A method for conducting bingo games includes using a server to collect game play requests from a plurality of electronic player stations. The server determines if a group of the collected game play requests meets one or more predefined conditions for establishing a quorum, and if so conducts a game with the group of game play requests. Even after the game is started, the server continues to collect game play requests in preparation for conducting additional games. When enough game play requests are collected, the server starts the next game, even if previous games are still in progress.