# Tutorial: 4x4 Hoya variant for ZZ solvers

#### AlphaSheep

##### Member
This is a tutorial for the method I use for solving a 4x4. It's based on the Hoya method and aims to give a smooth transition into the ZZ method for the 3x3 stage, with the EOLine mostly done.

Outline of the method mostly copied from the original post:
1. First 4 centres (F, B, D and then either L or R colour) and then hold the cube a with a y or y' away from your usual ZZ orientation so that the unsolved centres are on the front and top.
2. Solve line edges on DR and DL, and pair and orient any three other edges in BR, BL and DB. This step is mostly <R, r, U, l, L> The BR and BL edges need to be oriented bearing in mind a y rotation will happen later. I deal with this by:
• pairing the edges misoriented on UF, and then inserting with R' U' R or L U' L', or
• pairing the edges misoriented on DF, and then inserting D R D' or D L' D', or
• Pairing them oriented on DF or UF and doing R2 F R2 or L2 F' L2 (obviously this is less finger tricky than the other two options so should be avoided)
3. Last 2 centres - even easier than normal Hoya since DF doesn't need to be moved out the way. This is completely <r, U, l>
4. If a lucky edge is already paired, place it oriented on DF. Otherwise chain-pair 2 edges and place one of them oriented on DF. This trick comes from OBLBL and helps a ton with lookahead in the next step.
5. Pair the last 5 or 6 edges, with 2-3 or 2-2-2 pairing. In a more advanced variant, edge orientation can be influenced about half the time using Z4 tricks (see here to get started).
6. Something like a Petrus kind of EO from a y rotation for the last few edges (max 6). This can often be done completely <R, U, L>, but sometimes requires at most one F move.
7. Orientation parity can be fixed here using a slightly shorter alg than the standard one (x r U2 r' U2 l U2 r' U2 r D2 r D2 r' D2).
8. y' rotation followed by ZZ finish.
Some more example solves:

Scramble: L Fw' L R Uw' D' Rw' B' Uw F2 R2 D2 F2 L2 B R' U F B2 Rw2 F' Fw2 Uw' F2 B2 R2 D' F2 D2 R B2 Rw' B R F2 R2 F Rw' U' Uw2

// Solve 4 centres:
y' l'L d D' l'L d F2 d' // 2 opp Centres - F and B colours
r U F' D' l' F' l' // D centre
x r F r' F' l' U2 l x // 4th centre

// Pair + orient 5 edges
R' // First line edge
L D r U' r' D' // Second line edge
L' U L r U2 r' D2// 3rd edge
l' U2 l U' l' U l D R' D' // 4th edge
U' L U L' // 5th edge

// Last 2 centres
r U r' U' l' U2 l

// Edge pairing
R U R' F2 // Oriented edge on DF
U R U' R' u' R U R' F R' F' R u // 2 Edges
L' U2 L R U' R' u' R U' R' u // 2 Edges
R U' R' u' R U R' F R' F' R u // 2 Edges

// Petrus style EO
U F R U R'
U D2 r U2 r' U2 r' D2 r D2 x' r' U2 r U2 r' x // EO Parity

// Rotate+ZZ Finish
y U R2 U2 R' L U2 L2 U R' U R U L // Left block
R' U2 R U R' U' R' U R U2 R2 U' R2 U' R' // Right block
U' 3r' U' R U L U' R' U x // COLL
m2 U m2 U m' U2 2L2 U2 2R2 u2 2R2 u2 U2 m' U // EPLL+Parity
alg.cubing.net

Scramble: Fw2 U F2 D2 L2 F' Uw2 R U' F D F' B' L' Rw2 B L' Rw U2 Uw2 R2 U Rw U2 Fw R' Uw Rw' F2 Fw' Rw2 Fw R2 F' L' Rw2 U D F' U'

// Solve 4 centres
F2 d x' U2 r' y2 R u U r' F2 r z'// 2 opp Centres - F and B colours
F x' U l' U r U2 r2 x' r U' l U2 l2 x' // 3rd and 4th centres

// Pair + orient 5 edges
U' r U2 r' U r U' r' D R' // 1st Edge
F2 L U l' U2 l // Line edge
D L' D l' U2 l // Other line edge
D' U r U' r' D' L D // 4th edge
l' U2 l U' l' U l D2 // 5th edge

// Last 2 centres
l' U l U' r U2 r'

// Edge pairing
u' R U R' u U' F2 // Pair and orient DF
L' U L u' U R U' R' u // Pair 2 edges
R U' R' u' U R U' R' u // Pair 3 edges

