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JOLL v2 in depth explanation (+ROLL/JOLL learning tools are finally here!)

ottozing

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ROLL/JOLL learning tool by Tao Yu

How to use it

About a week or so ago I sent a wall of text similar to this to my email list... (link in signature to sign up)... However after some consideration I've decided that this info needs to be posted publicly since ROLL/JOLL resources are so scarce

I've previously written on JOLL v1 which can be found *here*, and my thread on ROLL, a similar concept which I will be glossing over in this thread without any beginner level explanation can be found *here*

anyway, the main problem with JOLL v1 (aka the way I personally learned JOLL via experience), is that you can't gather info about what EP you might get for your PLL 100% percent of the time. Since both ROLL and JOLL are PLL prediction methods, it would make sense for JOLL to actually give you at least SOME information every single time, rather than a percentage of the time

Thankfully, the fix to this with JOLL v2 is pretty simple. Initially I was worried about the slight downside of harder recognition, but I only think the recognition is a deal breaker for some specific cases (more on this later)

Basically, in order to guarantee that you get EP info with JOLL v2, you need to pinpoint two LL edges that are normally opposite colours when your standard OLL algorithm PLL skips. These two edges can be any of the LL edges, though you would ideally be choosing the two that are easiest to see from the OLL alg angle

~

With JOLL v1, the edges you looked at for EP info were ALWAYS the two misoriented edges in a 2 edge OLL (JOLL v1 was not intended for dot cases or cross cases). Any time the two edges were adjacent for when given OLL case would skip, you could only get data on your EP type if the edges were opposite in a solve. If they were adjacent, the fact that adjacent matches the adjacent you see with when the OLL case skips PLL didn't actually tell you anything about your PLL EP type

~

With JOLL v2, the edges you look at for EP info are ALWAYS two edges that are opposite colours when the OLL algorithm skips PLL. For example, with F R U R' U' F' (do F U R U' R' F' on a solved cube to see), the UF and LU stickers are opposite colours. In JOLL v2, these are the two stickers you look for before executing OLL in order to gather EP info and narrow down your possible PLL case from 21 to a number less than 21 (more on the actual numbers in a moment, since knowing full ROLL+JOLL v2 leads to some ridiculous case reduction, especially when you throw in "intelligent wit")

Before getting into some example solves using LL scrambles, here's a quick breakdown on how much better PLL prediction gets by using ROLL in combination with JOLL v2

With ROLL, PLL cases can be divided into 3 CP types. DiagCP (diagonally swapped corners), AdjCP (adjacently swapped corners), and EPLL (solved corners). Note that the level of PLL prediction doesn't actually require you to learn full ROLL. You can learn what CP cases correspond to DiagCP and EPLL, and not distinguish between the remaining AdjCP cases while still getting the same level of PLL case reduction (however this means you won't know where the headlights are for PLL, more on this later but it CAN help a lot)

With JOLL v2, PLL cases are further divided into 2 camps. One where two opposite edges are solved, and one where two adjacent edges are swapped. Because you're only using 2 edges to recognise JOLL v2 (as any more than this would seriously hinder recognition), you cannot distinguish between solved edges and an opposite swap edges (IE you can't know if you'll have Aperm over Tperm with ROLL/JOLL v2 alone)

Using both ROLL (full or simplified) and JOLL v2 (has to be v2, v1 won't work the same), you can narrow down your PLL into one of the following 6 categories

DiagCP AdjEP: Y perm, V perm (2/21 PLL cases)
DiagCP OppEP: Na perm, Nb perm, E perm (3/21 PLL cases)
AdjCP AdjEP: Ga perm, Gb perm, Gc perm, Gd perm, J perm, L perm, Ra perm, Rb perm (8/21 PLL cases)
AdjCP OppEP: Aa perm, Ab perm, T perm, F perm (4/21 PLL cases)
EPLL AdjEP: Ua perm, Ub perm (2/21 PLL cases)
EPLL OppEP: H perm, Z perm (2/21 PLL cases)

Worst case scenario, you have your PLL narrowed down to 8 possible cases or ~38% of the total PLL cases

Best case scenario, you have your PLL narrowed down to 2 possible cases or ~10% of the total PLL cases (half of the PLL categories are like this, with two of the remaining three being 3/21 and 4/21)

Since I'm of the belief that ROLL/JOLL v2 can be trained to a subconscious level of recognition with enough practice, ROLL/JOLL v2 clearly has a LOT of potential in my view :)

