# [Unofficial]15.827 Ao12 using ZZ-CT: The LL-Skip Method.

#### 4Chan

Scrambles and data in spoiler:
Statistics for Mon Apr 18 2016 22:53:13 GMT-0400 (Eastern Daylight Time)

Average of 12/12: 15.827
Standard deviation: 2.243
Number of DNFs: 0
Best time: 11.295
Worst time: 23.922

15.513, 15.865, 20.185, 15.849, 14.704, 14.469, 12.967, (23.922), 17.310, 18.677, 12.729, (11.295) = 15.827 ave12

1. 15.513 U2 R' F2 D2 F2 U2 L R2 B2 U B F R' B D' R' U' F2 L2 R
2. 15.865 F' L2 F2 U2 R2 U2 F R2 F' D' R B2 D2 L D' U' R' B2 L F
3. 20.185 L2 F2 D F2 U B2 D2 L2 D' R2 B2 L D' F2 D' L' R' B R' U2
4. 15.849 R2 U' B2 U' F2 D2 F2 D2 B' R' B2 L B D L U' L F' L
5. 14.704 B2 D2 L F2 R F2 R' F2 U2 L' U' L R F2 D B2 F2 D B U
6. 14.469 U2 B' R2 B D2 U2 F R2 D2 B2 U' L2 R2 D' B' L' D2 B2 L' D'
7. 12.967 L2 D L2 B U' L' U2 L2 F R B' D' B2 U2 D' F2 U L2 F2
8. (23.922) U' B2 R U2 R' U L2 F' B R' F2 R2 D2 F2 B' U2 F' R2 F2
9. 17.310 D' L2 B2 U2 B2 D' L2 U B F U F2 D' B' D2 F' L' U R
10. 18.677 R' B U D F2 B' D' F' B2 U' R L2 B2 R2 D2 B U2 L2 U2
11. 12.729 U2 F2 D R2 F2 L2 D F2 D' U2 B2 L U F' U2 B' L2 D2 U' F2
12. (11.295) L2 F2 R' B2 R2 D2 B2 R' B' R D' B' U' F' D U B' R2 F2

I want to preface this with a little something:
Back in 2009, I said something like, "in the future, people will be doing 1LLL methods", and we'd lol at 2 step LL, just like how we talk about wrist turning and suboptimal CF methods from the 1980s.

Now that it's 2016, we have bunches of people doing things like RLS, ZBLL, 1LLL, and so many more! It's totally coming true. o.o

We currently live in the future, so we need to go beyond the future OF the future. 1LLL isn't enough now, we need to LL skip everything. There's no limits, anything is possible.

So yeah, I took a break from studying and got this on video!
I had shaky hands, TONS of pauses and lockups, and my cube isn't great, but I think sub-15 should be doable soon. I've had almost linear progress going from 24->15 sec average with this method in the past 4000+ solves. I've only been doing this around a month, and this method has a lot of potential! I still need to get my algs down really good in my memory.

If you've been to a competition with me lately, I've probably asked your opinion about my new method LOL
This serves as my formal introduction post to the public! Here's a shortened version, which I'm copying from the wiki, which contains much more detail and information:

ZZ-CT is a ZZ variant with a unique 2 look LSLL, divided into TSLE and TTLL.

There are a total of 4 steps:
1. EOLine
2. F2L-1
3. TSLE: Insert last edge and orient corners. (Tran Style Last Edge - 108 cases) 100% 2-gen
4. TTLL: Force an LL skip. (Tran-Thompson Last Layer - 72 cases) 33% 2-gen

TSLE inserts the last edge whilst orienting all corners. All states can be solved by a linear combination of at most three R U R', R U' R', or R U2 R' triggers. You just remember which trigger comes after which for all cases. ez pz

TTLL forces an LL Skip with only 72 cases (42 if you want to mirror). Easy recognition too!

