Provides variety, diversity and quantity. It is needed for generating large worlds, levels for roguelikes, and balancing multiplayer games (when randomness favors newer players). It is also useful when players make plans and strategies based on information that is randomly generated.
Humans are bad at understanding odds because of cognitive biases. So game developers lie about numbers to match the broken understanding of probability in our heads. We are better at understanding analog things like dice (independent probability) and cards (dependent probability) and the randomness they bring.
Occurs before the player gets to make a decision — levels in a roguelike, drawing a card of hands. Unpredictable starting conditions might dictate the outcome, so, games should find clever ways to present good ones.
You make a decision and then luck takes over and tells you what happened — bullets hitting target based on probability, random encounters, or loot boxes. These can take away control from the player.
Information Horizon & Flow
Complete information transparency gives players too much information and may lead to analysis paralysis. Disrupting players’ plans with new information is exciting though.
Spikes in new information disrupts your plan and forces you to regroup and rethink. Spikes of high value information should happen at regular intervals with a slow regular flow of information between spikes.