On going through the old mail, I was a little surprised that
nobody uses the same algorithm that I do to solve the cube. But
since mine isn't terribly efficient, that's not much of a wonder.
Anyway, here it is.
1. Do bottom edges. Honest to god. I put all the bottom edges on
top by random dithering, then for each one, turn it so its
attached side facie abuts the color-matching face cubie, then
rotate that face 180o. That gets the bottom edges right, but
random hacking is almost as easy...
2. Do middle edges. (Getting colors right) I only use two moves
here. FR'F'R and R'FRF'. I pick a cubie that's on a top edge but
belongs on a middle edge - put its side facie adjacent to the
matching color face cubie (deja vu) and use FR'F'R if it has to
rotate right-and-down, or R'FRF' if it has to rotate
3. Get top edges in correct places. Essentially as in Singmaster,
but I use only one of two moves. Align top edges so either: all
are OK (skip rest of this step) or one is OK and 3 are wrong. (if
that's impossible, use one of this step's moves at random and
restart step - guaranteed to work.) Now either FURU'R' or FRUR'U'
can be used to get everything OK.
4. Flip top edges as required. I use two different moves for this
according to whether adjacent or opposite edges need to be
flipped. Opposite: let Q = "turn body-slicing slice 1 qtw
clockwise as seen from right". Then 4(QU) 4(UQ) flips FU and BU.
Adjacent: FR'F'R.RU'R'U.UF'U'F flips RF and UF - you must reorient
the cube to do this on two U edges. (I like this move because of
its symmetry and - somehow - completeness. It also rotates the
corner cubies adjacent to the edge cubies that it flips.)
5. Get the corners right. Here I have some fun, but the basic
moves are: 3(FR'F'R) = (LFU,RBU) (RFU,FRD); 3(FRF'R') which also
does a double interchange - tho' it's asymmetrical and I don't use
it much; and B'FR'F'RB which stirs 3 of the top 4 CW or CCW - I
never remember because I just use it twice for the "wrong"
6. Tumble any corners that need it. Usually not many because of
the nice color flipping properties of 3(FR'F'R) -try it. My
tumbling move is a monotwist 2(FR'F'R).L.2(R'FRF').L' -- or
replace the L and L' with LL if necessary - sometimes it's nastier
and you have to do it twice.
I've never counted worst-case moves. The algorithm is based almost
entirely on Singmaster's Y commutator, and once you get that into
your finger bones, you hardly ever make a mistake. On the other
hand, this algorithm is bad enough it hardly deserves a spoiler