// Petrus style EO
L' U' L R U R'

// Rotate then ZZ finish
y' L' U2 L R U' R' L U' R' U2 L' U2 L2 U2 L // Left BLock
R U2 R' U2 R U R' U2 R2 U' R' U R U' R' // Right Block
U2 R U2 R' U' R U' R' U2 R' U2 R U R' U R // ZBLL
alg.cubing.net

Scramble: D B' D' F' Fw2 B' D' L F Rw' B' Rw' B R B L' R D R' B' Uw2 L' R F' B' Uw2 R U2 D2 F2 L' Rw' R2 B Uw2 D' R U2 D L2

// Solve 4 centres
r' U2 r' U l' U2 l2 // First 2 centres
U' F l' U2 l // 3rd centre
z l' U' l U' D l2 U2 l2 x // 4th centre

// Pair 5 edges
U r U2 r' U r U' r' D R' // 1st edge
U' l' U2 l U' l' U l D' L // 2nd edge
F' U F2 r U' r' D2 // 1st line edge
U F r U' r' D // 2nd line edge
F2 l' U2 l D2 // 5th edge

// Last 2 ccentres
U' l' U' l F l' U2 l

// Finish edge pairing
U R U' R' u' R U' R' u R' F R // Pair 2 and orient DF
U R U' R' u' F' U F u // Pair 2 edges
F' U' F u' F' U F u // Pair 3 edges

// EO
F U F' R U2 R'

// Rotate and ZZ finish
y U R' U2 R U R U' R U2 R' U2 R U R' // Right Block
U2 L' U L U2 L2 U L' U' L U L' // Left Block
U' R U2 R2 U' R2 U' R2 U2 R // COLL
2R2 U2 2R2 u2 2R2 u2 U2 // PLL Parity
R2 U' R' U' R U R U R U' R // EPLL
alg.cubing.net

Scramble: R' F' L' Fw D' Rw D' L R' F2 Fw Uw2 F Fw2 U2 Rw2 Uw2 F' Uw2 L D L' U D2 F Fw2 B2 Uw Rw2 R' U2 Uw2 R F Fw B Uw2 F' Rw B'

// Solve 4 centres
x' U r U F l2 U' l' U' r' U2 r x' y U F' l' U2 l // 2 opp centres
z B' r2 U' r // 3rd Centre
U' F' r2 U r F2 r x // 4th Centre

// Pair 5 edges
B' U' B // 1st Edge
U2 r U2 r' U r U' r' // 2nd Edge
D' L F' L' D2 // Line Edge
U2 F2 U2 r U' r' D // Other Line Edge
R U' R' l' U2 l D R' D' // 5th Edge

// Last 2 centres
U2 r U2 r'

// Finish Edge pairing
R U R' u' R U R' u F // 2 Edges + Oriented in DF
F' U F u' F' U2 F u // 2 Edges
R U R' u' R U2 R' u // 3 Edges

// EO
R U R' F
r U2 r' U2 r' D2 r D2 x' r' U2 r U2 r' x D2 // EO Parity

// Rotate and ZZ Finish
y' R U2 R' U' R' U2 R' L' U2 L2 U2 L' U2 R' // Right Block
U L U2 L' U L' U L' U L U2 L' U L // Left Block
U2 3r U R' U' 3r' F R F' // COLL
U 2R2 U2 2R2 u2 2R2 u2 U // EPLL Parity
alg.cubing.net

Scramble: U' B' U R Rw Uw2 F2 Fw' Rw2 Fw2 B' Uw F' L2 Fw Rw' Uw2 B' R2 B2 D2 U2 Uw B2 Uw B' U2 Uw2 F R2 Rw' L' Uw' Fw2 F' R2 Uw2 F' Uw F

// Solve 4 Centres
x D U' r U' F' D r' x' R u2 3d l' U2 r // 2 opp centres
y D' r2 U' l' x // 3rd centre
F' r U' r2 D' r D l2 U2 l2 x // 4th centre

// Pair 5 edges
l' U2 l U' l' U l D R' // Pair 1st edge
F U F' r U' r' D' L // Pair 2nd edge
U r U2 r' U r U' r' // Pair 3rd edge
D2 F2 D U r U' r' // Line edge
D2 R U R' F2 r U' r' D // Other line edge

// Last 2 centres
U' l' U' l

// Finish edge pairing
F' // Oriented edge on DF
u F U2 F' u' // 2 edges
F U2 F' u' F R' F' R u // 2 edges
R U2 R' u' R U R' F R' F' R u // 2 edges

