Here are some more advanced tactics for the player who wants to go head-to-head against the best. Although these skills can be described, what counts in the number of hours you put in perfecting them. Enjoy.
In combat terms and in sports, a feint is a fake attack. It is a movement of misdirection that, when executed well, causes the other player to commit themself to a defense. If you know what their defense will be, you can follow the feint with a real attack that attacks their weak point.
If that babbling doesn't make any sense, don't worry. Feinting is a critical skill and we'll spend some time with it.
Let's look at the speed kill described at The Basics page. The normal way this is executed is by grinding the target's wall for a long time. As you approach the target cycle, you will turn out from his wall, then three times in the opposite direction, then one more time to bring you grinding against the other side of his wall.
A feint that builds on the speed kill might be to turn out and then make the first of the sequence of surrounding turns. At this point the other cycle is forced to make a defensive move of some sort and you know in advance that he will do that, because if he doesn't defend against your feinted attack, you will kill him. The normal defense against a speed attack is to turn in the direction of the attacker, interposing a wall. If done late enough, the attacker can be tricked into crashing into this wall. So knowing that the defender will make this defensive move, you can turn slightly earlier and then make your rapid second turn in the box. At this point, you know that the defender will attempt to defend against the box attack. Another turn away from the attacker is all it takes to finish the deed. TODO: get a picture of this too.
The best feints are feints where the defender must take the attack seriously not because he believes it to be an attack, but because he has no choice. This is comparable to a sword fight, where you feint towards the other fighter's heart. If he doesn't stop the thrust, you will kill him. But if he does, he may open up his side to an attack. A good feint will be followed through by an unpredictable attack, but making unpredictable attacks requires a certain amount of experience.
If the speed feint didn't make sense to you, consider this one, based loosely on a basketball move. In basketball, it's common for the person who has control of the ball to turn towards one teammate and start a passing move. This usually brings the defender around to try to prevent the pass. Many players will then pass the ball in the opposite direction to a different player. Consider the fake involved there. Now apply it to a light cycle. You are approaching more or less head on to another cycle. If you turn right or left, he'll follow you. If you go straight, he'll turn a wall into your path. What do you do?
You fake him. You turn left, then quickly turn right twice. This brings you in the opposite direction that he's expecting. Many players, upon seeing the left turn, will also turn left, intending to pass you and grind your wall, knowing they'll come around to an attack on you at the other end. Some players will turn to grind on your new wall and try to chase you. These players will be killed by your two quick right turns when they find themself in a dead-end. The other players, the ones intending to grind your wall and come around to fight, will be going the same direction as you. Two more well-timed left turns will bring you against his wall and leave him in a very small box.
The Battle of the Grinds
There are two excellent tactics associated with grinding. Very often you will find yourself traveling parallel to an enemy cycle at a distance where neither of you can mount a successful attack. Neither of you can advance, either, and if you turn around, you will be pursued, possibly at the pursuer's advantage. So you both drive straight, waiting for the other to make a move. Eventually you will come upon a wall and you will have to turn. What do you do?
The first thing that comes to mind is to tap the wall and turn away from the enemy cycle. This is a good move for new players because they will usually not be pursued, and the stalemate is very hard to break. Unfortunately, many players will grind closer to the wall and turn towards you. This means they will pursue you through that little space, shooting out between your cycle and the wall you're grinding and coming out at a considerable advantage to you. In this case, turning away is a bad move if you don't know what to do about it. While there are definitely counter-moves to deal with the player who turns towards you and attacks, there are other ways to deal with this.
One way is to turn in towards the other player. This doesn't make sense if you can't possibly grind closer to the wall than he can, does it? Well, it does. The trick is to turn again and get on his wall and grind away. While you usually won't kill the other player, the stalemate will be broken because when the two of you reach the ends of your walls, you will be going faster than he, and that speed conveys a considerable advantage.
Turning towards the other player also shows him that you're not scared to fight him. While it may not yield a kill right away, that player and any who are watching will remember that you did that. The next time they come against you, they will be inclined to try to grind as close to the wall as possible, and that is their mistake. It is more common to lose the Battle of the Grinds by overextending your grind and dying against the wall than it is to lose it by not grinding close enough.
The Lag Kill
The Lag Kill has an interesting requirement that most other tactics don't have: humility. If you have a need for the other player to always know and concede that you have killed him, then the Lag Kill isn't for you. In order to use the Lag Kill, you need to be able to deal with the other players blaming lag for the kill. Many players already blame lag when they die more often than it's true, but once you start using lag as a weapon, they'll be half right, and they will frequently completely miss the facts of the matter.
The mechanism that enables the Lag Kill is network latency. Look at your ping and look at the ping of your target. Ok, now add them together. Usually you'll come up with a number near 300 milliseconds. That means that the other player will not see the results of your turn for almost a third of a second. That's a long time! It also means that you won't see the results of his turn for the same time period, but every good attack has a danger you need to account for, and for this one, lag is it.
So consider the time it takes for the other player to see your moves and what he sees in the meantime, which is usually your cycle going straight. With a little misdirection, you can convince him you are somewhere else completely and essentially attack him from a blind spot.
The most basic form of this type of attack is as a defense. Picture yourself driving in a straight line. Now someone gets on your wall and starts grinding it on the left side, obviously aiming for a speed kill. You know that before the critical 1/3-second interval he's going to turn off to box you in, so before that interval you turn left. The other player now thinks you're turning left to block him, so he goes out a little farther, but greedily comes back to close you in. What he doesn't know is that the 1/3-second interval started right after your turn, and you've turned right again, putting you back in your original direction. As he goes in to finish his box, he doesn't find you trapped in it, he finds your wall instead, and it's entirely possible the server will kill him before he even sees your wall!
Another common form of this attack is when you are going nearly head-on towards another player. Before the cycles are within the 1/3-second interval, you turn right. Then the interval starts and you immediately turn left twice, leaving a short dead-end hallway. Many players will follow you after your first right turn and get stuck in the hallway, and again find themselves killed by the server before they even see the hallway.
The disadvantage to this tactic is that you get used to it, and eventually you will come up against someone who's ping is so low they can see your hidden moves and deal with it, and lag attacks don't work on those people.
As I said at the beginning, many players will not acknowledge that you killed them on purpose. Some players will acknowledge it only after you've killed them quite a few times, and you will find yourself being consistently underrated for your abilities compared to actual match wins, so you need to have a thick skin. You need to be able to wipe out the whole grid and deal with someone saying "How did he win? He sucks!" It's very hard to convince people that your attacks are real, that you really deserve credit for the kills, so you need to be able to satisfy yourself knowing you did a good job and not depend on other people to praise you for it.
The Dance of Time
This is a specialty tactic that is only useful when it's you against a bunch of people, 3 at the minimum, 5 is better. It's basically a dance, but it's a deceptive dance. The purpose of the dance is to trick the other players each into thinking they can dart out there and get you. When you have 4 or 5 or more people coming at you at once, you want them to think they can jump in and get you without getting killed and gently lead them into a wall. It's very difficult, and it's another move you can make that you won't get proper credit for making. The thing that makes it so hard to do is that every time is a custom job: you can't just train yourself to do it, it has to be tailored for the opponents. It's a rare tactic that's only really put here to try to force a table of contents to be generated for this page, but it's been known to work.