EOLine:

For advanced ZZ, you will want to move away from the traditional EOLine. Instead, you will want to choose something with more favourable ergonomics than normal ZZF2L, as there are relatively a lot of regrips and blind spots (stickers you can't see) in normal ZZF2L. Instead, we will want to aim for something which is more similar in ergonomics to CFOP F2L while preserving EO and all the other advantages of ZZ, so the most obvious option is...

EOCross

Fairly self-explanatory, instead of solving EOLine, you solve EO with a Cross. It is definitely more ergonomic, as you eliminate the blind spots at DR and DL and you eliminate half turns and most other moves which cause regrips, while reducing F2L to mostly quarter turns. This means that ZZF2L with EOCross is mostly regripless due to no rotations and only quarter turns. It also allows for a more automatic F2L. This is because there are half the number of F2L "cases" as in CFOP (20 compared to 41) and the centers are fixed. This means that if you know what your R and L colours are, you don't ever need to check where a pair belongs. This means that TPS can be maxed out without the need for rotating, unplanned F moves and flipped edges in slot. The biggest disadvantage of this approach is that the first 2 layers (including EOLine/EOCross) is approximately 7 moves less efficient, although the much higher TPS limit more than makes up for this in almost every case. A smaller one is that this is approximately equivalent to planning XCross every solve, although it is entirely possible.

Now that we've looked at EOCross, if you want a bit more of a traditional ZZ, this option might be the one for you. It's called...

EOArrow

This is the equivalent to solving EOLine plus either the DR or DL edge (the unsolved edge being on the side of your dominant hand). This is useful as you don't get nasty solutions for your weaker block by having all the pieces on the wrong side, as well as eliminating some of the regrips of your non-dominant hand. It also gives you the efficient and ergonomic "single block". This is because one block (in comparison to 2) only ever requires <RU> or <LU> and can be done very quickly with a high TPS and blind spots aren't a big issue. It is also more efficient than EOCross by approximately 3 moves, averaging out to be around 34 moves. There are some disadvantages though, with the main one being that it forces you to solve in a specific order (the side with the edge solved first) and there are still those double turns and regrips, even if less pronounced than in EOLine.

It is highly recommended that if you're serious about being fast you will want to switch to one of these 2 variants to up your TPS significantly.

XEO____

This is simply doing either EOArrow or EOCross but solving a pair as well. (Note that XEOArrow is exactly the same as XEOLine). This is a very advanced and probably not consistent technique for 15 seconds of inspection, but if mastered would boost your solves significantly. As it is so difficult though, it is more realistic to just know where your first pair (preferably one on your non-dominant side) will end up after EOCross/EOArrow, as this will theoretically allow for a perfectly smooth transition to F2L.

F2L

This step takes up a significant portion of the solve, so you will want to optimize it as much as possible. You can do that using several tricks and alternative solutions.

Keyhole

This is by far the most "bang for your buck" way of optimizing your F2L. It is really simple and utilizes D moves (which preserve EO). You know how in the beginner method we used D moves to insert corners? Well, it's exactly the same concept. If you have an edge solved but not the corner and another empty slot, use D to move the place where the corner belongs to be in that empty slot, insert the corner and undo. You can also apply this to an edge. If the corner is solved, turn the D layer so that an unsolved corner is below the slot, insert the edge then undo D. It is most effective though in multislotting. If you have an edge of one pair solved and a corner of another pair solved, move the D layer so that the unsolved corner is below the unsolved edge. Now, in the created slot, solve the corresponding corner and edge as if they were a pair. It is easiest to see if you do D R U R' D' on a solved cube. The DFR corner is solved, as is the FL edge, so you can do a D to move the unsolved corner underneath the unsolved edge. Solve this pseudo pair as normal, then undo D. Solving that case just RUL would require a lot more moves than with keyhole, plus, due to the good ergonomics, you can tur quickly.

