# OLL/PLL vs. COLL/EPLL vs CLLEF vs CMLL



## Nukoca (May 5, 2009)

Last layer statistics:

Full last layer skip: 1/1944

OLL/PLL:
Petrus OLL skip: 1/27
PLL skip: 1/72
Petrus OLL skip and/or PLL: 49/972 ≈ 5.0%.

COLL/EPLL:
COLL skip: 1/162
EPLL skip: 1/12
COLL and/or EPLL skip: 173/1944 ≈ 8.9%.


*Just a quick note: the stats below are false. I am corrected in the comments. The stats above are accurate, edited in so as not to confuse anyone who happens to come upon this topic in the future.*

I'm trying to figure out which last layer system I want to use along with my Petrus. I'm leaning towards CMLL, because it looks like the algs are shorter than COLL. I really don't want to learn OLL/PLL for a couple reasons: (*Edit*: Oh well, CMLL is for Roux. I thought it messed up the perm of the LL edges, but according to the post below me, it also messes up the M slice and UL and UR edges.)

1. OLL=57 algs, thus a 1/57 chance of OLL skip, and PLL=21 algs, which is 1/21 chance of PLL skip.

2. COLL/EPLL or CMLL/EPLL: COLL has 40 algs, so 1/40 chance of COLL skip. EPLL is only 4 algs, so 1/4 chance of EPLL skip! 

(I was about to calculate the chances of a full LL skip for both ways, and then I'm like, wait...) 




LarsN said:


> I like to use COLL for my fridrich solves and I know that there are a few people out there who does too.
> An argument not to use COLL is that COLL algorithms take longer to execute than the relevant OLL's. That's when an idea came to me...
> 
> What are the OLL's that most people hate. For me it's OLL's with no edges oriented correctly. Then I started to find different algorithms for the same OLL case with no edges oriented correctly.
> ...



Taken from here: http://www.speedsolving.com/forum/showthread.php?t=7809

CLLF isn't for me (Petrus ), but would you consider doing it if you were just starting out on Fridrich?


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## soccerking813 (May 5, 2009)

You can't use CMLL, because it also messes up the M slice and UL and UR edges.


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## Nukoca (May 5, 2009)

soccerking813 said:


> You can't use CMLL, because it also messes up the M slice and UL and UR edges.



Oh, it does? It must be for Roux, right? My mistake.


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## James (May 5, 2009)

Nukoca said:


> thus a 1/57 chance of OLL skip, which is 1/21 chance of PLL skip.
> COLL has 40 algs, so 1/40 chance of COLL skip. EPLL is only *4* algs, so 1/4 chance of EPLL skip!



I don't think it works that way because some cases occur more than others. I believe a PLL skip is *1/72*. If you do a COLL, I think there is a *1/12* chance of an EPLL skip. COLL skip is much more unlikely than 1/40.


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## Nukoca (May 5, 2009)

James said:


> I don't think it works that way because some cases occur more than others. I believe a PLL skip is *1/72*. If you do a COLL, I think there is a *1/12* chance of an EPLL skip. COLL skip is much more unlikely than 1/40.



What's the math behind that?

Edit: What are the stats for OLL?


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## MTGjumper (May 5, 2009)

Nukoca said:


> 1. OLL=57 algs, thus a 1/57 chance of OLL skip, and PLL=21 algs, which is 1/21 chance of PLL skip.
> 
> 2. COLL/EPLL or CMLL/EPLL: COLL has 40 algs, so 1/40 chance of COLL skip. EPLL is only *4* algs, so 1/4 chance of EPLL skip!




Flawed logic. PLL skip is 1/72, OLL skip is 1/216.

Aside: if you were to use that logic, wouldn't it be 1/(21+1) for PLL skip


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## Nukoca (May 5, 2009)

MTGjumper said:


> Flawed logic. PLL skip is 1/72, OLL skip is 1/216.
> 
> Aside: if you were to use that logic, wouldn't it be 1/(21+1) for PLL skip



I need to take a statistics class, lol. What are the statistics for COLL/EPLL?


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## brunson (May 5, 2009)

Nukoca said:


> What's the math behind that?


Left as an exercise for the student.

Did you take probability from this guy?
http://www.schneier.com/blog/archives/2009/05/mathematical_il.html


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## mazei (May 5, 2009)

But wait, isn't there only 7 cases for OLL if you use Petrus. Since you know, the edges are orientated and stuff. Unless you're doing Petrus without the EO.


