Another Alternative Ending to Fridrich?

[Bob]

I'm not sure if this has been suggested before. If it has, I'd be interested to read more about it. Otherwise, this is what I was thinking.

So recently I learned WV. It would be relatively easy to be able to mirror these cases. There is also what is known as Summer Variation (though not invented by any Mr. Summer that I am aware of). Almost all F2L cases end in one of these 4 cases (counting the mirrors). Now instead of RLS (216 cases) for only 1 of the 4 pair-types, one could apply one of the regular Winter/Summer Variation cases (again, I'll include mirrors here) disregarding edge orientation. There are only 27*4 = 108 cases for this stage. This would orient all corners of the last layer while inserting the pair.

Next, you will either have an OLL skip (1/8 chance--edges would have to be already oriented) and go straight to PLL, or one of the three OLLs in which the edges are flipped (H, X, or the one with just two adjacent edges to flip).

Though it is nice to only have 3 possible OLLs to deal with, let's take it one step further.

For most PLL cases, there are eight cases = 16*7 = 112 LL algs.
For Z, E, there are only five cases (symmetry) = 2*5 = 10 LL algs.
For H, N, N, there are only three cases (symmetry) = 3*3 = 9 LL algs.
Total: 131 LL algs (not including PLL which I assume is already known)
If I've made a mistake in calculating cases, please let me know.

LL recognition would be a bit difficult, but still not too bad probably. The toughest cases would definitely be the adjacent edge flips. There are only 21 X cases and not too many more "H" cases. Most of the cases would be of the adjacent flip type.

Anyway, here's what a solve looks like:
* Cross + 3 F2L pairs
* Insert pair and orient LL corners (108 cases)
* Orient edges and permute LL (131 cases + 21 PLL cases)

Am I missing something? Has this been suggested already? It's just something that came to mind the other day.

 

[Julian]

Funnily enough, the LL part of this strategy was mentioned here just recently.

 

[CubeRoots]

I think that even though it might give you an 'OLL skip' it's not really a skip since you had to put more effort in inserting the pair, but what you said about orient edges and permute LL that sounds pretty interesting. 131 cases is great. PLL cases just incase of OLL skip?

it sounds like COLL for edges. Kind of.

Anyway I was just wondering, i learned WV recently too for ZZ. Want to learn summer now, could you point me to some good algs?

cheers

 

[Bob]

I think that even though it might give you an 'OLL skip' it's not really a skip since you had to put more effort in inserting the pair, but what you said about orient edges and permute LL that sounds pretty interesting. 131 cases is great. PLL cases just incase of OLL skip?

it sounds like COLL for edges. Kind of.

Anyway I was just wondering, i learned WV recently too for ZZ. Want to learn summer now, could you point me to some good algs?

cheers

I haven't looked much into SV algs yet.

 

[Bob]

I haven't looked much into SV algs yet.

Actually, I just came by this.

http://www.speedsolving.com/wiki/index.php/Coall

It seems to be the same idea, though it says it's only 63 unique cases where I have 131. I think that's assuming only 21 cases each for each orientation, but it doesn't quite work that way.

 

[cubeflip]

Isn't Anti-ZBLL when all the corners are oriented and you solve the last layer in one step? Could this be considered 2-look Anti-ZBLL? If instead of doing EOLL and PLL in one alg, you do them separately. I know that's what you're saying I'm just putting it into perspective.

 

[rowehessler]

heres another method i thought up recently
cross + first 3 pairs
set up the last f2l pair to a SV or WV (whichever one is quicker for the case to set up to)
WV/SV
PLL

i think the setups would be the same number of algs as ZBF2l, so how many is that? plus 54 for SV and WV. This method seems totally dumb though I just thought id share and see what you guys think.

 

[Joël]

Erik suggested this this method a few years ago.. Maybe 2008/9? He worked out all the algorithms, and also memorised a whole bunch of them. He never learned all of them, though.

 

[Erik]

I made this in 2007 (and used the last pair + corner OLL already for 2x2 at Czech 2007, later that idea was 'stolen' and renamed SS method which still annoys me):
http://erikku.er.funpic.org/rubik/EALL.html
http://erikku.er.funpic.org/rubik/LP.html
http://erikku.er.funpic.org/rubik/LP2.html
(lol my old website)

Also I have a table of all cases for the last layer somewhere on my comp at home ;-)

Reason I didn't learn it was the number of 'last pair plus corner OLL' algorithms, plus general laziness. Also if I recall correctly from back then I came to the conclusion that the last pair algs were rather long in comparison with ZBF2L and because the EALL (which I called the last step back then) had some really bad cases with 17 moves optimal and stuff.

Reason I didn't share it: I wanted to be the first to learn it so I didn't publish it

 

[Ickenicke]

How hard would it be to learn to force so you never would get the adjacent flip?

Would you need to learn many more algs for LS?

LL would get much easier if you could do that.

 

[Bob]

I made this in 2007 (and used the last pair + corner OLL already for 2x2 at Czech 2007, later that idea was 'stolen' and renamed SS method which still annoys me):
http://erikku.er.funpic.org/rubik/EALL.html
http://erikku.er.funpic.org/rubik/LP.html
http://erikku.er.funpic.org/rubik/LP2.html
(lol my old website)

Also I have a table of all cases for the last layer somewhere on my comp at home ;-)

Reason I didn't learn it was the number of 'last pair plus corner OLL' algorithms, plus general laziness. Also if I recall correctly from back then I came to the conclusion that the last pair algs were rather long in comparison with ZBF2L and because the EALL (which I called the last step back then) had some really bad cases with 17 moves optimal and stuff.

Reason I didn't share it: I wanted to be the first to learn it so I didn't publish it

True, some of the last pair algs will be longer compared to ZBF2L...though since they can all be solved 2-gen, even the longer algs should still be pretty fast. I'm not sure how much it helps, but it should help a little bit that we can ignore EO during the last pair.