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Elliptical learning is a concept originated from my academic video game research. This is an attempt to apply it to the design of fire mechanisms.

Sebastien Hock-koon, Blogger

May 4, 2013

11 Min Read

What is Elliptical Learning ?

Bill Kunkel (2003) considers that a “great video game” should take “a minute to learn and a lifetime to master.” In my PhD research, I try to understand how this kind of game works in terms of learning. My main theoretical tools are Gibson’s affordances (Gibson, 1979). An affordance is an action possibility offered by the properties of an environment to the capacities of a subject. Affordances are independent from the subject’s perception. An affordance exists whether or not the subject is able to perceive it. According to Linderoth (2010), learning is “about becoming attuned to perceiving and being able to utilize specific sets of affordances.” Consequently, learning a video game refers to becoming able to perceive and to use the affordances it offers.

What does it imply for great video games? Any video game offers many possible actions to the player, which means many different affordances. Some are short and simple, such as rotating a tetramino in Tetris; some are extremely long and complicated, such as obtaining the “Grand Master” Rank in Tetris: the Grand Master 2. Mastering a video game would mean being able to perceive and use all the affordances it may offer. So, it would take a lifetime, or at least years, to be able to perceive and use all the affordances offered by a great video game. Such a game cannot be fully learnt in a minute. As part of my research, I trained myself for six months to perform a one-credit run on the arcade version of Alien vs. Predator. I studied the way I learnt this game (Hock-koon, 2012). It appears that great games “do not take one minute to learn and a lifetime to master; it takes one minute for the player to believe she or he has learnt the game while it takes years to actually master everything that can be mastered.” I call this particular learning “elliptical learning.”

The key elements of elliptical learning are closure and ellipsis. Closure refers to the action of completing or understanding something as well as the feeling that something has been completed, or understood. Ellipsis consists of the omission of some elements of a phenomenon. When ellipsis and closure are performed at the same time, the player might think she or he has understood something while omitting a part of it. In Alien vs. Predator, I made several successive elliptical closures about many of the game mechanisms. I had to go through several layers of understanding, or misunderstanding, before finishing the game in one credit. This succession of illusory understandings is elliptical learning.

Applying Elliptical Learning to Game Design

Affordances also tell us that if an action is possible, it means two things: the subject performing the action has the required capacities and the environment in which the action is performed has the required properties. Of course, affordances are about physical actions and learning is not, or at least not only, a physical action. However, if a player can go through elliptical learning with a video game, one might assume that she or he has the required capacities and that the game has the required properties for this type of learning. Concerning the player, the ability to perform ellipsis and closure is crucial. But, as a game designer, there is close to nothing you can do about it. You can only create the game, you cannot be sure that the player has the required capacities. So let us focus on the game’s properties allowing elliptical learning. I call “elliptical mechanisms” the mechanisms that have several levels of understanding and thus allow elliptical learning.

Elliptical mechanisms are not about the emergent complexity of a system resulting from the interaction of simple rules. Elliptical mechanisms are actually complex rules that the player can mistake for more simple rules. Every player is different: some want games that are easy to understand, some want games that are hard to master. Elliptical mechanisms allow a fast but rough understanding as well as a deep but long understanding. Of course, several elliptical mechanisms may also interact in order to create an even more complicated system. As elliptical mechanisms may be understood roughly, several different elliptical mechanisms may have the same first and inaccurate comprehension. The deeper the player’s knowledge becomes, the more different they will appear to be. To illustrate this, I will describe three different elliptical fire mechanisms with the same first and rough description: “Press a button to fire.” The three examples are Halo’s Plasma Rifle, Linn’s gun in Alien vs. Predator, and Star Fox 64’s laser.

Examples of Elliptical Fire Mechanisms

Halo’s Plasma Rifle is easy to use but not easy to use properly. At first sight, you may think that pressing the trigger to fire is all that you have to know. But this weapon has two fire rates: a fast one (compared to the Plasma Gun) and a faster one. The second rate is activated after holding the trigger for a few seconds. It is more powerful and less accurate but it also heats up much more. The most efficient way to use the Plasma Rifle is not to use the faster fire rate; it is to keep shooting at the first, slightly slower, rate. This allows you to fire longer with a fast and accurate weapon. But to do so, you need to press and release the trigger at the right rhythm. There is more to this weapon than just pressing to fire.

Linn Kurosawa is the character I chose to perform the one-credit run on Alien vs. Predator. Understanding the way her gun works has been fundamental in order to improve my game playing. When you shoot, the Gun Gauge empties; when it is completely empty Linn has to reload and she cannot move for a few seconds. There is a trick to be able to move while reloading (see this article) but even with this kept in mind, managing ammunition is critical to survive. When Linn fires, she starts shooting just in front of her feet and raises her gun. If the enemy is too far away, some bullets are wasted. But when she fires while jumping the angle is constant; it is possible to hit an enemy with every bullet if the player shoots at the right time.

