Score is a versatile pattern can be used as a motivation factor, as a goal or as a field for competition.
A game's ending condition may be based on a scoring system (e.g. the first player to reach a certain score wins). Scoring may be used as a reward mechanism, e.g. a highscore table or a hall of fame.
Scoring may be a resource for which the players may compete. It can be regulated so as to have different effects. Some variations can be:
Scoring can also be negative so as to force beforehand thinking and planning.
Complicated systems can be devised. For example, scoring could be tied to experience points, similar to role-playing games or videogames. In that case, the scoring might become opaque and it could be difficult for the players to relate how individual game actions impact the final score.
Scoring may be used to support other patterns. For example economic transactions might use points as an a means of exchanging information of digital objects, or stealing might be implemented over a pattern of scoring.