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COLS/"Summer Variation"/set of algs without a name

blah

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I've had this thought for a few hours already, I'm sure it's not a new idea because there's nothing special about it, but I haven't seen it anywhere, so I'll just post it here and leave it for you guys to criticize :)

We know there's VHF2L (hereafter known as VHLS). So why not have an LS method that orients all corners (hereafter known as COLS)? Or should it be OCLS? :confused: Anyone got a better name? :p

For the RU'R' case, we already have F2LL a.k.a. Winter Variation (someone mind telling me why it's called this?). For the RUR' case, I don't know of any set of algs that's already been generated, or is already in use, so I've generated my own algs, and I'm (temporarily) calling it the "Summer Variation" for fun, because I really can't think of a suitable name for such a small subset of algs (and because it's fun to call a set of algs Winter/Summer Variations :D).

Now, for a little comparison: VHLS requires 32 algs, which all need to be at least RUF 3-gen. COLS requires 108 algs :cool: And, like CLS, can also all be RU 2-gen (or RUL/RUF 3-gen for shorter solutions).

HOWEVER...

There's a (1/3)^3 = 1/27 chance of getting an OLL skip with VHLS, but this probability more than triples to (1/2)^3 = 1/8 with COLS. How would you like 1.5 OLL skips in an average of 12? :D You get to keep that 0.5 OLL skip as your second fastest time!

Besides, I personally don't really like all 3 OLL cases with 2 corners oriented (and all edges oriented too). Yeah, fine, they're short, but they just don't flow well for me. And the combined probability of getting any of these 3 cases is 12/27.

With COLS, however, I can only get 1 OLL alg I don't really like, the one with no edges oriented. Okay, so the probability of getting the rarest OLL case skyrockets from 1/216 to 1/8, but 1/8 is still much lower than 12/27. And I think I just might have that problem solved once I generate a few algs (read on to see what I mean).

We can always end VHLS/COLS with the normal OLL/PLL. But there are always alternatives. For VHLS, we can use COLL + EPLL as an alternative. For COLS, we have 3 different endings to choose from:
1. J perm/Y perm + ELL
2. 14 RUF 3-gen algs that clear the mess and leave you with EPLL (name?) + EPLL
3. 1-look LL (another name?)

With the first approach, you have a 2/3 chance of getting a J perm, 1/6 of getting a Y perm, and 1/6 of skipping straight to ELL.

With the second approach, you have to learn 14 more algs that are gonna be immensely useful for BLD, but that's not really the point here :p I've generated these algs too, all RUF 3-gen. I'll probably get an RrU list later too :rolleyes:

With the third approach, there are far fewer algs than ZBLL :D I don't know the exact number yet, but I'll update this post once I've calculated it.

So in conclusion... (winner/loser)

Number of algs to learn (including mirrors):
COLS 108 VHLS 32

Probability of getting OLL skip:
COLS 1/8 VHLS 1/27

Probability of getting OLL cases I (which means this isn't a very reliable stat) don't like:
COLS 1/8 VHLS 12/27

Number of algs to learn for alternate endings:
COLS 14 (the thing I mentioned) VHLS 42 (COLL)
COLS still wins if you use J perm/Y perm + ELL (24 ELL algs)

Fun fact:
Probability of skipping from COLS straight to ELL: 1/48
Probability of getting Sune or any one of your favorite OLL, any one: 1/54 or lower

With good edge control techniques throughout your F2L, COLS might just give you an OLL skip every single time.

Final conclusion, going by number of algs, COLS sucks :p Going by all the other step-skipping probabilities, it's much better than VHLS. Only downside I can think of right now is probably recognition...

Wait, there's still a final final final conclusion :p I personally won't use COLS. Same reason why many people don't use VHLS: Move count, and an additional step to the pure Fridrich method. Just isn't worth it. Still, if there are supporters of VHLS, there should be some for COLS :)

And in case you're interested, I've generated all the algs needed. PM me if you want the list.

I bet this thread's only gonna get 2 replies or so... :eek:
 
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Lotsofsloths

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Generate the algorithms and post them here.
I have tried Winter's Variation, and it was OK, I liked it, but never really had the commitment to learn them, but I like this idea a lot better! I haven't memorized an algorithm since more than 6 monthes ago lol. I'll take this up, hit me up with the algs.
 

