Belt method similiar to LCBM

Discussion in 'How-to's, Guides, etc.' started by miotatsu, Feb 9, 2012.

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  1. miotatsu

    miotatsu Member

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    Oct 21, 2010
    Minnesota
    YouTube:
    miotatsu
    Here I have documented the method that I use to solve the 3x3x3 Rubik's Cube.
    This method could be described as a "belt method". Many of the ideas and algorithms come from another method called LCBM.
    I came upon this method while trying to optimize HTA for speed solving.
    I hope that these documents will be useful to others interested in this method.

    Overview of method:
    1. Edge orientation - place edges in the group <F2, B2, L, R, U, D> (or equivilant)
    2. Belt - solve 4 edges of the equator (E slice)
    3. Parity - create a situation in which corners can be solved with OCLL cases
    4. EPOCBL - orient all corners while preserving equator and edge orientation
    5. Seperation - permute corners to their correct layers
    6. EPPCBL - permute all corners while preserving equator and edge orientation
    7. L8E - solve the remaining eight edges

    I am no teacher, so I will simply provide links that can explain each step better than myself.

    Step 1: Edge Orientation:
    This is the same as EOLine without the line.
    http://cube.crider.co.uk/zz.php?p=eoline
    http://www.youtube.com/watch?v=a6tkUlkjnOE

    Step 2: Belt:
    Intuitive. Remember not to use single turns on F and B.

    Step 3: Parity:
    If you do not have OCLL cases on U/D:
    Step 4: EPOCBL:
    Memorize the algorithms for each case.

    Step 5: Seperation:
    Intuitive. Use only moves of the group <F2, B2, L2, R2, U, D>. I recommend only using <L2, R2, U, D>.
    Do not forget that you must restore the equator after breaking it.
    For example instead of bringing 2 U face corners from positions DLF and DLB to the top face with L2 you must do
    something that will not destroy the belt such as:
    U2 L2 U2 L2 U2

    Step 6: EPPCBL:
    Memorize the algorithms for each case.

    Step 7: L8E:
    I solve these using the exact same system used in Roux for LSE minus the edge orientation
    http://grrroux.free.fr/method/Step_4.html (4b and 4c)
    http://wafflelikescubes.webs.com/rouxmethod.htm (4b and 4c)
    http://rouxtorial.webs.com/lse.htm (4b and 4c)


    Example solves:

    F2 R2 D2 R2 F2 D R2 U B2 L2 F U' R2 B' R' B F2 L2 U L'
    EO: R' D R U2 B
    Belt: U2 D' R' D' L
    Parity: none
    EPOCBL: U2 D2 L' U' L' U2 L U' L
    Seperation: D' L2 U D L2
    EPPCBL: D x2 R U R' F' R U R' U' R' F R2 U' R' x2
    L8E: U2 M U2 M' D' M2 D M2 U M U2 M U M2 U x U2 M2 U2 M2

    B' U2 B' L' R D2 F L R2 D2 U2 B' U' B' U' R2 F2 R D B U2 R U2 F2 L'
    EO: D F' R2 D F2 D F'
    Belt: U' D2 R' B2 L2
    Parity: none
    EPOCBL: D' L' U' L2 U' L' U2 D' L2 U' L'
    Seperation: L2 U' L2
    EPPCBL: D x2 F' L U L F D2 F' L' U' L' F U D x2
    L8E: M2 U M U2 M' D M2 D' M2 U' M U2 M U' M2 U' M' U2 M'

    U F2 D F2 U2 F2 L2 U' F2 U' R U' L2 D R U2 B' R2 B' R2 F'
    EO: F D' B' D B
    Belt: F2 R' U R L' D' L
    Parity: L2 U' L2
    EPOCBL: f R U R' U' f' F R U R' U' F'
    Seperation: U2 L2 D' U2 L2
    EPPCBL: U F' L U L F D2 F' L' U' L' F U D2
    L8E: M' U2 M D M2 D' U M2 U2 M2 U' M U2 M' U2 M2

