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

[Nukoca]

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...)

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.
Now I've found a full set of COLL algorithms that orients and permutes the corners of the last layer, and flips all four of the last layer edges. I call them CLLEF: "Corners Last Layer and Edge Flip"

So, is it worth it?
Compared to using COLL you have 40 cases to learn with CLLEF and COLL, recognition is also the same and the end result is an edge only PLL or PLL-skip.
CLLEF algorithms are longer than COLL on average, but that's not a fair comparison. Instead, COLL algorithms are longer then the respective OLL algorithms, but CLLEF algorithms are (so far) exactly 12.0 moves compared to 12.0 of the respective OLL's (taken from cubewhiz.com).

One negative point about CLLEF is that it is not very useful with other methods like Petrus og Roux.

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?

 

[soccerking813]

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

 

[Nukoca]

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.

 

[James]

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.

 

[Nukoca]

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?

 

[MTGjumper]

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

 

[Nukoca]

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?

 

[brunson]

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

 

[mazei]

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.

 

[Escher]

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

 

[Waynilein]

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.

 

[Nukoca]

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?

 

[Nukoca]

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.

 

[irontwig]

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

 

[Nukoca]

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

 

[Lord Voldemort]

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

 

[Nukoca]

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.

 

[Lord Voldemort]

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.

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.

 

[Ellis]

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 :rolleyes: 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%

 

[Lord Voldemort]

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.