MistArts

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Interesting... I'll learn this after EG. I'm very interested in the 1look-LL too.
 

yurivish

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This would go well with ZZ. But then again, so would ZZLL. :p

Or what about doing VH3S and then COLS? Lots and lots of algs, but with enough practice you can do them both without pausing for a "look" and work your way to a slow-turning F2L/OLL and then a 1-look PLL last layer.
 

blah

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I just thought of something:
ZZ + COLS = guaranteed OLL skip

Boy was I stupid not to have thought of this before.

Now it's a battle between ZZ + MGLS and ZZ + COLS. I personally think MGLS wins though :p With MGLS, you get a 3-move ELS 4/5 of the time, and an ELS skip 1/5 of the time.
 

blah

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I have tried Winter's Variation
Winter is a guy's name?! :p Then Summer's Variation isn't very appropriate is it? :eek:

Also, I wanted to post something about 1-look LL. I suppose this 1-look LL that follows COLS should be easier to recognize than ZBLL, but still difficult to recognize all the same :(

Edit:
By the way, in case it wasn't clear: COLS + the 1-look LL without a name, is NOT equivalent to ZBF2L + ZBLL!!! It's only equivalent to VHF2L + ZBLL. So it might not be worth learning so many algs after all :p
 
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blah

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Triple post, just thought of something else.

It probably won't be too hard to come up with a recognition technique that would allow us to instantly choose between J or A perms, and Y perm or AUF-Y perm, to force only U perms (or 3-cycle ELL cases), or even a PLL skip!
 

fanwuq

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I just thought of something:
ZZ + COLS = guaranteed OLL skip

Boy was I stupid not to have thought of this before.

Now it's a battle between ZZ + MGLS and ZZ + COLS. I personally think MGLS wins though :p With MGLS, you get a 3-move ELS 4/5 of the time, and an ELS skip 1/5 of the time.
3 moves 3/5 of the time. 4 moves 1/5 of the time. 0 moves 1/5 of the time. ;)

I like VH3S. I like MGLS a bit better, I think that's less algs and easier recognition.

Because I'm so lazy and I might want to get into 2x2 eventually, I'll settle with VHF2L and COLL for now.
 

blah

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3 moves 3/5 of the time. 4 moves 1/5 of the time. 0 moves 1/5 of the time. ;)
Ah, how could I forget!

I'm pretty sure VH3S isn't necessary at all. In fact, right now, I think it's silly, but I may be wrong... VH3S is adding WAY too many moves for F2L, besides, how are you supposed to VH (that's right! VH just became a verb!) if there are no or few U edges on U?

I think sledgehammering alone should be enough to get all LL edges oriented by the last slot, unless you're so unlucky that every one of your first 3 slots end with RUR'?!
 
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blah

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Okay, note to all who requested the algs: They're very raw.

I haven't optimized any of them yet. And I haven't mirrored them yet. You'll have to wait a few more days, I really didn't expect so many requests, sorry!

In the meantime, check out the Winter Variation here: http://pagesperso-orange.fr/absolutemind/f2ll-angl.htm
Start learning these first, they're easier to recognize than the RUR' cases :)
 

blah

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Is the number of algs for COLS the winter variation + the summer variation?
Yup. Actually, like CLS, there really aren't that many algs to learn. Just like CLS consists of a few moves before an F2L pair insertion, COLS is just RUR'/RU'R' followed by the entire Sune family, with move cancellations in between.

Edit: "The entire Sune family" = 7 cross OLL cases, in my lingo :p
 

JohnnyA

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So it's really a way of predicting what cross OLL you are going to get, and cancelling out moves?

Sounds ideal for ZZ in my opinion.
 

Lofty

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Hmmm I definitely think that is an interesting idea. How many algs would the 1LLL be? I'm assuming its less then ZBLL right? However they can't be RUL like ZB/ZZLL can be.
You should post the alg list online somewhere as I'm sure some of us would at least be willing to look at the list even if we don't use it.
I think this will be very similar to MGLS only MGLS has the few moves added on the front for CLS that guarantee the OLL skip.
What is VH3S I haven't heard of this one?
Also how did you find these algs?
 

blah

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Hmmm I definitely think that is an interesting idea. How many algs would the 1LLL be? I'm assuming its less then ZBLL right? However they can't be RUL like ZB/ZZLL can be.
1/8 of the time, you get PLL, which can be RUL. Is this optimistic enough? :eek: Otherwise, no. Because the 1LLL would involve flipping edges, and you can't flip edges using only RUL, trivial.

