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.

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