Statistically, ZZ-CT is bretty gud for sick singles if you like to gamble:
1. PLL occurs 20% of the time (1 out of 5 solves). Leading to a well known algorithm that most cubers already know.
2. True LL skip (fully solved cube after TSLE) occurs 1 out of 360 solves (0.27%), which is multiple orders of magnitude greater than 0.0064% in CFOP(1 out of 15552 solves), and 0.051% in ZZ(1 out of 1944 solves).
3. 2-Gen EVERYTHING occurs 29% of the time, which is twice as much as ZBLL (15% chance), and sixteen times greater than CFOP (1.8% chance).
4. Individual TTLL probabilities are similar to OLL. In comparison, the statistics for ZBLL cases are profoundly lower. Some ZBLLs only pop up every few days, meaning that TTLL comparably requires much less practice to execute TTLL than ZBLL.
5. TSLE is skipped 1 out of every 405 solves (0.24%), which adds another level of reduced single times.

If you're curious, Gyroninja and I have been collaborating and will post algorithms soon!

BIG THANKS TO THE FOLLOWING PEOPLE WHO MADE THIS POSSIBLE:
1. BLAKE THOMPSON FOR BEING AWESOME
2. elrog for inspiration.
3. Gyroninja for his contributions to TSLE generating and tabulating algs.
4. Phil Yu for morale boost by telling me my method was cool.
5. Brest for giving me algorithm guidance and doing some generating for me.
6. Sarah Strong and Stachu for making the CLS pictures that I used as reference.

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#### OLLiver

##### Member
I have been following the creation of this method. This looks like a good one imo.
You are a real inspiration, and I admire your dedication and motivation to cubing.

#### TDM

##### Member
Nice average, and it looks like there's still lots of room for improvement too. I can see this getting really fast - possibly one of the fastest ZZ variants.

(by the way, is the probability of 2-gen TTLL a third? I thought it would be 1/3 - 1/36, since some cases will be 2-gen in both orientations)

#### irontwig

##### Member
Nice average, and it looks like there's still lots of room for improvement too. I can see this getting really fast - possibly one of the fastest ZZ variants.

(by the way, is the probability of 2-gen TTLL a third? I thought it would be 1/3 - 1/36, since some cases will be 2-gen in both orientations)
It will always be 2-gen in both orientations.

#### TDM

##### Member
It will always be 2-gen in both orientations.
Oh, really? I though there would be 1/6 of the cases 2-gen in one orientation and 1/6 in the other.

#### 4Chan

Thanks a lot!!

I'll be honest, I have no idea what pieces are moving where, and why 1/3rd of my algs are 2-gen. I'm sure if I track the corners, I can understand the probabilities and stuff, but I'm too busy lately. I didn't bother because in some cases, it was a 5 cycle and it wasn't really relevant to getting faster times. (Which is ignorant of me, bah. I'll do it eventually out of curiosity!) x____x

I just generated my algs based on colours, and I just know it's 33% because the algs turned out that way.
I think the term is "a posteriori" ? LOL

EDIT:

TDM, referring to the relative speed of ZZ methods, I'm really honoured that you think so! Below is my opinion regarding ZZ speeds:

ZZ with ZBLL is about 2-3 moves less on average, and at the highest level of skill, with extreme practise and youth, I believe ZZ with ZBLL is faster on average.

However, for lazy people without the time, skill, and youth, I think this is the ideal step above OLL/PLL with ZZ! It's a fun method when the crazy singles happen during an average, due to all the probabilities for a skipped or easy step!

My favourite is whenever x (R' U R U')*3 comes up, because it's such a fast way to end a solve!

I recommend this to moderately lazy ZZ cubists, simply because the singles that can occur are really fun.
But for the truly competitive, I think ZZ-A is better.

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#### wir3sandfir3s

##### Member
This will be my new main method soon, hands down.
Until a better method comes out, which I don't think will happen for quite some time.
Only one thing: allllggggggssss...
Really hard to get past if you can't focus for your life, any suggestions??

#### AlphaSheep

##### Member
I've just been trying TSLE and it seems possible to do intuitively in slow solves and flows quite nicely. Can't wait for the TTLL algs so I can try the full method.

I'm not convinced by the probability of 2gen solves. My understanding is that the rest of the solve is 2-gen only if CP is solved after the first 2x2x3. That's got a 1 in 6 chance. Since this method only varies from standard ZZ after the 2x2x3, I don't see how the probability could be different.

