Cardinality of Gameplay

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The cardinality of gameplay refers to the degrees of freedom the player has with respects to movement (or the control of movement) in a certain game. For example, the player may control a character that moves left and right or have to place tokens on a 2-dimensional board. Other games, allow the player to control movement in 3 dimensions.

It is important to note that the cardinality of gameplay is related, but not necessarily the same as the cardinality of the gameworld. For example, while the classic game of Monopoly is played on a two-dimensional board, the players tokens are limited to move along one dimension and always in the same direction. In this example, the cardinality of gameplay is 1D.

We also note that the cardinality is only with respect to the movement the player can perform and this is independent of other actions, or that the effects of those actions may occur in some other dimension. For example, in Space Invaders the player controls a ship that can move from left to right along the bottom of the screen. The players ship can also fire shots that travel upwards along the screen. In this case, the cardinality of gameplay is 1D, despite the fact that the gameworld is 2D and that the players shots have effects outside of the limits of the players movements.


Strong Example

Super Metroid

Super metriod has complete cardinality in two dimensions, with a slight hint of a third. The player is allowed to jump, crouch, walk, run, scale walls (through the use of wall jumping or bomb levetation), and swim in water. At times, the player may pass behind or infront of some seemingly solid item, giving the impression of depth and the idea of a third dimension in the the gameplay. (you need to go BEHIND that wall to get the powerup.)

World Of Warcraft: The Burning Crusade

In the expansion to the MMORPG World Of Warcraft, players are entertwined in a fully functional three demensional gameworld. Movement on the ground includes forwards, backwards, left and right, including jumping and/or flying on a player purchased mount such as a Griffon. The third dimension is further explored through water when the player is allowed to swim.

Space Invaders

In the classic Space Invaders, the cardinality of gameplay is one-dimensional, since the player can only move from side to side.


The cardinality of gameplay is two-dimensional. You move left, right and down. There is the gravity factor that forces the piece down, and even though you cannot move up, it still is two-dimensions.

Cave Story

In the PC/Mac platformer "Cave Story", the cardinality of gameplay is two-dimensional, as the player controlled character, a robot, can walk left to right, and can jump and fall.

Descent 3

In Descent 3, the cardinality of game play is entirely three-dimensional. The player ship can move forward, backward, up, down, as well as pitch and yaw through completely three dimensional space. Much of the gameplay involves exploring all angles of the environments.

Lord of the Rings: Battle for Middle-Earth 2

In Lord of the Rings: Battle for Middle-Earth 2, cardinality of gameplay is two-dimensional. The player can control units, but they can only move North, South, East, or West (up, down, right, or left on the screen)

Final Fantasy Tactics

During battles, the characters can be moved in 3 dimensions according to the grid-like map. That is, they can move in a rotate-able XY coordinate plane and move vertically depending on the terrain comprising the battlefield.

Weak Example

Scorched Earth

A weak instance of cardinality of gameplay can be found in Scorched Earth, a battle of wits with cannons, where the player selects the angle of rotation and the speed of the shot to hit her enemies. The angle rotates around one axis, while the speed selected constitutes a second, weak axis, since the shot can only go forward (not backwards). However, a three-dimensional version of the game made by fans allows two-dimensional cardinality, since the player can in the four directions to destroy the invaders. Scorched Earth also featured an optional purchasable item, fuel, which would allow the player limited horizontal movement across the terrain. The movement was limited by the slope of the terrain the tank was trying to navigate, often allowing the player to fall into pits which left them stuck and prone.

Mario Party Series

The cardinality of gameplay is difficult to measure in the games. This is due to the fact that you are moving your players along an interactive gameboard. You have no choice in what direction they are moving. Also, when you engage in the mini-games, the cardinality of gameplay is completely different. The question that comes to mind is that becasue the mini-games have cardinality, does that constitute the enitre game as having cardinality?

Tales of Symphonia

While ToS exhibits a strong indication of cardinality of gameplay when the character is roaming the maps and dungeons, it has very weak cardinality of gameplay within the battles. Inside of the battle system, the player is only able to move two ways: back and forth. He cannot move to his left or right according to the way he is currently facing. However, if he changes his point of orientation, i.e. switching his target from one enemy to another, he will be on an angle of moving back and forth compared to that object, which may in fact cross over his old path of movement. Regardless, this is a poor way of providing freedom in battles; therefore I feel Tales of Symphonia has very limited cardinality of gameplay within its battle system.

Project Justice

This game would be a strong example of a 2D cardinality were it not for the inclusion of a sidestep dodge. The player can move the character in a 2D plane with the ability to move forward, back, jump and duck. However with the push of the L button the character sidesteps away form the camera, this is not true 3D cardinality either as the player can only sidestep in a single direction, away from the camera. The camera also moves with the player giving an impression of a rotating 2D field.

Relations with other elements of the Ontology




Scorched Earth, PC-DOS, 1991

Space Invaders, Bally Midway, 1978

3D Space Invaders