Linn's fire patterns

Aliens Vs. Predator

Shooting also knocks the targets back. When a skilled player combines ammunition and movement management, Linn’s gun truly becomes the most powerful weapon of the game. As far as I am concerned, I would tend to think that it is possible to finish the game just with this gun, while it is impossible to do so with only one of the other guns.

The last example, Star Fox 64’s laser, may be the deepest and the most elegant fire mechanism I have ever encountered. There are two ways to use the laser. If you press the fire button, the ship fires lasers; if you hold it, the laser is charged and locks onto an enemy to shoot a homing ball that explodes on impact. Let us begin with the first. To shoot a blast of laser, the player needs to press the fire button repeatedly. She or he will get a fire rate equivalent to her or his button-pressing pace. But like the Plasma Rifle, the laser may be used more effectively. When the fire button is pressed only once, three lasers are fired at a very fast pace. If the player presses the fire button again at the right moment, she or he can get another three-laser burst right after the first, and so on. With the right rhythm, the fire rate will be equivalent to the one of the automatic fire function.

Things get even more interesting with the charged laser. When it touches an enemy that has been locked onto, the explosion may take down some additional enemies. If the player is facing an enemy formation, locking onto the right enemy may kill them all with one shot. Destroying a basic enemy with the regular laser or the charged laser only gives one point. Destroying the same enemy with the explosion of the charged laser gives one additional bonus point. Let us take a four-enemy formation as an example (the brown object is an obstacle):

Four-enemy formation close to an obstacle

StarFox 64

If the player shoots all four enemies with the regular laser, she or he will only get 4 regular points. If the player shoots #2 or #4 with a charged laser, only three enemies will be destroyed: one by the shot itself, two by the explosion. If the player destroys the fourth enemy, she or he will get a total of 6 points (4 regular points and 2 bonus points). If the player shoots #1 or #3, all four enemies will be destroyed. She or he will get 7 points (4 regular points and 3 bonus points). But it is not over yet, one more point may be earned.

By pressing the Z and R triggers, the player disables the lock so that the charged laser will shoot straight. It may seem useless at first; but it is critical to master this to get a very high score. Shooting the charged laser without locking allows the player to destroy the entire formation with the explosion. If the player shoots a non-homing charged laser on the obstacle at location #5, all four enemies will be taken down by the explosion. In this case, she or he will have 4 regular points and 4 bonus points, which is twice the score attributed for destroying the formation in a normal way.

In addition to this outcome, the laser takes about half a second to lock a target once it is charged. When the lock is disabled, it is possible to fire as soon as the laser is charged. So if a player is able to aim precisely, disabling the lock will allow her or him to fire the charged laser faster. Used correctly, this additional fire power may take down more enemies and earn more points.

Ways to Create Elliptical Fire Mechanisms

Of course, none of these three mechanisms require years to be mastered. But if every mechanism in a video game is elliptical, it might actually take a very long time to master. I had been playing Alien vs. Predator for years before the beginning of my training. I thought I knew how it worked, but I was wrong. I had to play Halo in Heroic and Legendary modes to discover the subtleties of its weapons. And I had to study Star Fox 64 as a part of my research to find how to get a high score.

Here are few guidelines to create elliptical fire mechanisms inspired by these examples:

  1. A trigger has four states not two: A single button may be held down or not, but it may also be pressed and released. It gives four different states that may have different effects.

  2. A fire mechanism may be altered according to a variable: The way a weapon works may be changed according to a variable. It may be time, ammunition, the state of the character, or another such variable.

  3. Alterations should be more or less efficient according to the situation: Alterations should not only differ in raw power, they should have different characteristics. These should be more or less efficient depending on the situation and the way the weapon is used.

  4. The most difficult way to use a weapon should always be the most powerful or the most rewarding: If the easiest way to use a weapon is also the most powerful or the most rewarding, the player might have little motivation to learn anything else. Learning may be hard. Some players may find their own motivation; but many will not. It is better to give them a good reason to learn. Basically speaking, there should be an easy way that anyone can use and a hard but more efficient way that has to be mastered.


Gibson, J. J. (1979). The ecological approach to visual perception. Houghton Mifflin.

Hock-koon, S. (2012). Affordances of Elliptical Learning in Arcade Video Games. In Proceedings of DiGRA Nordic 2012 Conference. Presented at the DiGRA Nordic 2012 Conference: Local and Global – Games in Culture and Society, Tampere, Finlande. Retrieved from http://www.digra.org/dl/db/12168.59440.pdf

Kunkel, B. (2003). How Alex Pajitnov was Tetris-Ized! Why Tetris’ creator got the cultural bends upon his arrival in America. Good Deal Games. Retrieved May 4, 2009, from http://www.gooddealgames.com/articles/Tetris_Alex_Pajitnov.html

Linderoth, J. (2010). Why gamers donʼt learn more. In DiGRA Nordic 2010 Proceedings. Presented at the DiGRA Nordic 2010: Experiencing Games: Games, Play, and Players. Retrieved from http://www.digra.org/dl/db/10343.51199.pdf

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