#### TDM

##### Member
Thanks a lot!!

I'll be honest, I have no idea what pieces are moving where, and why 1/3rd of my algs are 2-gen. I'm sure if I track the corners, I can understand the probabilities and stuff, but I'm too busy lately. I didn't bother because in some cases, it was a 5 cycle and it wasn't really relevant to getting faster times. (Which is ignorant of me, bah. I'll do it eventually out of curiosity!) x____x

I just generated my algs based on colours, and I just know it's 33% because the algs turned out that way.
I think the term is "a posteriori" ? LOL

EDIT:

TDM, referring to the relative speed of ZZ methods, I'm really honoured that you think so! Below is my opinion regarding ZZ speeds:

ZZ with ZBLL is about 2-3 moves less on average, and at the highest level of skill, with extreme practise and youth, I believe ZZ with ZBLL is faster on average.

However, for lazy people without the time, skill, and youth, I think this is the ideal step above OLL/PLL with ZZ! It's a fun method when the crazy singles happen during an average, due to all the probabilities for a skipped or easy step!

My favourite is whenever x (R' U R U')*3 comes up, because it's such a fast way to end a solve!

I recommend this to moderately lazy ZZ cubists, simply because the singles that can occur are really fun.
But for the truly competitive, I think ZZ-A is better.
But how likely are the 2-gen cases to come up? I think it will be slightly different to 33%, even if that's the proportion of algs which are 2-gen. However I really don't know, so maybe you're right.

Yep, I agree, it probably isn't as fast as ZZ-a. But it might be better than OCLL-PLL and COLL-EPLL - though I've not seen the algs yet.

I'm not convinced by the probability of 2gen solves. My understanding is that the rest of the solve is 2-gen only if CP is solved after the first 2x2x3. That's got a 1 in 6 chance. Since this method only varies from standard ZZ after the 2x2x3, I don't see how the probability could be different.
You can do a y' before TTLL and some cases will still be solvable with <R, U>, and since you've done a rotation it's not just 1/6.

#### AlphaSheep

##### Member
You can do a y' before TTLL and some cases will still be solvable with <R, U>, and since you've done a rotation it's not just 1/6.
So obvious in hindsight. I didn't think to rotate in a ZZ solve... Haha

#### 4Chan

Ahhhh, TDM, I know what you mean about probability vs. alg percentages. Particularly in PLL and ZBLL.

Qualitatively, I have no idea.
I hope someone good with probabilities can clarify!

I'm also happy that it's being well received so far, I put a lot of work into it!

#### gyroninja

##### Member
Nice work man. You'll be sub 15 with this method soon, can you taste it?

#### 4Chan

Nice work man. You'll be sub 15 with this method soon, can you taste it?
THANKS I HOPE SO

I can't wait to start practicing next week, and use it at a comp this weekend.

#### Jason Green

##### Member
I don't understand most of that, but sounds cool. Good job!

#### AlphaSheep

##### Member
Ahhhh, TDM, I know what you mean about probability vs. alg percentages. Particularly in PLL and ZBLL.

Qualitatively, I have no idea.
I hope someone good with probabilities can clarify!
I'm not going to pretend I'm good with probabilities, but I'm a decent programmer and this is easy to brute force. I threw together an embarrassingly sloppy MATLAB script to calculate individual case probabilities. (script is here)

Exactly 30% are 2-gen in some orientation... In hindsight, I think it's because the only overlap between the 2-gen and 2-gen after a y' are the PLLs, and these make up 1/5 of the solved cases.. 1/6 + 1/6 - 1/(6*5) = 30%.

Spoiler contains individual case probabilities as percentages. In terms of fractions, every case has a probability of either 1/90, 1/180 or 1/360.

I don't know how you're representing the cases but I just numbered the corners 1-5 and the edges 1-4 and identified cases by which numbered corner or edge was in which location. Other than the PLLs, the cases are rotated so the D layer corner is in UBL. You can work out which case is which.

