Open games are fragments of games in the sense of game theory, that can be used to build games compositionally. They can also be thought of as games in the sense of game semantics between a System and Environment, in which the moves are states and payoffs. The System is jointly controlled by n noncooperative utility-maximising players, and the goal of the System is to be in game-theoretic equilibrium. This game-semantic viewpoint is a useful way of thinking about compositional game theory, with its often-mysterious composition operators becoming quite transparent when viewed in terms of game-semantic strategies.