    Algs:
    EPOCBL Beginner (2-look) - 7 cases:
    ====================================================
    Sune: on U: R U R' U R U2 R'
    antiSune: on U: L' U' L U' L' U2 L
    H: on U: y F (R U R' U') (R U R' U') (R U R' U') F'
    U: on U: R2 D' R U2 R' D R U2 R
    T: on U: r U R' U' r' F R F'
    L: on U: y' F' r U R' U' r' F R
    Pi: on U: f (R U R' U') f' F (R U R' U') F'

    EPPCBL Beginner (2-look) - 2 cases:
    ====================================================
    Y: F R U' R' U' R U R' F' R U R' U' R' F R F'
    J: R U R' F' R U R' U' R' F R2 U' R' U'

    EPOCBL Intermediate (1-look) - 25 cases:
    ====================================================
    Sune: R U R' U R U2 R'
    H: y F (R U R' U') (R U R' U') (R U R' U') F'
    U: R2 D' R U2 R' D R U2 R
    T: r U R' U' r' F R F'
    L: y' F' r U R' U' r' F R
    Pi: f (R U R' U') f' F (R U R' U') F'
    sune/sune: R' U' R' U R U2 D R' D' R
    anti/sune: R' U' R U2 R (U' D) R2 U R'
    H/sune: U' R (U' D) M2 U' r2 U R'
    U/sune: R' U2 R' U D R2 U2 R' U' R
    T/sune: L D' L' U' r2 U2 L' U' L'
    L/sune: R D r2 R' U R U2 r2 R'
    Pi/sune: L U D L' U D2 L' U2 D L'
    H/H: R2 (U' D) L (U D') M2 (U D') L
    U/H: R D R' U D2 l2 U2 R' U' R'
    T/H: L D L' U' D2 r2 U2 L' U' L'
    L/H: L U' L2 R2 U' L' l2 D U2 L
    Pi/H: R' U' L2 U R2 (U' D) r2 R' (U' D) R'
    L/U: D' L' U' L' U2 L U' L
    Pi/U: L' U R U2 R' U L R U R'
    L/T: U R U D2 R' U' D2 R'
    Pi/T: L' U' L l2 U' l2 U' L' U2 L
    L/L: L U' D' L U D L'
    Pi/L: L' U' L2 U' L' U2 D' L2 U' L'
    Pi/Pi: L U D L' U2 D2 L U D L'

    EPPCBL Intermediate (1-look) - 5 cases:
    ====================================================
    Y: F R U' R' U' R U R' F' R U R' U' R' F R F'
    J: R U R' F' R U R' U' R' F R2 U' R' U'
    J/J: F2 U' R2 U D R2 D' F2
    J/Y: F' L U L F D2 F' L' U' L' F
    Y/Y: F2 U2 R2 U2 R2 U2 F2


    EPOCBL Advanced (1-look) - 70 cases
    ====================================================
    One case:
    Sune: on U: R U R' U R U2 R'
    Sune: on B:
    antiSune: on U: L' U' L U' L' U2 L
    antiSune: on B:
    H: on U: y F (R U R' U') (R U R' U') (R U R' U') F'
    H: on B:
    U: on U: R2 D' R U2 R' D R U2 R
    U: on B:
    T: on U: r U R' U' r' F R F'
    T: on B:
    L: on U: y' F' r U R' U' r' F R
    L: on B:
    Pi: on U: f (R U R' U') f' F (R U R' U') F'
    Pi: on B:
    Two cases:
    Sune: on B:
    Sune: R' U' R' U R U2 D R' D' R
    antiSune: R' U' R U2 R (U' D) R2 U R'
    H/Double Sune: U' R (U' D) r2 R2 U' r2 U R'
    U/Headlights: R' U2 R' U D R2 U2 R' U' R
    T/Chameleon: L D' L' U' r2 U2 L' U' L'
    L/Bowtie: R D r2 R' U R U2 r2 R'
    Pi/Wheel: L U D L' U D2 L' U2 D L'

    antiSune: on B:
    Sune: L U L' U2 L' (U D') L2 U' L
    antiSune: L' U L U' L U' D2 L U L'
    H/Double Sune: U' L' (U D') l2 L2 U l2 U' L
    U/Headlights: U R U' R2' D2 R U2 R U' R'
    T/Chameleon: R' (U2 D2) R' D R2 U2 D R
    L/Bowtie: L U R U' L U2 L2 U' R'
    Pi/Wheel: R U2 L2 U R U D r2' R U R

