Game Categories

In Roger Cailois' book 'Man, Play and Games' from 1961 (or 1958 for the French version, 'Les Jeux et les Hommes') the French sociologist explains how all games can be placed into four categories: Agòn, Alea, Mimicry and Ilinx.
Agòn is any game that involves competition, examples of this include wrestling, chess and Call of Duty.Alea are games that incorporate chance into the main mechanics and rules of the game, examples of this include heads or tails, gambling and rolling dice. Mimicry is the act of role play or pretending to be someone/something else, examples of this include Skyrim, young children's dress-up games and The Stanley Parable. Ilinx is games that bring about a sense of vertigo, examples include roller coaster simulators, children spinning games and dancing.

I have chosen six games and analysed them using Cailois' four categories, as seen in the table below.

League of Legends - Agòn with aspects of Alea

It's a very competitive game with the main objective being the demolition of the enemy base. The players also aim to achieve more kills than the enemy team and even more than their own team-mates.
It hosts a competition including teams from around the word, showing that people have dedicated their lives to becoming better than the rest
At first glance League looks like it would fit into the Mimicry category, however this is not the case as the game lore explains how the player is a 'summoner' who controls the in-game characters (champions); this separates the player from the world in which League is set as they are not playing as any other characters directly but as themselves.
There are some Alea aspects in the game; in ARAM (All Random, All Mid) every player's champions are chosen at random, leaving a chance that they will have to play as weak champions or that the enemy team may get characters that directly counter their team.
In addition to this, there is a game mode in which the player cannot see the enemy team's champion choices until the game begins, leaving the chance of picking characters that are weak to the enemy's, similar to in ARAM.

Portal 2 - Mimicry with aspects of Agòn and Ilinx

It perfectly fits into the Mimicry category as the player enters the world Aperture Science Laboratories and plays as Cell, a human trapped in a deep underground science center, who must fight against the many obstacles she faces throughout the game.
Agòn plays a part in the game as the player can choose to try and beat their previous times on speed-runs. The player is also 'competing' against the main antagonist to try and survive.
Ilinx is incorporated too as the player gets thrown around a lot during the game, especially when encountering infinity loops and spring boards.
There are no aspects of Alea at all as it is a very linear story-driven game; nearly everything that happens within Portal 2 has been designed to happen by the game designers.

The Binding of Isaac - Alea and Mimicry

Alea is a huge part of this game as the dungeons are randomly generated: the layout of the maps are random; the monsters' spawn points are random; the treasure items are random; secret rooms are random and even the final bosses are random.
The player cannot plan how they are going to play the game, as is possible with other games such as Portal 2, as it is down to complete chance as to whether or not the player will receive good items or come across particularly challenging enemies.
It also includes Mimicry as the player becomes Isaac, the main protagonist of the game. The player tries to escape the different types of dungeons and eventually must defeat Isaac's own mother.

Mirrors Edge - Mimicry, Ilinx and aspects of Agòn

The player witnesses the story of Faith and her fight to save her sister. The viewpoint of this game is first-person, making the Mimicry aspect very intense for the player as they are seeing through the eyes of Faith as she runs across rooftops.
The game also involves Ilinx as there is a lot of falling and tumbling as the player traverses across the city skyline; the player can even fall off of the edge of a skyscraper and watch from Faith's point of view as they plummet, right up until they are meters from the ground.
There are aspects of Agòn as the player can try to beat their own/other players' fastest times on speed-runs.

P.T. Demo (not a full game) - Alea, Mimicry and Ilinx

Alea is incorporated into this game as 'Lisa' (a ghoulish woman) can appear at nearly any moment in the game. Some people claim that there are certain actions that make her more likely to appear, although this has not been entirely confirmed. Nearly every play through of the demo is partially different.
The player must also play as a mystery character who seems to be trapped in a loop of walking through the same hallway over and over whilst investigating the goings-on of the family who had lived there previously.
The idea that this game fits into the Ilinx category could change depending on a player's personal experience whilst playing the demo, however it could be argued that the unnerving and tense atmosphere of the game can bring about a sense of 'vertigo' or a loss of control.

The Last of Us - Mimicry

This game is almost completely Mimicry as the player delves into the world of Joel and Ellie where they must fight the 'infected' humans and follow their story as they try to find a cure for such a disease. With an emotional story-line, the player really connects with Ellie whilst playing as Joel and creates a strong connection between the player and the world that the characters live in.
There is no Alea as everything is planned by the game creators, much like Portal 2.
There are no strong aspects of Agòn, however it could be argued that the player is 'competing' against the enemies to survive and complete the game.