NOTE: For each example I'm going to give two scrambles and I would encourage you to follow along on two separate 3x3's at the same time

One scramble will generate the OLL case such that it leads to a PLL skip. The second will show the same OLL case but going into a random PLL

#1a: F R' F' R2 r' U R U' R' U' M'
#1b: U2 F R2 B2 D2 F L' F' D' B D' B R2 F' U'


ROLL&JOLL v2 notes for 1a

CP case is sexysledge aka UFL & UFR match the UBR piece
UL and UR are opposite colours

ROLL&JOLL v2 notes from 1a applied to 1b

We see that the CP case is the mirror of 1a with the UFL & UFR stickers matching the UBL piece. Therefore, our standard OLL algorithm which is M U R U R' U' r R2' F R F' will give a diagonalCP

Without looking at JOLL v2, the only possible PLL case we can get is Eperm, Nperm(s), Vperm or Yperm, so 5 possible PLL cases

Looking at UL and UR, these are not opposite colours like they were in 1a. Therefore, the edges will be adjacently permuted

This rules out Eperm and the Nperms, meaning the only possible PLL case we can get is Vperm or Yperm using ROLL and JOLL v2

#2a: F R' F' R U R U' R'
#2b: F' U2 F' R2 B L2 D2 B' R2 F L2 U' L' U L F


ROLL&JOLL v2 notes for 2a

CP case is again sexysledge, UBL & UFL match the UFR piece
UF and LU are opposite colours

ROLL&JOLL v2 notes from 2a applied to 2b

This time the CP is noswap with UBL & UFL being opposite colours to RUB & RUF. According to ROLL recognition, our standard OLL algorithm will give us an adjacentCP with headlights on left

One thing to quickly note is that knowing where the headlights will be is good because for most people, no matter what PLL algorithms they use, the majority of their algorithms will start with headlights on left (or right if they're a left hand dominant solver)

Since we know we're getting headlights on left and that we're a right hand dominant solver (otherwise we would be doing U2 L' U' L U L F' L' F lol), we can take a mental note that it's *likely* we won't have to AUF before PLL

anyway, before moving onto JOLL v2 we can conclude that the PLL will be Aperm(s), Fperm, Gperm(s), Jperm, Lperm, Rperm(s), or Tperm

Moving on to JOLL v2, we see that UF and LU are not opposite colours, and again this means that edges will again be adjacently permuted. This rules out Aperm(s), Fperm, and Tperm leaving us with Gperm(s), Jperm, Lperm, and Rperm(s) as the possible PLL cases (8/21 PLL cases are possible)

This next part isn't ROLL&JOLL v2 related, but because of the fact that the standard OLL algorithm (2a) preserves blocks in 3 places (2 blocks with the misoriented pieces, and one with the UR & UBR pieces), we can actually narrow down the PLL possibilities even further quite easily by noting the fact that 2b has two of those 3 blocks

This means that Gperm(s) and Rperm(s) are no longer possible cases, thus reducing the possibilities to again two PLL cases in Jperm or Lperm (So 2/21 with a little extra wit, but 8/21 with strict ROLL&JOLL v2

Also, depending on what algorithms you use for Jperm and Lperm, you could further conclude that you definitely *don't* need to AUF before PLL, which is yet another useful thing that could potentially be added to your deductive reasoning

#3a: M' U R' U2 R U R' U R2 r'
#3b: R2 D' R2 B2 D2 B2 U' L2 U L2 R2 F D U R F' U' F' R U2


ROLL&JOLL v2 notes for 3a

CP is noswap (UFL&UBR opposite colours, UFR&RUB opposite colours)

UF and RU are opposite colours

ROLL&JOLL v2 notes from 3a applied to 3b

CP is one of the 4 that corresponds with adjacentCP for PLL (UBR&UFR opposite, RUB&UFL same). This case again happens to be the one that corresponds with headlights on left, so again you can take a mental note of "unlikely AUF before PLL". We have the same possible PLL cases as example #2 from the exact same angle

UF and RU are once again not opposite colours, so we conclude the exact same thing as with example #2 and that it has to be Gperm(s), Jperm, Lperm, or Rperm(s)

