Agôn (Competition) – Examples include: racing, wrestling, billiards, chess. Contests of skill, sports in general. Agreed upon rules.
Alea (Chance) – Examples include: Counting-out rhymes, heads or tails, betting, roulette, lotteries.
Mimicry (Simulation) – Examples include: Games of illusion (role-playing), tag, masks, disguises, charades. Theater and spectacles in general.
Ilinx (Vertigo) – Examples include: Swinging, whirling, carnival rides, rock climbing. A negative example or corruption is intoxication or mind-altering drugs.
These classifications can be combined. You might have a game that involves competition and chance, like Settlers of Catan, or one that involves simulation and vertigo. Caillois favors some combinations over others, but I’m not sure I buy it. Can a game have competition and simulation, or competition and vertigo?