Improvements for M2/R2

[Johannes91]

[X, Y] = X Y X' Y'

[U R2 U', M'] = U R2 U' M' U R2 U' M
[M', U R2 U'] = M' U R2 U' M U R2 U'

(This forum software is pretty good at messing up formatting.)

 

[AvGalen]

I still don't understand.

What does the bracket mean?
What does the comma mean?

 

[Stefan]

Arnaud, you're kidding, right? Or did someone crack your account? Or did you take Erik's pot? But just in case you're serious, yourself, and sober: Brackets and comma are the notational frame, and when Johannes provided the definition of the notation, X and Y weren't cube rotations but variables that can represent any algs. Aren't you good at fewest moves? Aren't commutators somewhat a requirement to be good at that?

 

[masterofthebass]

Hmm... I just realized that these algorithms are messed up. If your buffer is the FD piece, then you have to perform an x' z2 before doing the algorithm. That's the only way that I could get these to work.

 

[Lucas Garron]

Hmm... I just realized that these algorithms are messed up. If you're buffer is the FD piece, then you have to perform an x' z2 before doing the algorithm. That's the only way that I could get these to work.

Did I seriously make that mistake? I was being so careful...
I'll fix it, but if you know comms they should be easy enought to understand...

We need a 4x4x4 simulator that uses normal notation...
[Note to self: Implement that via PHP]

 

[AvGalen]

Arnaud, you're kidding, right? Or did someone crack your account? Or did you take Erik's pot? But just in case you're serious, yourself, and sober: Brackets and comma are the notational frame, and when Johannes provided the definition of the notation, X and Y weren't cube rotations but variables that can represent any algs. Aren't you good at fewest moves? Aren't commutators somewhat a requirement to be good at that?

OK, now I understand. It were just unclear examples because:
[X, Y] = X Y X' Y'

[U R2 U', M'] = U R2 U' M' U R2 U' M (not clear if the second U R2 U' is X or X')
[M', U R2 U'] = M' U R2 U' M U R2 U' (not clear if the second U R2 U' is Y or Y')

So let's make the example more clear:
[X, Y] = X Y X' Y'
[R U F, L D B] = (R U F) (L D B) (F' U' R') (B' D' L')

Just for the record: No pot was involved now or before. I don't know anything about the combination of Erik and Pot. I am good at Fewest Moves. It is completely unneccessary to know about commutators to be good at Fewest Moves. (but it doesn't hurt if you know how to use them either). I am good at Fewest Moves because I can find good beginnings and because I can avoid bad endings.

 

[philkt731]

Yeah I got the same thing as dan for Lucas' algos
so
D [U R2 U' , M'] D' M2'
M2' D [M' , U R2 U'] D'


should be:
B [F L2 F', M] B' M2
M2 B [M, F L2 F'] B'
or
B' [F' R2 F, M] B M2
M2 B' [M, F' R2 F] B

I don't know about these, I think I'll stick with my variation of Erik's

 

[Lucas Garron]

Yeah I got the same thing as dan for Lucas' algos
so
D [U R2 U' , M'] D' M2'
M2' D [M' , U R2 U'] D'


should be:
B [F L2 F', M] B' M2
M2 B [M, F L2 F'] B'
or
B' [F' R2 F, M] B M2
M2 B' [M, F' R2 F] B

They could be. But they shouldn't be. The only reason I added half turns was to avoid a setup on B or F (and E/d in the comm, and maybe because it felt clearer to shoot the bufffer or "anti-buffer" with a modified M2 that blends better with the method). Didn't anyone think to see what the comm was doing and switch the two halves?

Anyhow, I corrected the algs in my post a while ago...

 

[philkt731]

oh! I didn't see you fixed them! Thank you, those are nice, I think I'll probably use them now.

 

[mrCage]

Stefan posted this in another M2 thread.

I still have one more to learn (stupid UB).

Maybe you like this one better:
(U R' U' l U' R U) M2 (U' R' U l' U R U')

It only solves UB but it does work pretty well. I like the idea of being able to do a 3-cycle though.

Hmm, (B' U R' B U') M2 (U B' R U' B) does the same. Am i using illegal generators here ?? :-?