We can actually do the same extra deductive reasoning to rule out Gperm(s) and Rperm(s), however I'll leave this as an exercise for the reader since it's a lot less obvious and not as realistic as ROLL&JOLL v2 recognition, which is comparatively much easier to codify (HINT: Look at the UBR&UL stickers as well as the UF&UFR stickers)

#4a: S R U R' U' R' F R f' (Yep, I'm making you use a weird OLL that most people don't use even though it's pretty nice. Deal with it)
#4b: U F2 R2 F2 U' F2 R2 F2 U2 B' R' B R' U' R U R


ROLL&JOLL v2 notes for 4a

CP is inverse sexysledge (UBR&FUR both opposite of UFL)
UF and LU are opposite

ROLL&JOLL v2 notes from 4a applied to 4b

CP is a perfect match, so we're basically doing OLLCP here. This is the main reason I wanted to show this case with something other than U2 R' F R U R' U' F' U R (other than the fact that I like flexing under-utilised OLLCP algs)

ROLL&JOLL v2 doesn't have to end after you've learned the rules for every standard OLL case. You can and should apply this knowledge to viable OLLCP cases that you use, because although the CP info may not be a big deal, the JOLL v2 info IS quite nice...

anyway, we know before looking at the JOLL stuff, the PLL has to be Uperm(s), Hperm or Zperm

Looking at the JOLL stuff, UF and LU are opposite. For the first time, our edges are actually opposite instead of adjacent like in the previous 3 examples, meaning we can narrow down the EP in a different way!

Because we have opposites here, EP will be an opposite type thus ruling out the Uperms (unfortunate because they're the nicer EPLL's but whatever)

2/21 possible PLL cases, pretty solid case reduction aye? Not good enough for me, so time to flex some more intelligent wit (much more practical than example 3 I promise)

You may have noticed with 4a that there are some colour blocks with the UF&UFL pieces as well as the UR&UFR pieces

Look at 4b, and you'll notice opposite colours in place of normal blocks

Now, between Hperm and Zperm which are the two possible PLL's based on ROLL&JOLL v2 reduction, what do those opposite colours resemble more?

You guessed it, Hperm. Using ROLL&JOLL v2 along with some fairly simple wit, we literally know the exact PLL case B)

#5a: F' L F L' U' L' U' L U L' U L
#5b: B2 L2 U2 B L2 B' L2 F U2 R2 F2 L B' L F' R2 F2 U'


ROLL&JOLL v2 notes for 5a

CP recog UFL&FUR are opposite to UBR

UL and RU are opposite This is the one JOLL v2 case I don't like recognising (technically LU and RU would be worse, but that's only possible with cross OLL's and I use hella ZB so it doesn't impact me)

ROLL&JOLL v2 notes from 5a applied to 5b

CP here is the "opposite" case to 5a and corresponds with a diagonalCP, so Eperm Nperms Vperm Yperm

UL and RU are adjacent, which just like example 1 rules out Eperm and Nperms, meaning it has to be either Vperm or Yperm

#6a: F U R U' R' U R U' R' F'
#6b: R' U' R U' R' U2 R U R U2 R' U' R U' B U B' U' R' U (Not randomly generated, just a case I wanted to show that's different from everything else thus far)


ROLL&JOLL v2 notes for 6a

Noswap CP, UBR & UFR match, UBL & UFL opposite colours

UF and UR are opposite colours, this is basically JOLL v1 recognition which is lucky, best of both worlds :)

ROLL&JOLL v2 notes applied to 6b

CP here is the "opposite" of 6a with UBL&UFL matching and UBR&UFR now being the opposites. Diagonal CP, only Eperm Nperms Vperm and Yperm are possible

UF and UR are opposite, so we can rule out Vperm and Yperm meaning only Eperm and Nperms are possible (3/21 PLL's)

The wit here is a bit counter intuitive, but with practice this is something you can naturally get better at even though it's something I cannot easily codify at this point in time

Basically, we can rule out Nperms based on the fact that 6b has blocks with the UF&UFR pieces, as well as a sticker block with the UR&UBR stickers

The reason this works as legitimate case reduction is because with 6a, these sections are normally made up of adjacent colours in these block positions. Again, adjacent colour blocks... hmm... does that sound like an Nperm to you?

Hell nah son, Nperms are all about opposite colours out the wazoo. Therefore, it has to be an Eperm no matter what

Again, this kind of advanced witty case reduction requires a lot of knowledge beyond standard codified ROLL&JOLL v2, but it's quite possible with enough practice!
 
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