    H: on B:
    Sune: D R (U D') L2 R2 U' r2 U R'
    antiSune: D' L' (U' D) L2 R2 U l2 U' L
    H/Double Sune: R2 (U' D) L (U D') L2 l2 (U D') L
    U/Headlights: R D R' U D2 l2 U2 R' U' R'
    T/Chameleon: L D L' U' D2 r2 U2 L' U' L'
    L/Bowtie: L U' L2 R2 U' L' l2 D U2 L
    Pi/Wheel: R' U' L2 U R2 (U' D) r2 R' (U' D) R'
    U: on B:
    Sune: R U' R2 D L' R2 U R' U' L
    antiSune: L' U R U' L l2 U l2 U R'
    H/Double Sune: R U R' U2 D R2 U2 R' U' R'
    U/Headlights: U2 L' U L' U' r2 U' L U L'
    T/Chameleon: R (U' D) R U' R' U2 D' R'
    L/Bowtie: D' L' U' L' U2 L U' L
    Pi/Wheel: L' U R U2 R' U L R U R'
    T: on B:
    Sune: L U' L' D' L2 U2 L' U' L'
    antiSune: R' (U2 D2) R' U R2 U D2 R
    H/Double Sune: L U L' U2 D' L2 U2 L' U' L'
    U/Headlights: L2 U2 L' U' L U2 L' U' L'
    T/Chameleon: R (U2 D2) R' (U2 D2) R'
    L/Bowtie: U R U D2 R' U' D2 R'
    Pi/Wheel: L' U' L l2 U' l2 U' L' U2 L
    L: on B:
    Sune: R U L2 U2 L' U R' U' L'
    antiSune: x2 L U R U' L U2 L2 U' R'
    L D R D' L D2 L2 D' R'
    H/Double Sune: L U L2 U' L U' D2 L U2 L
    U/Headlights: U' L' D' L' D2 L D' L
    T/Chameleon: D R U2 D R' U2 D' R'
    L/Bowtie: L U' D' L U D L'
    Pi/Wheel: L' U' L2 U' L' U2 D' L2 U' L'
    Pi: on B:
    Sune: L U D L' U2 D L' U D2 L'
    antiSune: D R U L2 U D R U2 r2 U' R'
    H/Double Sune: R' U L2 U' R2 (U D') L2 R (U' D) R'
    U/Headlights: R' U' r2 D2 U' R' U r2 U' R
    T/Chameleon: L' U' L2 D2 L U2 D' L U' L
    L/Bowtie: D L' U' D' L D R2 U L R2
    Pi/Wheel: L U D L' U2 D2 L U D L'

    EPPCBL Advanced (1-look) - 35 cases
    ====================================================
    Case J/:
    L: R U R' F' R U R' U' R' F R2 U' R' U'
    R: (y) R' U L' U2 R U' R' U2 L R U'
    F: R' U L' U2 R U' R' U2 L R U'
    B: R U' L U2 R' U R U2 L' R'
    Case Y/:
    F R U' R' U' R U R' F' R U R' U' R' F R F'
    Case /J:
    L:
    R:
    F:
    B:
    Case /Y:
    Case J/J:
    L/L: F2 U' R2 U D R2 D' F2
    L/R:
    L/F:
    L/B:
    R/L:
    R/R:
    R/F:
    R/B:
    F/L:
    F/R:
    F/F:
    F/B:
    B/L:
    B/R:
    B/F:
    B/B:
    Case Y/Y:
    F2 U2 R2 U2 R2 U2 F2
    R2 U2 R2 U2 y' R2 U D' R2
    R2 U2 R2 U2 F2 dD' R2
    R2 U2 R2 U2 F2 E R2
    U' R2 U2 R2 D2 F2 E' L2
    Case J/Y:
    L: F' L U L F D2 F' L' U' L' F
    R:
    F:
    B:
    Case Y/J:
    L:
    R:
    F:
    B:
     
