# Branching OLL to PLL Cases?

#### Note

##### Member
I'm not sure if anyone has discovered this before but at some point when I was practicing OLLs, I noticed a few PLL cases pop up after OLL. However, only 6 or 5 out of the 21 were sure to have a chance of popping up. For example, I would finish this case: and then I'd get a Z perm or a U perm, but only out of those 2, so I wouldn't get something like a N perm or an E perm. If this is the case for every OLL case, then it'll be easier to guess which case will be next out of the 21 by narrowing it down to the only possible ones, depending on the OLL. (Maybe then I could beat Mats Valk. )

..Another example if you couldn't understand what I meant.. There are 3 paths. A, B, and C. Go through A and you get a choice of 3 sub-paths. A1, A2, A3, et cetera. Of course, I could be wrong about this branching thingy or someone could have beaten me to it, but it's just an idea I had.

#### ryak2002

##### Member
That would be awesome! Someone should definitely look into this!

#### mDiPalma

##### Member
nah, all PLLs can happen after all OLLs, unless you do some fancy OLL stuff.

#### TDM

##### Member
This isn't actually what happens. As mDiPalma said, all PLLs happen with the same probability after every OLL, unless you influence PLL in some way.

Reminds me of this thread, which I found looking at past forum awards...
4000 posts

#### qqwref

##### Member
You were probably getting the same PLLs every time because you were practicing OLLs starting from a solved cube. In a normal scramble, every possible permutation of pieces can occur with every possible OLL, so if you want to restrict which PLLs you will get after a given OLL, you will have to learn multiple OLLs for each case and decide which one to use based on the non-yellow stickers. I think a lot of people do this for some simple OLL cases (such as sune or FRURUF) and there are methods like COLL or OLLCP that do this for more OLLs.

I'd get a Z perm or a U perm, but only out of those 2
Notice that Z and U perms have solved corners. If the OLL keeps the relative position of corners solved, then if you do it over and over and end up at a PLL, it will always be a PLL with solved corners. Any OLL algorithm using only R, r, U, u moves should have this property, and some others do too (like F (R U R' U')2 F').

#### SpeedCubeReview

##### Member
I posted something like this when to do Sune or Anti-Sune. I look for certain pairs of colors and instead of memorizing every single case, know that if I do a specific OLL I might skip the last layer or at least the corners. When I have OLL case 21 (with headlights on either side. If Everything is matching up top and the colors on either side are matching I do F (R U R' U')3x F' with headlights facing me. When I have matching colors on the top but mismatched on the sides I do R U R' U R U' R' U R U2 R' with the headlights to the side.

#### goodatthis

##### Member
It's likely because you were using a LL scrambler. I find that they give select LL cases and do not use all 6000 or whatever. All PLLs have an equal chance at showing up after OLL, and at every AUF. Besides, it would be impractical to try and predict PLL every time because you have 4 possible AUFs a PLL could show up at, so if you do a little math involving case symmetry and whatnot, there are 72 possible PLL cases for each (nonsymmetric) OLL. I have a decent post about case probability and symmetry if you want to learn more, it's on one of the recent pages in the Random Cubing Discussion.

basically all you need to remeber is that every LL case has an equal probability of showing up, but some orientation and permutation cases in their own repect show up more than others, which is why a PLL skip happens 1/72 instead of 1/22.

In short, you are probably recognizing 1LLL cases. Every 1LLL case has an equal probability of showing up, but if you use a scrambler dedicated to doing OLL practice, it will only select certain 1LLL cases rather than others. Remember, if you do alg A to 1LLL case B (to solve the OLL), you will always get PLL C, from the same angle.

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#### Note

##### Member
Ahh.. I see.. Thank you guys for explaining everything. And really, this was my first time looking into Cube Theory type stuff (Hopefully not the last time.. ^^).

#### goodatthis

##### Member
I understand, cube theory was pretty confusing to me at first too. I remember when I couldn't figure out for the life of me why there were certain probabilities of certain PLLs to come up. I thought that it was done by some sort of empirical trials system or something.