Code:
    UBL_1    UBR_2    UFR_3    UFL_4    DFR_5    UB_1    UR_2    UF_3    UL_4     Prob      Solved    PLL    RU2gen    yRU2gen
_____    _____    _____    _____    _____    ____    ____    ____    ____    _______    ______    ___    ______    _______

5        4        3        2        1        4       3       2       1        1.1111    0         0      0         0
5        4        3        2        1        4       2       1       3        1.1111    0         0      0         0
5        4        3        2        1        4       1       3       2        1.1111    0         0      0         0
5        4        3        2        1        3       4       1       2        1.1111    0         0      0         0
5        4        3        2        1        3       2       4       1        1.1111    0         0      0         0
5        4        3        2        1        3       1       2       4        1.1111    0         0      0         0
5        4        3        2        1        2       4       3       1        1.1111    0         0      0         0
5        4        3        2        1        2       3       1       4        1.1111    0         0      0         0
5        4        3        2        1        2       1       4       3        1.1111    0         0      0         0
5        4        3        2        1        1       4       2       3        1.1111    0         0      0         0
5        4        3        2        1        1       3       4       2        1.1111    0         0      0         0
5        4        3        2        1        1       2       3       4        1.1111    0         0      0         0
5        4        3        1        2        4       3       1       2        1.1111    0         0      0         1
5        4        3        1        2        4       2       3       1        1.1111    0         0      0         1
5        4        3        1        2        4       1       2       3        1.1111    0         0      0         1
5        4        3        1        2        3       4       2       1        1.1111    0         0      0         1
5        4        3        1        2        3       2       1       4        1.1111    0         0      0         1
5        4        3        1        2        3       1       4       2        1.1111    0         0      0         1
5        4        3        1        2        2       4       1       3        1.1111    0         0      0         1
5        4        3        1        2        2       3       4       1        1.1111    0         0      0         1
5        4        3        1        2        2       1       3       4        1.1111    0         0      0         1
5        4        3        1        2        1       4       3       2        1.1111    0         0      0         1
5        4        3        1        2        1       3       2       4        1.1111    0         0      0         1
5        4        3        1        2        1       2       4       3        1.1111    0         0      0         1
5        4        2        3        1        4       3       1       2        1.1111    0         0      0         0
5        4        2        3        1        4       2       3       1        1.1111    0         0      0         0
5        4        2        3        1        4       1       2       3        1.1111    0         0      0         0
5        4        2        3        1        3       4       2       1        1.1111    0         0      0         0
5        4        2        3        1        3       2       1       4        1.1111    0         0      0         0
5        4        2        3        1        3       1       4       2        1.1111    0         0      0         0
5        4        2        3        1        2       4       1       3        1.1111    0         0      0         0
5        4        2        3        1        2       3       4       1        1.1111    0         0      0         0
5        4        2        3        1        2       1       3       4        1.1111    0         0      0         0
5        4        2        3        1        1       4       3       2        1.1111    0         0      0         0
5        4        2        3        1        1       3       2       4        1.1111    0         0      0         0
5        4        2        3        1        1       2       4       3        1.1111    0         0      0         0
5        4        2        1        3        4       3       2       1        1.1111    0         0      1         0
5        4        2        1        3        4       2       1       3        1.1111    0         0      1         0
5        4        2        1        3        4       1       3       2        1.1111    0         0      1         0
5        4        2        1        3        3       4       1       2        1.1111    0         0      1         0
5        4        2        1        3        3       2       4       1        1.1111    0         0      1         0
5        4        2        1        3        3       1       2       4        1.1111    0         0      1         0
5        4        2        1        3        2       4       3       1        1.1111    0         0      1         0
5        4        2        1        3        2       3       1       4        1.1111    0         0      1         0
5        4        2        1        3        2       1       4       3        1.1111    0         0      1         0
5        4        2        1        3        1       4       2       3        1.1111    0         0      1         0
5        4        2        1        3        1       3       4       2        1.1111    0         0      1         0
5        4        2        1        3        1       2       3       4        1.1111    0         0      1         0
5        4        1        3        2        4       3       2       1        1.1111    0         0      0         0
5        4        1        3        2        4       2       1       3        1.1111    0         0      0         0
5        4        1        3        2        4       1       3       2        1.1111    0         0      0         0
5        4        1        3        2        3       4       1       2        1.1111    0         0      0         0
5        4        1        3        2        3       2       4       1        1.1111    0         0      0         0
5        4        1        3        2        3       1       2       4        1.1111    0         0      0         0
5        4        1        3        2        2       4       3       1        1.1111    0         0      0         0
5        4        1        3        2        2       3       1       4        1.1111    0         0      0         0
5        4        1        3        2        2       1       4       3        1.1111    0         0      0         0
5        4        1        3        2        1       4       2       3        1.1111    0         0      0         0
5        4        1        3        2        1       3       4       2        1.1111    0         0      0         0
5        4        1        3        2        1       2       3       4        1.1111    0         0      0         0
5        4        1        2        3        4       3       1       2        1.1111    0         0      0         0
5        4        1        2        3        4       2       3       1        1.1111    0         0      0         0
5        4        1        2        3        4       1       2       3        1.1111    0         0      0         0
5        4        1        2        3        3       4       2       1        1.1111    0         0      0         0
5        4        1        2        3        3       2       1       4        1.1111    0         0      0         0
5        4        1        2        3        3       1       4       2        1.1111    0         0      0         0
5        4        1        2        3        2       4       1       3        1.1111    0         0      0         0
5        4        1        2        3        2       3       4       1        1.1111    0         0      0         0
5        4        1        2        3        2       1       3       4        1.1111    0         0      0         0
5        4        1        2        3        1       4       3       2        1.1111    0         0      0         0
5        4        1        2        3        1       3       2       4        1.1111    0         0      0         0
5        4        1        2        3        1       2       4       3        1.1111    0         0      0         0

