Edge Orientation (EO)
By err0rcuber
Here's a video! Below is the written version with interactive cubes.
Introduction
Edge Orientation (EO) is the way edge pieces are twisted on the cube. This is the key concept to Step 1.
"Solving" EO means twisting the edges in a certain way to make the rest of the solve nicer. It feels like magic!
Not only is EO the foundation of ZZ, it's very useful for CFOP and essential to FMC!
1. How EO works
Natural moves
There are six basic kinds of moves on the cube. R, U, L, D, F and B moves. We can split them into two groups:

Natural moves: All R, U, L, and D moves. Let's call them "natural" because they're fast and comfortable for your hands.
Examples: R, D2, L', U 
Unnatural moves: All F and B moves. Let's call them "unnatural" because they're more awkward (unless in specific hand positions).
Examples: F, B', F2
In a good speedsolving method, we want to use many natural moves and few unnatural moves. But that begs the question: can we use only natural moves to solve the whole cube?
Almost! This is the closest we can get, usually something like this:
With only natural moves, we can solve the corners and move the edges to the right place. But the problem is that natural moves can't twist edges. Some edges could be solved just fine👍, but others remain twisted wrong👎.
There are two ways an edge piece can be twisted, or "oriented" on the cube:
 👍Good edge: oriented in a way that's solvable with natural moves. Also known as "oriented".
 👎Bad edge: oriented in the other way, which is unsolvable with natural moves. Also known as "misoriented".
The purpose of EO
The idea of ZZ is to add a step at the beginning of the solve, which will speed up the rest of the solve.
Twist all bad edges so they become good edges.
This is called solving EO, or orienting the edges. Then the whole cube can be solved with natural moves only! Solving EO eliminates the need for F/B moves or cube rotations, allowing us to turn in a fast and streamlined way.
Plus, EO reduces the number of cases you'll encounter during the solve.
 Unlocks realistic 1look last layer (ZBLL)
 Makes 2look last layer (OCLL+PLL) easier to learn
Orbits
Earlier, we discovered that natural moves can't twist edges. Why is that?
When doing R, U, L, D turns on the cube, the edge stickers move in a restricted way. (Stickers are the coloured tiles on the cube.)
Here we have a greenred edge. Let's press ▶️ and watch the green sticker, see where it can move.
The green sticker can only visit the region of spots marked with purple below. It can't visit the region of spots marked with light grey. The red sticker is the opposite! We call these two regions "orbits".
The spots marked in purple, let's call it the purple orbit. It covers all the edge stickers on the Up and Down sides, plus two on the Front and two on the Back. Remember this, it's important later!
The other spots are marked with light grey, and we'll call it the outer orbit.
During natural moves, the stickers on one orbit will always stay on that orbit. Press ▶️ to see!
Also notice that every edge has one sticker in the purple orbit, and the other sticker in the outer orbit. For example, this bad edge has a red sticker in the purple orbit, and a green sticker in the outer orbit.
In order to twist this edge, we must switch red and green around. But that means red (on the purple orbit) must move to where green was (on the outer orbit), which is impossible with natural moves! That's why natural moves can't twist edges.
This explains why the edge is "bad". It's only solvable if we use unnatural moves, which are the only moves that can move stickers between orbits.
We can do F' U' R'
to twist the frontright edge.
The F'
changed the orientation of the bad edge, making it a good edge solvable with natural moves (U' R'
in this case).
We call this process orienting an edge: turning a bad edge into a good edge with an unnatural move. Our goal is to orient all of the edges.
But how can we tell that an edge is bad or good? If an edge is in its solved place but twisted wrong, it's definitely bad (natural moves can't twist edges!) But what if it were somewhere else? Not as obvious.
In the next section, we'll learn a simple system to detect these bad edges. And after that, how we can orient them all.
2. Recognizing bad edges
Perspective
When looking for bad edges around the cube, there is a problem: edge orientation depends on your perspective!
If you turn the whole cube around, some edges can change from bad to good or good to bad.
For example, if you do a y
cube rotation, F moves (unnatural) become L moves (natural).
So a bad edge that needs to be solved with F
becomes a good edge that can be solved with L
.
This is how CFOP orients edges during F2L! If you use CFOP, recognizing EO
helps eliminate unnecessary y
rotations.
In order to recognize bad edges, we should not turn the cube around. For each solve, pick a center to stay at the top, and another to stay at the front.
Now we're ready to recognize bad edges! Follow along with this scramble:
F' R' D B U2 R' U R D2 L B2 R L U2 F2 B2 L B2 R'
When following scrambles, always have the white center at the top, green center at the front. After that, we can choose how to hold the cube. For example, orange center top, green center front.
We have two rules for finding bad edges:
Rule #1
Rule #1: look for L and R stickers on the purple orbit. Their edges are bad.
"L and R stickers" means the stickers that match the color of Left and Right centers. In our example, we're looking for yellow and white stickers on the purple orbit. Edges with those stickers are bad.