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## Escher (May 5, 2009)

EPLL skip is as rare as a H perm using COLL. That is, 1/12. No idea about the rest of it.


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## Waynilein (May 5, 2009)

Ok, I'll save the situation before Mr. Pochmann comes in here and kills you...

Statistics for dummies: The chance of a COLL skip is the chance of the corners being correctly oriented and permuted.

Each corner can be oriented 3 ways, so it's 1/3 per corner. However, the orientation of the last corner is always determined by the other ones (that part is cube theory, not statistics), so we only need (1/3)^3 for the 3 corners that we can rotate.

You can place the first corner in 4 spots, the second in 3, the third in 2 and the last corner in the only slot that's left. So that's 1/(4*3*2*1) chance of them being permuted correctly, for a total of 1/648 chance of a COLL skip. However, a COLL skip with an AUF still counts as a skip, so just multiply that by 4.


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## Nukoca (May 5, 2009)

mazei said:


> But wait, isn't there only 7 cases for OLL if you use Petrus. Since you know, the edges are orientated and stuff. Unless you're doing Petrus without the EO.



Oh yeah....

So can someone with good statistics ability give me the chance of getting a COLL skip?

What I've been told so far:

OLL skip: 1/216 
PLL skip: 1/72

COLL skip: ...? <---Anybody know?
EPLL skip: 1/12

At any rate, it looks like the stats are better for COLL/EPLL.

BTW What are the stats for CPLL/CEOP? (when you put the (a) corners in the right places, and (b) permute the edges and orient corners?


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## Nukoca (May 5, 2009)

Waynilein said:


> Ok, I'll save the situation before Mr. Pochmann comes in here and kills you...



Thanks. I spent a while on my last post, so I didn't catch it when you posted before me.


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## irontwig (May 5, 2009)

Well, with Petrus you already got EO, so:

OLL skip: 1/27
PLL skip: 1/72

Thus: LL skip: 1/1944, and from that:

COLL skip: 1/162
EPLL skip: 1/12


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## Nukoca (May 5, 2009)

What are the chances of getting an OLL OR PLL skip?
What are the chances of getting a COLL OR EPLL skip?


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## Lord Voldemort (May 6, 2009)

You're provided with the individual probabilities for the skips you want, so don't you just add the probabilities?


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## Nukoca (May 6, 2009)

Lord Voldemort said:


> You're provided with the individual probabilities for the skips you want, so don't you just add the probabilities?



Because my logic and statistics so far have been faulty.


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## Lord Voldemort (May 6, 2009)

Nukoca said:


> Lord Voldemort said:
> 
> 
> > You're provided with the individual probabilities for the skips you want, so don't you just add the probabilities?
> ...



Sorry, I meant you're been provided.

Assuming irontwig's numbers are correct, 
OLL/PLL = 5.09% chance of OLL skip OR PLL skip.
COLL/EPLL = 8.95% chance of COLL skip OR EPLL skip.

Of course, COLL/EPLL has more algorithms, 44, vs the 28 with OLL/PLL.
YOu could also learn Winter Variation, which is 28 algorithms, and with Petrus it will force an OLL skip every time.


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## Ellis (May 6, 2009)

Lord Voldemort said:


> Of course, COLL/EPLL has more algorithms, 44, vs the 28 with OLL/PLL.
> YOu could also learn Winter Variation, which is 28 algorithms, and with Petrus it will force an OLL skip every time.



Or learn MGLS  but that's a lot of algs. 

And where are you getting your OLL stats from? Petrus? I'm pretty sure the chance of getting an OLL or PLL skip with fridrich is more like 1.9%


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## Lord Voldemort (May 6, 2009)

Yes, Petrus.
I'm not sure if that's correct, but I used 1/27, 1/72, 1/162, and 1/12 for OLL, PLL, COLL, EPLL respectively based on what irontwig posted.


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## Johannes91 (May 6, 2009)

Lord Voldemort said:


> You're provided with the individual probabilities for the skips you want, so don't you just add the probabilities?


Using that logic, the probability that you won't skip either step is (26/27) + (71/72) > 1, so no, you can't just add them.

The correct probability that you skip Petrus OLL and/or PLL is 1 - (26/27) * (71/72) = 49/972 ≈ 5.0%.

Similarly for COLL and/or EPLL skip: 1 - (161/162) * (11/12) = 173/1944 ≈ 8.9%.

