainly a very innovative idea with many possibilities for improvement.
 

Thermex

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:/ I guess PSC is less efficient than I thought, thank you for the tests though. Despite a slightly higher movecount than I estimated I still think it has potential if a better method for L8E is thought up. With your adjusted estimates, isn't it still around 42-43 moves?
 

Spencer131

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I think this method loses out to petrus/zz with zzll on by several moves for a similar alg count.
If zzll and petrus beat a 43 move method by several moves, then one would figure that makes zzll sub 40 moves. I think everyone would be using zzll if that were the case.
 

shadowslice e

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If zzll and petrus beat a 43 move method by several moves, then one would figure that makes zzll sub 40 moves. I think everyone would be using zzll if that were the case.
The point is this probably isn't a 43 move method on average. And just because something is better does not mean everyone would be using it. That's sort of the converse of a common logical fallacy.
 

Thermex

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@shadowslice e This IS a 42-43 move method on average, check out @mDiPalma's statistics. Originally I thought this was going to be like 40 moves but we added like 2-3 moves due to the crappy PSC algs. I think @Spencer131 was just pointing out that if any method was sub-40 moves more people would be using it than the amount of people currently using zzll.
 

shadowslice e

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@shadowslice e This IS a 42-43 move method on average, check out @mDiPalma's statistics. Originally I thought this was going to be like 40 moves but we added like 2-3 moves due to the crappy PSC algs. I think @Spencer131 was just pointing out that if any method was sub-40 moves more people would be using it than the amount of people currently using zzll.
Those are optimal movecounts stepwise. If we ran it for roux I'm pretty sure it would give a 42 move average or something.
Realistically,
Blocks: 10 (given there is a 6 move FB on average or something but people often get 8 or so)
Orient: 5 (generously speed optimised)
Permute: 9
Edges: 7
LSE: 14 (by roux solvers such as kian, kavin, vincent etc)
Total: 45
And the algs will likely be longer when speed is favoured over efficiency.

It is possible that given a few changes and improvements you could feasibly speedsolve in 42-43 but the current version is inadequate to do so.
 

Thermex

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Those are optimal movecounts stepwise. If we ran it for roux I'm pretty sure it would give a 42 move average or something.
Realistically,
Blocks: 10 (given there is a 6 move FB on average or something but people often get 8 or so)
Orient: 5 (generously speed optimised)
Permute: 9
Edges: 7
LSE: 14 (by roux solvers such as kian, kavin, vincent etc)
Total: 45
And the algs will likely be longer when speed is favoured over efficiency.

It is possible that given a few changes and improvements you could feasibly speedsolve in 42-43 but the current version is inadequate to do so.
Those seem like pretty reasonable estimates for now, but really we can't prove any of these "estimates" right until the algs have been genned and we've done testing with actual humans. With a lot of practice I could honestly see people shaving a move or 3 off that estimate (FBs & LSE can probably be done more efficiently with practice) but I'll let those averages stick for now. I feel like with some optimizations to L8E this could easily be sub-43 or so, so I'll be focusing on that in the upcoming weeks. Like you and @mDiPalma said, it has potential but isn't quite there yet.
 

Neuro

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I know that movecount would decrease ever so slightly if you allow either FLFR or ULUR to be solved in L8E. I suppose you could finish in a style similar to LMCF's variants or something?
 

Thermex

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@Neuro ahh good point, that'll take a move off as well. You could easily take another move off from the 14-move LSE estimate, so I say maybe 43 is a good estimate for now. Of course none of this really matters until we've done our real tests and all the algs are made, so yeah.

Using the knowledge I have of the corners first methods, you would finish L8E by solving the FLFR edges since you need to leave the m ring for the last step. However, I might ask @efattah about possible ways the first and last steps could be tweaked to allow maximum efficiency for solving the last couple of edges.
 

Gomorrite

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I apologize if it wasn't clear, the alternative name "Higgs" is just my last name. The method can also be referred to as Higgs, but is normally called BOPE, similar to how the names "CFOP" and "Fridrich" work.
Most famous methods are called by the surnames of their creators. I believe Fridrich was not the creator of CFOP, she just popularized it.
 

efattah

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Forcing that you solve FR/FL is very restrictive and the algorithms to do that (although short) will be awkward.

