1. A network game system including a plurality of game machines each having a server function and a client function, in which each of the plurality of game machines operates as a client and at least one of the plurality of game machines also operates as a server, thereby providing a game to be played by players of the plurality of game machines, comprising: play evaluation value calculating means for calculating a play evaluation value corresponding to each of at least one of the plurality of game machines during the game; switching determination time monitoring means for monitoring to see whether or not a predetermined switching determination time arrives; and server switching means for switching a game machine operating as the server from a game machine currently operating as the server to another game machine of the plurality of game machines, based on the play evaluation value calculated by the play evaluation value calculating means, in the event that the switching determination time arrives.