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Thread: Guimond Revisited

  1. #1
    Member cubacca1972's Avatar
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    Default Guimond Revisited

    After checking out the Rice Method, I decided to review my old notes on Guimond's Corners First method (Orient all corners, Separate U and D corners, Permute all corners).

    I first thing I noticed was how bad my algorithms were. Very poor as far as finger tricks go, and as it turns out, very poor for move count.

    Just for fun, I revised the algorithms, and checked the frequencies of each case.



    In Step 1, 3 of the D layer corners are oriented, but may belong to either the U or D layer. On the D face, all of the D facelets, with the exception of the DRB corner have either a U or D color. The DRB cubie has a U or D color on its R facelet (There are 8 mirror algorithms if the odd cubie on the D layer is twisted counter-clockwise)

    Here are the Step 1 algorithms:

    R' U R'
    F R F'
    F R2 F'
    R2 U' R
    R' F R' F
    R2 F2 U' F'
    R' F2 U R'
    R U' R' F R2 F

    You will be able to orient all corners in 3 moves in 14/27 cases (28/54 including the reflections).
    You will be able to orient all corners in 4 moves in 12/27 cases.
    You will need 6 moves in 1/27 cases.

    In 1/35 times that you complete the first step, the U and D layers will be separated already (if it matters which color winds up on top, you will have to do x2 half the time). If you are really good at tracking, you could alter the probabilities by doing the reverse of each last move in the above algorithms (doing R instead of R' at the end of the last algorithm for example). Otherwise, separating the U and D corners is fairly trivial.

    You will have a 1/36 chance of skipping the last step, where you permute both U and D layers.
    Last edited by cubacca1972; 04-05-2012 at 05:53 PM. Reason: correction of math error

  2. #2
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    Sorry but I think you should revisite your math too There are 27 different orientation cases, not 21. Out of them, 10 can be solved in 3 moves, 16 in 4 moves and 1 in 6 moves.

    For separation, the skip probability is 1/35 not 1/40 (\frac{4!^2*2}{8!}=\frac{1152}{40320}=\frac 1{35}).

    At least the probability of 1/36 for PBL skip is correct.

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    The best thing about those algs you listed is that they are essentially the backbone to most orientation -> PBL methods
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    Member cubacca1972's Avatar
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    Quote Originally Posted by TMOY View Post
    Sorry but I think you should revisite your math too There are 27 different orientation cases, not 21. Out of them, 10 can be solved in 3 moves, 16 in 4 moves and 1 in 6 moves.

    For separation, the skip probability is 1/35 not 1/40 (\frac{4!^2*2}{8!}=\frac{1152}{40320}=\frac 1{35}).

    At least the probability of 1/36 for PBL skip is correct.

    I just checked my work on the separation step, and found my error. 2/70 is correct, as you point out, not the 2/40 that i miscalculated. I wasn't too sure about the correct math on this one, so worked it out logically, and would have published correctly had I added correctly (facepalm).

    I Just checked my work on the the first step frequencies, and detected my error. Will re-calculate.
    Last edited by cubacca1972; 04-04-2012 at 10:51 PM.

  5. #5
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    After recalculating, the first step can be done in 3 moves in 14/27 cases, 4 moves in 12/27 cases, and 6 moves in 1/27 cases.

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