Using LMCF pair/triplet/quadruplet algorithms to solve some combination of FR/FL/UR/UL then allowing expanded 2-look LMCF L6E will be way faster, however it once again introduces a lot of algorithms. On the plus side the BOPE method does allow you to gradually expand your L8E speed by gradually learning new sets with almost no limit as to how much you can learn and consequently improve. However as we all know once your algorithm knowledge passes a certain amount, cubing becomes a little more of a chore since common solving is no longer sufficient to 'refresh' every case often enough, and drills are needed to keep algorithm sets fresh (I have recently had to go that route as I 'learned' too many algorithms).

The expanded LMCF pair/triplet/quadruplet algorithms place fewer restrictions on which pieces you solve. Pretty much any variant of piece locations can be solved. If you allow LMCF-L6E and Waterman L6E then prior to L6E, one unsolved edge counts as solved (as it is solved automatically during the L6E algorithm).

All the triplet algorithms are very fast to execute (sub-1).

Example 1:
Scramble: L' F' R U' M U' M2 U2 L' U' M U2 M' L R' U M U' M' R'
Set up: R L'
U' L U2 M2 U M' U R' F // solves DF->UR, UR->UL, UL->BL
U' M U' M U' M' U2 M' U R
U2 M U2 M2
// 24 STM

Example 2:
Scramble: M U2 M U M' R U M' U' R' U M2 L' U M U' M' L
L' U' M U // E2L pair
r L U M' U' M' // UR edge and setup
U M' U' M U M U' L' // solve UL and orient midges
E2 M E2 M' // permute midges
// 19 STM

Example 3:
Scramble: R M' U2 M' U M' R' U M' U' R U' M2 L' U M U' M' L U2 R'
R F U' M U M' F' // E2L triplet
M' R' // setup
M' U M U2 M U // solve UR while orienting midges
M' U2 M2 U2 M // permute midges
// 19 STM

Example 4:
Scramble: R M' U2 M' U M2 R' U' M' U R U' M2 L' U M U' M' L U2 R'
M L' // setup
U r U' M U R' U' // E2L pair
M2 // Setup Waterman Set 2 and observe top 3 facelets for case
M U2 L M' U' M' U L' U2 R // Waterman Set 2
M' U2 M' U2 M2 // permute midges
// 24 STM

Example 5 (same scramble as example 4, different solution)
M2 F' U M2 U' F R // E2L pair
M // setup LMCF L5E r-set
M' U2 M' U' M U' // solve UL/UR orient midges
l' U2 M2 U2 M // permute midges
// 19 STM
 

Thermex

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Most famous methods are called by the surnames of their creators. I believe Fridrich was not the creator of CFOP, she just popularized it.
That's an interesting fact, I never knew that! I'm still gonna use Higgs as a name for the method though.

Forcing that you solve FR/FL is very restrictive and the algorithms to do that (although short) will be awkward.

Using LMCF pair/triplet/quadruplet algorithms to solve some combination of FR/FL/UR/UL then allowing expanded 2-look LMCF L6E will be way faster, however it once again introduces a lot of algorithms. On the plus side the BOPE method does allow you to gradually expand your L8E speed by gradually learning new sets with almost no limit as to how much you can learn and consequently improve. However as we all know once your algorithm knowledge passes a certain amount, cubing becomes a little more of a chore since common solving is no longer sufficient to 'refresh' every case often enough, and drills are needed to keep algorithm sets fresh (I have recently had to go that route as I 'learned' too many algorithms).

The expanded LMCF pair/triplet/quadruplet algorithms place fewer restrictions on which pieces you solve. Pretty much any variant of piece locations can be solved. If you allow LMCF-L6E and Waterman L6E then prior to L6E, one unsolved edge counts as solved (as it is solved automatically during the L6E algorithm).

All the triplet algorithms are very fast to execute (sub-1).