4        3        2        1        5        4       3       2       1       0.27778    0         1      0         0
4        3        2        1        5        4       2       1       3        1.1111    0         1      0         0
4        3        2        1        5        4       1       3       2        1.1111    0         1      0         0
4        3        2        1        5        3       4       1       2       0.55556    0         1      0         0
4        3        2        1        5        2       1       4       3       0.27778    0         1      0         0
4        3        1        2        5        4       3       1       2        1.1111    0         1      0         0
4        3        1        2        5        4       2       3       1        1.1111    0         1      0         0
4        3        1        2        5        4       1       2       3        1.1111    0         1      0         0
4        3        1        2        5        3       4       2       1        1.1111    0         1      0         0
4        3        1        2        5        3       2       1       4        1.1111    0         1      0         0
4        3        1        2        5        3       1       4       2        1.1111    0         1      0         0
4        3        1        2        5        2       4       1       3        1.1111    0         1      0         0
4        3        1        2        5        2       3       4       1        1.1111    0         1      0         0
4        3        1        2        5        2       1       3       4        1.1111    0         1      0         0
4        3        1        2        5        1       4       3       2        1.1111    0         1      0         0
4        3        1        2        5        1       3       2       4        1.1111    0         1      0         0
4        3        1        2        5        1       2       4       3        1.1111    0         1      0         0
4        1        2        3        5        4       3       1       2        1.1111    0         1      1         1
4        1        2        3        5        4       2       3       1        1.1111    0         1      1         1
4        1        2        3        5        4       1       2       3       0.27778    1         1      1         1
4        1        2        3        5        3       2       1       4       0.55556    0         1      1         1
4        1        2        3        5        2       3       4       1       0.27778    0         1      1         1

#### wir3sandfir3s

##### Member
Anyone got algs yet? Or are they somewhere obvious and I'm dumb?

#### TDM

##### Member
I think it's because the only overlap between the 2-gen and 2-gen after a y' are the PLLs
This was the part I wasn't sure about; I thought there would be other cases but wasn't confident. Interesting to know, thanks for sharing!

#### 4Chan

Nice job, Alpha Sheep!
Computational brute force to solve problems which otherwise would have involved critical thinking is something I REALLY appreciate.

@Wiresandfires, I have the algs, but I currently want to redo like, 10 cases. I'm super busy with finals week at school right now though.
My algs will probably be posted in June, but now that people know the concept, there's nothing stopping people from generating and learning for themselves if they wanted to.

#### ottozing

##### Platinum Member
I've been following this method for a while now, and I have to say I really like it, even though it'd never work for me, a CFOP user with a decently sized bag of LS+OLL tricks

Speaking of the whole more 2 gen solves thing, one thing that's cool (which may have already been figured out) about the last step is that for 2 gen cases involving a y' before the alg, you can just offset the D layer. For example, instead of doing y' U R' U R U' R' U2 R U R' U' R, you can do D R' U R U' R' U2 R U R' U' R

I just think that's a super sick property to have in a step :3 It can also work to cut down on rotations if you do the second last step from any other slot