 On the Up side, there's a white sticker so its edge (⬜🟩) is bad.
 At the Front two spots, there are no whites/yellows.
 On the Down side, there's one white and one yellow so we found two more bad edges (⬜🟦, 🟨🟥).
 At the Back two spots, there are no whites/yellows.
We found three bad edges so far, let's mark them with tape.
Rule #2
Rule #2: Look for U and D stickers on the outer orbit. Their edges are bad.
In our example, we're looking for orange and red stickers on the outer orbit.
 On the Left side, there are no oranges/reds.
 At the Front two spots, there's a red sticker so 🟥🟩 is the 4th bad edge.
 On the Right side, there's an orange sticker so 🟧🟦 is the 5th bad edge.
(The red sticker is on an edge we already know is bad.)  At the Back two spots, there's an orange sticker so 🟧🟩 is the 6th bad edge.
We've found all 6 bad edges! Here they are.
There will always be an even number of bad edges, from 0 to 12.
The Rules Explained
The rules can seem magical, but this is why they work:
Rule 1: L and R stickers on the purple orbit cannot be solved with natural moves, because their solved positions are all on the outer orbit. Natural moves can't move stickers between orbits, so those edges are bad.
Rule 2: It's the same logic for the U and D stickers.
3. Solving EO
Finally we'll learn how to fix these bad edges! Here is our main strategy:
Strategy: Fix 4 bad edges
F
or F'
flips the orientation of all 4 edges on the Front layer. If they are all bad, they become all good.
Press ▶️ to see! (Bad edges are red, good edges are green)
That means we can place 4 bad edges on the Front layer with natural moves, do F
/F'
and they'll become all good!
Continuing our example:
 We see there's already 2 bad edges at the front.
 We can do natural
L'
to move a 3rd edge to the front.  Then natural
U2
for the 4th edge.
Then there's 4 bad edges at the front, we can do unnatural F
to orient them.
L' U2 F
Great, we've fixed 4 bad edges at once. Before we solve the remaining bad edges, let's master this strategy.
Using F2 to place edges
We're using natural moves to place the bad edges on the Front layer because they don't mess up the orientation of edges.
In addition, we can also use F2
, it doesn't change edge orientation either!
F2
is like doing F
twice. Flipping the orientation of edges twice is the same as doing nothing.
Here's an example where using only natural moves would be hard:
Moves:U' L U D
With F2
, it's much simpler:
F2 U2
In summary, we can use natural moves and F2
to move edges around without affecting EO.
Placing bad edges at the back
Everything we've learned about the Front layer works for the Back layer too!
B
and B'
flip the orientation of all 4 edges on the Back layer.
So we can also place 4 bad edges on the Back and do a B
or B'
to fix 4 bad edges.
This is useful when there are already more bad edges at the Back than the Front.
B2
also doesn't affect EO, so we can move edges around with B2 as well.
Summary
To fix 4 bad edges at once:
 Use natural moves,
F2
andB2
to collect 4 edges on the Front or Back.  Then do
F
/F'
orB
/B'
to orient them.
Repeat this strategy, fixing 4 bad edges each time. We'll either orient them all, or there will be 2 leftover bad edges. In our example, we have 2 leftovers. We need a strategy for that!
Strategy: Add 2 bad edges
There's no way to directly orient 2 edges, so our strategy is to add 2 more bad edges to get 4 total. Then we can use the previous strategy to orient the 4 edges.
The idea: place exactly 1 bad edge on the Front or Back, and flip with F
/F'
or B
/B'
. 2 new bad edges will appear.
Let's try that on our example.
There's already exactly 1 bad edge placed at the Back, so we can do B
to make two more edges.
B
Now we have 4 bad edges, so we can use the strategy from before to fix them.
R' B
Now EO is solved, congrats! 🎉 You've learned the fundamental concept of ZZ. Here are some tips and tricks to help you get started with EO.
4. Tips & tricks
Keeping track of bad edges
In this tutorial, we've marked the bad edges with tape to keep track of them. But in your own solves, it can be hard at first to remember where the bad edges are.

As a start, you can put your fingers on the bad edges.

Try drawing imaginary shapes. 2 bad edges can make a line, and 3 on the same side can make a triangle. That can be a lot easier to remember.

If you have more bad edges than good edges, you can track the good edges instead. For example, 8 bad edges means there are 4 good edges that you can track instead.
Strategy for 6 or 10 bad edges
To orient 6 or 10 bad edges we learned to do this:
 Orient 4 edges (once or twice) to get down to 2 bad edges
 Add 2 bad edges to have 4 in total
 Orient the 4 edges
Here is a special trick that can simplify your solutions:
 Orient 2 edges at the beginning
 Orient 4 edges (once or twice) to get down to 0.
Place exactly 3 bad edges on the Front or Back, and flip with F
/F'
or B
/B'
.
2 bad edges will disappear.
We couldn't use this trick when we had only 2 edges left, because this trick requires at least 3 bad edges. That's why it's useful for 6 or 10 bad edges.
Practice
At the beginning, EO will be hard to do. But it gets much easier with practice. You'll be able to recognize bad edges quicker, find solutions more easily and plan more of it during inspection.
What's next?
Congrats! You've learned EO. We suggest doing some untimed EO solves to get more familiar with EO. Then you're ready to move onto EOCross.