A game system has a plurality of slot machines, each slot machine having a controller for executing a basic game, and capable of making a transition to the second game from a middle of the basic game when a prescribed condition is realized; a second game device for executing the second game, which is provided as a physically separate device from the slot machines; a display for displaying images according to a game status of the second game device; and a center controller capable of communicating with these devices by being connected with them through a network. When a withholding of a right to make a transition to the second game is notified from any slot machine, the center controller temporarily stocks that right. Then, when a transition to the second game is notified from the slot machine whose right is stocked, within a period during which a transition to the second game is possible, the center controller controls that slot machine and the second game device to start the second game.