Caillois' way of Describing Games

Paidea

Paidea is when games are played for fun, its not to win or lose or prove your intelligence or skill, it is just simply to play a game for enjoyment. This is linked with games that have less strict rules and give the player more freedom to play.

Ludos

This is when the game is competitive and you play to win and beat your opponents. these games tend to be based more on skill than luck (alea) to give it competitive dynamics. 

'Agon', 'Alea', 'Ilinx' and 'Mimicry' 

These words are a way of describing what type of game a game is. These definitions can intersect and overlap like Padiea and Ludos can.

Agon
This is when games a competitive and there is a lot of struggle in the game to beat the opponent. A good example of this would be any MOBA game.
Alea
Alea is games that depend on luck, these games are balanced by probability of certain outcomes. there is not as much skill or ways to employ strategy in these games normally. it all comes down to who is the luckiest player. Games that have dice or cards are strong 'alea' type games.
Ilinx
This is games based around movement. this could be race games like Snakes and Ladders. Or it could be a game like Monopoly where the movement of each player decides what happens to them in the games.
Mimicry
Mimicry is about being something or somewhere in a game you are not in real life, like a serial killer or a pro footballer or a goat for example like in the game 'Goat Simulator'

Its easy to see how the intersect with each other. in the game Forza 5 you are a proffesional racing car driver which is mimicry and Ilinx then you can race other players which is agon.