// EO
R U' R' F
r U2 r' U2 r' D2 r D2 x' r' U2 r U2 r' x D2 // EO Parity

// Rotate and ZZ finish
y' U' L' U L U2 R' U2 R U2 L // Left Block
U2 R2 U2 R' U' R' U' R' U R U' R' U' R // Right Block
R' U' R U' R' U2 R // OCLL
U2 R U2 R' U' R' F' R U2 R U2 R' F R U' R' U' // PLL
alg.cubing.net

Last edited:

#### AlphaSheep

##### Member
EOPairing Algorithms

I use u moves to slice over during chain pairing. Here are some alternative pairing algs for influencing EO during chain pairing (basically, you can just use VHLS algs instead of the standard inserts).

First, set up the edges such that uFL can be paired with dFR with a u slice move. Then to determine which alg to use, look at the orientation the edge at dFR, and then compare the orientation of uFR with the orientation of it's matching edge in the U layer (this you already have to do, it's actually on;y the orientation of dFR that you're looking at). Remember that you need to recognise orientation from a y rotation away from your final ZZ position.
The algs below assume the second edge to pair is in UF. In some cases, you have to flip an edge in U. In these cases, it's best to choose an unpaired edge to avoid flipping an edge you've already paired and oriented.

• If dFR is bad, and uFR and it's matching edge have opposite orientations:
• If dFR is good, and uFR and it's matching edge have the same orientation:
I should point out that I actually don't use this, because I find that orienting at the end is more move efficient.

#### PapaSmurf

##### Member
I know that this is kind of a thread bump, but how fast do you think this method could be? I average around 50-55 seconds with yau, and I love the idea, but can it get sub 30 averges?

##### Member
I know that this is kind of a thread bump, but how fast do you think this method could be? I average around 50-55 seconds with yau, and I love the idea, but can it get sub 30 averges?
It's actually less efficient than Yau (and "normal" hoya) iirc so even if you would need to turn about 15% faster to gt the same times

#### PapaSmurf

##### Member
Shame, because I was just messing about with it and it seemed pretty nice, but I could tell that step 2 wasn't that great. I just hope that someone (I'll try too) comes up with a zz 4x4 method to rival yau and meyer.

#### alwin5b

##### Member
This method is really well thought out. It doesn't look like much at first, which is why I tried developing my own 4x4 ZZ method based on the Ewert method. I thought my method turned out pretty decent, but then I compared it to Hoya-ZZ and, well, Hoya-ZZ is 10 times better than what I came up with (maybe it's just because Hoya is better than Ewert to begin with, but I didn't realize that at first). As of now, I'm fairly sure Hoya-ZZ will become my main 4x4 method.

In step 2 I think it might be better to place the cross edge in DB instead of placing any oriented edge in DB.

In step 4, if no lucky edge is paired, I place the cross edge in DF instead of a random one. If your main 3x3 method is not actually ZZ, you could even place the DF and DB cross edges every time, so that you now have the easiest F2L phase you can think of (oriented edges and cross done). So this method could even be used by CFOP users who hate rotations.

In step 6 if you can sometimes use Roux style EO (if you get an 'arrow' case), but that is part of 'modern' Petrus anyway. Just be good with M slice turns on 4x4 if you do that. I find that a fast way to do an M turn on 4x4 is to place the thumb on top of the UF edge and push the M layers down.

step 7: The parity alg I use is

Rw2' F2 Rw U2 Rw U2' x U2 Rw U2' Rw' U2 Rw U2' Rw2 U2' x'

which I prefer to the alg above (and it's only one turn longer). It doesn't mess up the F3L, so it allows for better look-ahead.

LL (step 9/10 I guess): definitely (had to look up the spelling on this one...) use COLL/EPLL, especially if you're good with M turns on 4x4. I made a thread about some nice COLL algs nobody uses a while back, and I actually compiled my COLL algs with big cubes in mind (basically prefer RUF algs over RUL algs if they're equally fast on 3x3, because with RUL algs you usually have to do small regrips which don't slow you down on 3x3, but which are horrible on big cubes).