Example 1:
Scramble: L' F' R U' M U' M2 U2 L' U' M U2 M' L R' U M U' M' R'
Set up: R L'
U' L U2 M2 U M' U R' F // solves DF->UR, UR->UL, UL->BL
U' M U' M U' M' U2 M' U R
U2 M U2 M2
// 24 STM

Example 2:
Scramble: M U2 M U M' R U M' U' R' U M2 L' U M U' M' L
L' U' M U // E2L pair
r L U M' U' M' // UR edge and setup
U M' U' M U M U' L' // solve UL and orient midges
E2 M E2 M' // permute midges
// 19 STM

Example 3:
Scramble: R M' U2 M' U M' R' U M' U' R U' M2 L' U M U' M' L U2 R'
R F U' M U M' F' // E2L triplet
M' R' // setup
M' U M U2 M U // solve UR while orienting midges
M' U2 M2 U2 M // permute midges
// 19 STM

Example 4:
Scramble: R M' U2 M' U M2 R' U' M' U R U' M2 L' U M U' M' L U2 R'
M L' // setup
U r U' M U R' U' // E2L pair
M2 // Setup Waterman Set 2 and observe top 3 facelets for case
M U2 L M' U' M' U L' U2 R // Waterman Set 2
M' U2 M' U2 M2 // permute midges
// 24 STM

Example 5 (same scramble as example 4, different solution)
M2 F' U M2 U' F R // E2L pair
M // setup LMCF L5E r-set
M' U2 M' U' M U' // solve UL/UR orient midges
l' U2 M2 U2 M // permute midges
// 19 STM
I'm not really seeing it reflected in the movecounts much, but the LMCF L8E approach seems to be much better than the original plan. I honestly think I'll change the steps I have written in the first post, since this is pretty much the same thing as doing FRFL->EORL but you can solve any edges you want. Although it does increase the amount of algs, I think this a much better approach for any professional speedsolvers and it's not TOO many more algs.

Here's an interesting (and possibly bad) idea that might shave off a couple of moves:

This is what I call "BOPE+" or "Terrific Eagle". Basically you just utilize TEG and add 150 or so algs.

1. First blocks (9/9)
2. Get the two D-layer corners into the D-layer with at least one of them oriented (3/12)
3. y rotation+"Terrific eagle", in other words solving all the corners with Twisty EG and forcing in the FL edge (10/22?)
4. Crafto's L7E method (17/39)

Optimistic movecount and a lot of algs, but this could have potential. My main concern is whether TEG+FL edge would even work, but it worked for TCLL. There's also the issue that the FL edge can get stuck in the FR slot, in which case I have no idea what to do. Maybe during step two you could try to force the FL edge into the m-ring. Is this just a terrible idea with two many algs or is it a pretty good upgrade for people willing to learn the extra algs?
 
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Thermex

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Apologies for the double post, but I have a few updates on bope.

First of all, OSC algs have been finished and I plan on finishing generating PSC algs this week. Those will all be released on this thread when they're done.

Second, it should be noted that Twisty EG can also be used for the LSC step, although it does double the number of algorithms that need to be learned while only saving 1-2 moves. However, as one of the creators of Twisty EG (aka TEG) I plan on using it for the LSC step since I'll already know the algs (I've currently generated 1/4 of the TEG algorithms). Twisty EG can be used by

a.) Forcing both d-layer corners into the d-layer, making sure at least one of them is oriented, and
b.) Finish off the corners by using one of 250 "TMEG" algs.

Finally, after a couple of days of testing, I think I've found the best system yet for solving L8E. It's based off of @crafto22's system for solving L7E and goes as follows:

1. Place two oriented edges at either UL and UR or FL and FR (ultra fast, ~1.5 moves)
2. Orient the remaining 6 edges while solving either UL and UR or FL and FR (~8 moves?)
3. Permute the remaining 6 edges (7 moves)

I still can't really grasp how step 2 would work and these movecounts are a bit optimistic, but I feel like this is a step in the right direction. This probably will end up as just an idea to build off of, but this is the kind of thing I'm looking for to solve L8E. If anybody can think of an improvement of this go ahead and post it :)
 
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