• Welcome to the Speedsolving.com, home of the web's largest puzzle community!
    You are currently viewing our forum as a guest which gives you limited access to join discussions and access our other features.

    Registration is fast, simple and absolutely free so please, join our community of 40,000+ people from around the world today!

    If you are already a member, simply login to hide this message and begin participating in the community!

Guimond Revisited

cubacca1972

Member
Joined
Jan 3, 2009
Messages
147
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:

TMOY

Member
Joined
Jun 29, 2008
Messages
1,802
WCA
2008COUR01
Sorry but I think you should revisite your math too :p 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.
 

cubacca1972

Member
Joined
Jan 3, 2009
Messages
147
Sorry but I think you should revisite your math too :p 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:

cubacca1972

Member
Joined
Jan 3, 2009
Messages
147
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.
 
Top