As for EPLL on even cubes, you can get W perms and O perms, which I do like this:

W Perm:
m2 U m' U2 m U 2L2 U2 2R2 Uw2 2R2 Uw2 U2 ( = Ua Perm then PLL parity)

O(cw) Perm: (align corners before alg execution)
m2 U' m2 U' m' U2 2R2 U2 2L2 Uw2 2L2 Uw2 U2 m' ( = Z Perm with PLL parity in between)

O(ccw) Perm: (align corners before alg execution)
m' U2 Uw2 2R2 Uw2 2R2 U2 2L2 U2 m' U m2 U m2 (inverse of O(cw))

Even though you could just as well fix PLL parity and then do an EPLL, I think its well worth it learning the W and O Perms, because it allows you to 1-look EPLL+parity every time. Also these cases come up very often (EPLL+parity are just 9 cases...)

#### PapaSmurf

##### Member
I think you’d like to see my yau based zz variant. It’s pretty similar to yau, but I think it’s slightly less efficient. I’ve got my pb single of 43.1x seconds with it. Not too fast, but it’s faster than yau for me.

1. L and R centres

2. Pseudo yau cross. There are 3 types of edges for this step and you solve three of them, oriented, where the yau cross would be:
L cross edge
Line edge
2xany other F2L edge.

Make sure you don’t do both line edges. That gives awkward solutions.

3. L4C

4. Solve the final edge that you didn’t do for step 2.

5. Put the pseudo cross on D and 3-2-3 edge pairing.

6. Put pseudo cross on L and solve line while preserving the orientation of the other 3 pseudo cross pieces.

7. Do a y rotation and Petrus style eo.

You can combine steps 6 and 7 by doing LEOR style stuff, but it’s a bit awkward.

8. ZZF2L

9. LL, and as you said, COLL then EPLL + parity.

Tell me if that’s unclear.

#### alwin5b

##### Member
This is also quite good. Thanks for sharing this. I think I prefer Hoya to Yau because it's almost rotationless, but I've thought about using Yau for ZZ as well (unsuccessfully), and it's nice to see a solution to this problem.

#### PapaSmurf

##### Member
Yeah, if you prefer zz Hoya, go with that tbh, but I’m gonna stick with zz-yau just because I find it more fun.

#### AlphaSheep

##### Member
In step 2 I think it might be better to place the cross edge in DB instead of placing any oriented edge in DB.
I agree. I generally do go for one of the cross edges unless there's an obvious easy case. It's easier for lookahead to have some idea what you're looking for before you see it.

In step 4, if no lucky edge is paired, I place the cross edge in DF instead of a random one. If your main 3x3 method is not actually ZZ, you could even place the DF and DB cross edges every time, so that you now have the easiest F2L phase you can think of (oriented edges and cross done). So this method could even be used by CFOP users who hate rotations.
I usually just dive into chain pairing with whatever edge is in uFR, and then once the first two edges are paired, push whichever is easiest into DF. Because of my F2L technique in the 3x3 stage, having both cross edges solved is actually a hinderance (I use the R face to pair pieces to insert into the L block).

LL (step 9/10 I guess): definitely (had to look up the spelling on this one...) use COLL/EPLL, especially if you're good with M turns on 4x4. I made a thread about some nice COLL algs nobody uses a while back, and I actually compiled my COLL algs with big cubes in mind (basically prefer RUF algs over RUL algs if they're equally fast on 3x3, because with RUL algs you usually have to do small regrips which don't slow you down on 3x3, but which are horrible on big cubes).
Yup. I really like COLL+EPLL as well.

I think you’d like to see my yau based zz variant. It’s pretty similar to yau, but I think it’s slightly less efficient. I’ve got my pb single of 43.1x seconds with it. Not too fast, but it’s faster than yau for me.

1. L and R centres

2. Pseudo yau cross. There are 3 types of edges for this step and you solve three of them, oriented, where the yau cross would be:
L cross edge
Line edge
2xany other F2L edge.

Make sure you don’t do both line edges. That gives awkward solutions.

3. L4C

4. Solve the final edge that you didn’t do for step 2.

5. Put the pseudo cross on D and 3-2-3 edge pairing.

6. Put pseudo cross on L and solve line while preserving the orientation of the other 3 pseudo cross pieces.

7. Do a y rotation and Petrus style eo.

You can combine steps 6 and 7 by doing LEOR style stuff, but it’s a bit awkward.

8. ZZF2L

9. LL, and as you said, COLL then EPLL + parity.

Tell me if that’s unclear.
Honestly, I do suspect that Yau is faster than Hoya, and from the few reconstructions I've used, I think that the move count in your Yau variant is a tiny bit lower too. At the end of the day though, like you, I tend to use the method I enjoy most. It really comes down to which method suits your personal solving style.