- Per

 

[philkt731]

To go along with Joel's idea, we can do the same for FU and BD (using DF as buffer). for FU set up the next edge at DR (or DL) and do y' M' U' M D M' U M D' and for BD setup the next at DR (or DL) and to y' R2 M' U M D M' U' M D' R2

 

[macky]

Interesting thread.

I don't like having to shoot to FU or RD to deal with bad targets. That actually requires thinking! Since I've been experimenting with a lettering scheme, I've found it natural in M2 to associate each letter, not each position, to an algorithm.

To make things easy, I'll use DF as the buffer in this post. I'll write (s) to represent the move in M2 that brings s, which can be any sticker in R/L layer, to UF, and (s)' for the inverse of (s). For example, (FR)=URU'. We can then handle the bad targets as follows:

(Next two stickers memorized: solution)
FU s: M2 (s) M (s)' M
s FU: M' (s) M' (s)' M2
BD s: M2 (s) M' (s)' M'
s BD M (s) M (s)' M2

For example, to do (DF BD FR), use the third line: M2 (FR) M' (FR)' M', or M2-URU'-M'-UR'U'-M'. This way, we don't have to think at all where to shoot. For example, BD=X and FR=G in my current lettering scheme, so that cycle is XG. I've already associated G with URU', so I just substitute that into (FR); I don't even think about where G actually is.

This combined with normal M2 methods allow us to solve two stickers, exactly one of which is in the M slice, very easily and actually pretty efficiently. I know, for example, that Stefan's way for FU is faster, but the difference is only an M2.

With these tricks, it looks like we're heading in the direction of systematic 3-cycling, i.e. picking one sticker as the buffer and learning the solution to each of the 22*20=440 possible 3-cycles of stickers starting with the buffer. I think using DF or FR as the buffer makes all these cases actually pretty easy to organize. Plus, that way, you can start incorporating some of these cases into M2.

There are 6*16*2=192 cases involving exactly one sticker in the M slice, which we already covered. In addition, there are 3P2*2*2=24 cases where both stickers are in the M slice. It's probably not too bad to just memorize these cases. Can anyone think of a way to deal with the remaining 16*14=224 cases that's efficient and easy to learn?

Of course, we could split this into special cases. For example, if there is exactly one sticker in U layer, do an appropriate number of U turns to reduce to either UB or FU. That might require "too much" thinking, though.

-macky

 

[Lucas Garron]

Hmm, I'm likng freestyle.
The greatest thing would be to use M2 and freestyle the M-slice pieces (easy), but unfortunately DF is a bad freestyle buffer...

Hmm, maybe I wanna actually try M' instead of M2, shooting to BU with Uf as a buffer? Since we're obviously heading toward getting used to it as 440 cases, we might as well go for slightly fewer moves...

Anyhow, I really gotta publish my freestyle comms with j'ey and Rowe...

And Macky: Don't memo the M-slice cases, it's easy to check whether two adjacent ones are exchangable (otherwise, do a double twist) and then Setup into a comm... The only exceptionsare M'U2MU2 type...

 

[macky]

Since we're obviously heading toward getting used to it as 440 cases, we might as well go for slightly fewer moves...

LOL Can't we strike some balance between efficiency and ease of memorization? Anyway, by the time we're done, we'll have blindfold cubing completely Fridrich-ized. Making blindfold cubing not very fun is so much fun.

And Macky: Don't memo the M-slice cases, it's easy to check whether two adjacent ones are exchangable (otherwise, do a double twist) and then Setup into a comm...

Yeah, I figured, but that would require me to convert from letters to positions and actually think a bit. I don't yet know how if that's a problem in practice yet. I guess you don't need to worry about this as much since you memorize visually.

but unfortunately DF is a bad freestyle buffer...

Could you give me an example of a good freestyle buffer?

Oh, I wasn't aware that you three were working together on this. I look forward to reading that.

 

[Lucas Garron]

Since we're obviously heading toward getting used to it as 440 cases, we might as well go for slightly fewer moves...

LOL Can't we strike some balance between efficiency and ease of memorization? Anyway, by the time we're done, we'll have blindfold cubing completely Fridrich-ized. Making blindfold cubing not very fun is so much fun.

Fine, I'll do MGBLD instead.
And corneres will still be hard.

And Macky: Don't memo the M-slice cases, it's easy to check whether two adjacent ones are exchangable (otherwise, do a double twist) and then Setup into a comm...

