A game system has a plurality of slot machines, each slot machine having a controller for executing a basic game, and transmitting a signal for making a transition to the roulette game when a prescribed symbol combination is stopped on a payline; a second game device for executing the roulette 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. If the roulette game is already executed when a signal for requesting a transition to the roulette game is received from a slot machine, the center controller keeps a transition to the roulette game waiting, and controls that slot machine and the second game device to start the roulette game at a timing where a transition to the roulette game becomes possible.