You should post the alg list online somewhere as I'm sure some of us would at least be willing to look at the list even if we don't use it.
Good point. I'll post it once I've cleaned it up.

I think this will be very similar to MGLS only MGLS has the few moves added on the front for CLS that guarantee the OLL skip.
Not similar to MGLS, this has one added step, that's what makes it worse than normal Fridrich, just like VHLS + COLL + EPLL. People keep missing this point :(

Fridrich
Step 1: Cross + first 3 slots
Step 2: Last slot
Step 3: OLL
Step 4: PLL

MGLS
Step 1: Cross + first 3 slots
Step 2: ELS
Step 3: CLS
Step 4: PLL

COLS
Step 1: Cross + first 3 slots
Step 2: Setup last corner-edge pair
Step 3: COLS
Step 4: 14 algs thingy OR J/Y perms
Step 5: EPLL OR ELL

Unless you combine Steps 4 and 5 into a 1-look LL and learn loads of algs, it's gonna take more steps than Fridrich/MGLS, which means more time spent looking and not executing moves, which means slower times. Even if you learn all the 1-look LL algs, the number of steps would still only be equal to Fridrich/MGLS and not fewer.

I think I made this clear enough. Like VHLS, it's not that worth learning, unless you love the joy of getting skips. You'd get LOADS of skips with this method, one step or another :D

What is VH3S I haven't heard of this one?
VH first 3 slots. Someone just made that up, I think. I guess it simply means edge control for the first 3 slots so that you get all LL edges oriented when you reach the fourth.

Also how did you find these algs?
Cube Explorer and ACube. Abuse technology.
 

MistArts

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I think there are (less than?) 175 cases for 1LLL. I could be wrong.

There are 4 different case for edge orientation, the "L", the "line", the "cross", and no edges oriented.

For the cross, or all edges oriented, there's 21 PLL's. (The solved cases is omitted.)

For the line, or two edges oriented opposite from each other, there's 22 cases for the horizontal line and 22 for vertical. (The 2 edge flip cases cancel a case out and so does the "H-perms." The reason why I put less than 175.)

For the "L", or two edges oriented adjacently, there's 22 cases for all 4 "variations" of the "L" (Some cases are canceled here, for example, the "Z-perms")

For no edges oriented, or no edges oriented, there's 21 "PLL's" plus the four edges flip.

((1*22)-1)+(2*21)+(4*22)+(1*22)=175
 

blah

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I think there are (less than?) 175 cases for 1LLL. I could be wrong.

There are 4 different case for edge orientation, the "L", the "line", the "cross", and no edges oriented.

For the cross, or all edges oriented, there's 21 PLL's. (The solved cases is omitted.)

For the line, or two edges oriented opposite from each other, there's 22 cases for the horizontal line and 22 for vertical. (The 2 edge flip cases cancel a case out and so does the "H-perms." The reason why I put less than 175.)

For the "L", or two edges oriented adjacently, there's 22 cases for all 4 "variations" of the "L" (Some cases are canceled here, for example, the "Z-perms")

For no edges oriented, or no edges oriented, there's 21 "PLL's" plus the four edges flip.

((1*22)-1)+(2*21)+(4*22)+(1*22)=175
I got a different number, but that doesn't really matter at this stage. We know it's less than 200, or maybe just a bit more.

For all of you VH guys out there. Stop learning VH and come over here to learn this!

VHLS + ZBLL is equivalent to COLS + the 1LLL Without a Name (LLWN).

BUT, VHLS + ZBLL has 32 + 494 = 526 algs. COLS + LLWN, on the other hand, has "only" 108 + 200-ish = 308-ish algs. Together with the much more frequent skips, COLS + LLWN wins VHLS + ZBLL hands down and feet down.

(I don't know about move count though, but for some bad LLWN cases, I've gotten 18 move RUF algs, that doesn't sound too good.)

Another BUT, if you wanna compare COLS to full ZB, then ZBLS + ZBLL wins "ZBCOLS" + LLWN in terms of number of algs. "ZBCOLS" means the ZB version of COLS, i.e. orient all corners (instead of edges) while inserting the last F2L pair. Just to give you an idea, COLS has 108 algs for 4 F2L cases (the 3-move ones and their mirrors). If you were to learn full ZBCOLS for all 41 F2L cases, that's an estimated 1080-ish algs. You'd be better off learning 1LLL with 1211 algs.
 
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