Pair solutions

You will want to make sure that for any pair that you solve that it's the fastest solution for that pair. It's not a difficult concept to grasp, just mess around with the cube and watch videos (CFOP ones will help a lot but you have to be careful that what they do doesn't mess up EO). This is especially important for EOCross solvers, as all of your F2L is pairs, so having almost good solutions 50% of the time will doubly impact you compared to EOArrow solvers. You will also want to use different tricks in last slot to help influence last layer. For example, you can learn 8 simple and ergonomic commutators that will help you skip OCLL for an extra move when they come up or you could learn the simple ZZ-C cases so that you can skip OCLL for no extra effort. There are also a couple of WVCP cases that are very simple and easy to learn. There are some on the doc in External Resources, as well as suggested last slot solutions. Another aspect of this is multislotting. This is simply where you influence the next pair while solving your current one. In ZZ, you can do things such as inserting with U2 instead of U, or doing an L before you insert your pair. They only have to be simple things, but they can become very beneficial.

Block solutions

This can only really improve by doing lots of solves and focusing. You should aim for an average of 13 moves for a single block, but beyond that it's just practice. You can implement other tricks though such as keyhole, as the <RU> or <LU> moveset is just a general guide, not a fixed rule, as is the <RUL> in ZZF2L. Over time, you will start to pick out patterns and generally good ways to solve the whole block.

Lookahead

This is probably the most important part of any F2L, as knowing all these tricks but pausing for a second after each one will only make you slower. Instead, aim for a smooth solve with no pauses and gradually increase TPS, always pushing yourself, but whenever you feel like you are pausing again, turn slightly slower. The aim is to turn at a speed which pushes your lookahead without hampering your TPS. This comes from solves and just a general focus on it all the time. The one time where you shouldn't do this is just before a competition. Instead of pushing yourself, find a turning speed at which you can get your best times without pausing that is comfortable. This means that you can be more consistent in the competition itself.

Last Layer

This is the most algorithm intensive part of your solve, so knowing the best way to deal with any situation is key.

During last slot

You will want to gather as much information about your last layer as possible during this stage, such as OCLL/COLL or the EP. This will set you up for a smooth transition.

The optimal way to solve it

If you could only choose one way to solve your last layer, ZBLL is by far the best. Even if there are certain situations where it isn't as good as another variant, they're definitely in the minority and full ZBLL is the best. This means that for all 493 cases you need to have the algorithm at a decent speed (sub 1.5 preferably) and have a consistent recognition system. You could either use Baum-Harris, Tran, blocks or one which utilizes 2 sided PLL recognition. With Baum-Harris you recognize the COLL case and the position of the UF and UR edges in relation to a specific reference corner. This can be made AUFless by having 2 possible reference corners for each COLL case, one a U2 from the other and you can just tilt the cube to recognize the ZBLL case by looking at the corner if it's in UFL instead of UFR. Tran style is similar to Baum-Harris, but instead of looking at the UF and UR edges, you look at the 2 edges which would be solved in UF and UR. This requires looking at more than 2 sides of the cube or AUFing though, but using process of elimination you can prevent this in certain cases. Block recognition is where you recognize the COLL then look for patterns unique to that case anywhere. For the one based off 2 sided PLL recognition, you mentally twist a corner to see what PLL case you get, then do the algorithm specific to that case. It is good as it allows for 2 sided recognition instantly, but bad as you have to mentally twist a corner almost every time it's used. As you can see, there are several different options. Choose the one you find the most natural.

Option Select

This is a very advanced concept and requires knowledge of more algorithms over ZBLL. The short of it is when you have a case where another variant is better than insert then ZBLL, you do that instead. Here's a simple example: do R2 U R2 U R2 U2 R2 U' R U R' on a solved cube. As you can see, you have a pretty average F2L case but a very good TSLE. It is only 3 moves, R U' R'. Then you do TTLL, which is generally equal to a ZBLL. That means for the good TSLE cases you can have the equivalent of a 3 move insert then ZBLL equivalent instead of a 7 mover then ZBLL. You wouldn't want to do ZZ-CT every time though, as it forces the FR slot if you're not slot neutral with TSLE, or awkward ergonomics if you are. It is also less efficient than ZZ-A. Currently, option select isn't very well explored for ZZ and is definitely an area that has a lot of potential to improve ZZ further.

Final thoughts

As an advanced solver, the rest of your ZZ speedsolving journey will be a mix of optimizing your F2L for speed and learning ZBLL then other algorithm sets. If you can master both aspects you will be well set for being one of the fastest solvers out there. The people who worked on this all hope that this helps everyone who comes across it to become a better speedcuber.