Yeah, I figured, but that would require me to convert from letters to positions and actually think a bit. I don't yet know how if that's a problem in practice yet. I guess you don't need to worry about this as much since you memorize visually.

I inted to adopt letter/word memo. But there must be a nice way to generally comm these.
(What if you hit an M slice pair with M2 off? Like: DB (DR UF) (BU LF). Execute separately? Convert?)

but unfortunately DF is a bad freestyle buffer...

Could you give me an example of a good freestyle buffer?

UF. I use it. Rowe uses it. (And Mátyás? He probably does ultra-free freestyle...)
Joey uses UR because it goes with old Pochmann, possibly allowing recourse to T-perms for bad cases. Erik uses UF[corrected from UR] forTuRBo (a "restricted freestyle 3-cycle" [vs. M2 as basically 2-cycle]).

Oh, I wasn't aware that you three were working together on this. I look forward to reading that.

We're not, really. But I've discussed with both that we should post some algs and comms. I will, at least, and Joey's making a table (also for corners).

Anyhow, the best would be to use both. But DF is the best buffer compromise, and I really don't like that... I'm going to experiment with M' and see how it turns out. I just want fast times

By the way, you're not also up applying for Caltech, are you?

 

[joey]

but unfortunately DF is a bad freestyle buffer...

Could you give me an example of a good freestyle buffer?

UF. I use it. Rowe uses it. (And Mátyás? He probably does ultra-free freestyle...)
Joey uses UR because it goes with old Pochmann, possibly allowing recourse to T-perms for bad cases. Erik uses UR forTuRBo (a "restricted freestyle 3-cycle" [vs. M2 as basically 2-cycle]).

I think Mátyás also uses UR like me, he probably saw me using it an decided to switch

TuRBo actually uses UF as a buffer aswell.

I have actually been thinking about using UR -> UF -> UL -> UB, all as buffers. It does reduce the number of cycles needed, but I will have to see what the thinking time is like, since I would need to be good at seting up pieces with all 4 buffers.

 

[Stefan]

I found another improvement for M2 and r2. Well, it reduces the number of moves, but it makes it less braindead. You be the judge.

Scramble:
(U R U' M2 U R' U')
(L U' L' U M2 U' L U L')

Usually you'd do the inverse of that to solve the two edges. But notice the four setup moves for the UL edge. It would be so much nicer to just set it up with a U turn, but argh, the setup moves must not change the M slice except for the UB edge. So this doesn't work:

U M2 U'
(U R U' M2 U R' U')

However, if you integrate the other edge, it's no problem:

U M2 (U R U' M2 U R' U') U'

So you can bring the first target to UB with one or two moves, "solve" it with an M2 move, then solve the second target before you undo the setup moves of the first. If the setup moves of the first target don't move the second target, the latter can even use the normal M2 algorithm, like in the above example.

This has many easy variations:

L* U M2 (otherTarget) U' L*
L* U (otherTarget) M2 U' L*
L* B' M2 (otherTarget) B L*
L* B' (otherTarget) M2 B L*
(and the same with R instead of L.

It can be particularly helpful for r2 I think, including the l-slice edges. For example, shoot to DBl and then to FRd like this:

B2 r2 (U R U' r2 U R' U') B2

Oh and while I'm at it, here's a new R2 alg for target FLD which I like much better than my old one (will try to improve others and then update my website):
(U' L' U x' U L U') R2 (U L' U' x U' L U)

 

[joey]

Stefan: Joel VN has actually talked about this somewhere on the forum before. I can't remember where it is right now, maybe I'll have a little digg. I have also been messing around with this doing this during my M2 'solves'. (I say 'solves' since I only mess around with the method, and don't use it for BLD)

edit: hehe, it was on the first page of this thread! http://www.speedsolving.com/showpost.php?p=18578&postcount=8

 

[Stefan]

Gah, me and my bad memory. You know, when both you and Chris recently mentioned how the three of us talked about 2gen blindsolving in Budapest, I was like "We did?!?". Happens more and more often. I'll reread this thread.

 

[joey]

You're getting old Stefan, no wonder you don't do BLD anymore!

edit: Stefan, do you remember saying you would buy me a v-cube for my birthday?