  2. Erzz

    Erzz Premium Member

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    Sep 9, 2010
    Canada
    YouTube:
    Erzz197
    The last thing I expected when I came to this site was to see "LCBM" in a thread title @_@
    I'd try this out, but I really can't figure out your organization of algs. You have things like "Sune on B", which will not happen, since you have already solved parity. "H on B" is the same as having T on both, but harder to recognize (imo). You could clean it up a lot by removing those.
    The algorithms I listed are the only possible cases (after solving parity). Without solving parity, there is a ridiculous increase in the number of cases, with most of them not able to be referenced as "known OLL on B".
    Another thing, you don't really need to permute the corners of both layers, since it is rather easy to solve the corners of the D layer (or even the whole D layer) during separation. You could just use Y and J perms to solve the top corners, then go into L8E. However, if you can solve the full D layer during separation, a simple PLL will solve the cube (and there is no difference between this and normal LCBM :p) I haven't been around for a while though, and am unsure if the moves saved by not solving the D corners during separation would justify the algorithms for EPPCBL. I would need to test some more.
     
  3. StachuK1992

    StachuK1992 statue

    3,806
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    Jul 24, 2008
    West Chester, PA
    WCA:
    2008KORI02
    YouTube:
    StachuK1992
    Example solve with more optimized algs, and better L8E;

    R2 D2 F2 R2 D L2 F2 D R2 F2 D L' D L F' R' F2 R' D' R2 F2
    EO: D R F' x2 (3/3)
    Belt: U' D2 R
    D' U' L
    (6/9)
    CO parity; skip
    CO: L' U' D' L' R2 D R2 U L (9/18)
    Separate: L2 U2 L2 (3/21)
    CP: D R2 D R2 U2 B2 U B2 U (9/27)
    Finish L+R: D' L2 D' S2 D L2 D S2 (8/35)
    M: U2 M' U2 M (4/39)
    Not sure how many the L+R cases would be, I'll compute this today, likely.​
     
  4. Pyjam

    Pyjam Premium Member

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    Oct 8, 2010
    Paris, France

    No mistake ?​
     
  5. StachuK1992

    StachuK1992 statue

    3,806
    10
    Jul 24, 2008
    West Chester, PA
    WCA:
    2008KORI02
    YouTube:
    StachuK1992
    I can't see what I did wrong. :/
    Here's another, hopefully I don't mess this one up.
    U2 R2 F2 L' B2 L D2 L B2 L2 R' D' R2 U B2 L R2 D2 B' D
    EO: D' B' (2/2)
    Belt: U' D L
    D' R D R' [finish right] (7/9)
    CO Parity: U (R2 (R U R' U R U2 R') R2) simplifies to U R' U R' U R U2 R (8/17)
    CO: U2 B2 U B L2 D2 L2 D2 B (9/28)
    Separate: x2 U' D R2 U R2 (5/35)
    CP: D' U2 [this was a /really/ easy force during separation] (2/37)
    EP1: M' U2 M U2 [I've decided to just reduce to Roux after 4a here.] (4/41)
    Roux 4b: x2 y M2 U M' U2 M' (5/46)
    Roux 4c: U' M2 U2 M2 (4/50)​
     
    Last edited: Mar 7, 2012
  6. Pyjam

    Pyjam Premium Member

    568
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    Oct 8, 2010
    Paris, France
    I expected R U R' (right). U' D2 R does nothing good on my cube.

    It's D' B', I think.
    Thanks for this second sample.
     
  7. miotatsu

    miotatsu Member

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    Oct 21, 2010
    Minnesota
    YouTube:
    miotatsu
    Sorry if my organization of algs is confusing, now that you mention it I see that it is pretty messy heh. Basically for the corner orientation step I use your system, pretty much all same algs although for mirror cases I prefer mirroring a single alg. Personally what I currently do is use the 25 alg set I have listed, half of the time you do a x2 for setup. In regards to the corner permutation I use EPPCBL because it makes the solving style more algorithm driven without requiring much to memorize. In terms of efficiency though I would not be too surprised if intuitively placing the bottom corners first is better.
    thank you for the examples, very nicely done! In this example I would have done either D2 L2 or U2 R2 and then fixed the belt during separation for the parity step, but it seems I get a bit longer of a solution that way
     
    Last edited: Mar 11, 2012

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