Someone good at math hopefully corrects me if I made a mistake (it's 5:36am here).


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## irontwig (May 6, 2009)

Johannes91 said:


> Lord Voldemort said:
> 
> 
> > You're provided with the individual probabilities for the skips you want, so don't you just add the probabilities?
> ...



Maybe he presumed or=xor instead of or=and/or. It's 4:52am here, yay!


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## Johannes91 (May 6, 2009)

irontwig said:


> Maybe he presumed or=xor instead of or=and/or. It's 4:52am here, yay!


Possibly, though I think and/or is more interesting practically. For completeness:

Skipping Petrus OLL xor PLL: (1/27) * (71/72) + (26/27) * (1/72) = 97/1944 ≈ 5.0%.
Skipping COLL xor EPLL: (1/162) * (11/12) + (161/162) * (1/12) = 43/486 ≈ 8.8%.

Is this correct?


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## Lord Voldemort (May 6, 2009)

They are not mutually exclusive. My mistake.
So you were correct, irontwig, that I wasn't including and. 
Subtracting the "AND" possibility and the neither possibility corrects the probability, as well corrects the flaw that you proposed.

Hm... almost a 9% chance of a COLL/EPLL skip, or both means in most averages of 12, I''ll get 1. Maybe those extra 40 COLLs might be worth it.


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## deco122392 (May 6, 2009)

learning coll is always worth it =D its applicable for tons of methods =)


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## Nukoca (May 6, 2009)

8.9%, eh? Not too bad... I hear COLL recognition is bad, but I'll get faster over time. Thanks everybody!


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## deco122392 (May 6, 2009)

Its not all to bad. 
And naturaly, like everything else, it will get better with time.

Read this page:http://jmbaum.110mb.com/coll.htm

Mess around with it. Basically you Identify the oll then apply the corresponding algorithm.


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## Lord Voldemort (May 6, 2009)

deco122392 said:


> learning coll is always worth it =D its applicable for tons of methods =)



40 algorithms is a lot though.
I mean, I've learned 2 PLLs (I still haven't found a good N perm) and 36 OLLs, and it takes a while. I never really have a strict alg-learning routine, every once in a while I go "Hey! There's my alg sheet! I'll learn this OLL! Yay!"


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## JLarsen (May 6, 2009)

Dude OLL PLL for Petrus is only 28 algs, and the oll's are super super fast because they're so short. I can sub 1.5 all of them.

The "classic" set up for petrus is COLL and EPLL.


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## Lord Voldemort (May 6, 2009)

No, I was just saying that I am fairly slow at learning algs well.
I'm switching to ZZ, so I'm considering learning COLL.

I think I'll just learn the Pi, T, U, and L cases.
I can sub-1 Sune, Anti-Sune, and Double-Sune, so the speed probably won't be affected. For the Jason Baum page, on the L COLL page, are both cases dealt the same way, or is he giving you two views?


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## deco122392 (May 6, 2009)

The first moves: U, or U' or U2 are setups for the same algorithms because other wise there would be twice to memorize otherwise. But seeing as they are just reflections of each other you can solve them with a simple setup move and the same algorithm. 

So yes, its the same case from different points of view and are delt with the same way.

(edit): wooooo 200th post!!!!


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## Nukoca (May 6, 2009)

By the way, what is it that makes one case more likely than another?


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## byu (May 6, 2009)

I'll use a simple example.

In EPLL, U-Permutation happens 2/3 of the time, Z permutation happens 1/6 of the time, and H permutation happens 1/12 of the time.

U-Permutation:
It can be done Clockwise and Counterclockwise, from 4 anges (2*4=8)

Z-Permutation:
It can be done from two angles (that give different results) (2)

H-Permutation:
It can be done from only one angle (1)

Solved state:
There is only one solved state (1)

8+2+1+1=12

So U-Perm is 8/12=2/3
Z-Perm is 2/12=1/6
H-Perm is 1/12
and solved state is 1/12

Remember, this is for EPLL only.


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## deco122392 (May 6, 2009)

haha that was quick, explanatory and to the point


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## Nukoca (May 6, 2009)

byu said:


> I'll use a simple example.
> 
> In EPLL, U-Permutation happens 2/3 of the time, Z permutation happens 1/6 of the time, and H permutation happens 1/12 of the time.
> 
> ...



I thank thee for thy care and honest pains.


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