Game system in which a plurality of participants transmit to at least one central play station (3) participant play data for taking part in at least one game (31, 32, 33) in special messages by means of mobile radio devices (2) through the mobile radio network (1). The central play station (3) carries out games according to predefined game rules and transmits central game data in special short messages through the mobile radio network (1) to the mobile radio devices (2) of the participants. The mobile radio devices (2) include a SIM card (21) for the game system, which has a memory, programmed means and a processor in order to show to a participant playing instructions and game results on a display (22) of a mobile radio device (2), and to convey the data to the central play station (3) by means of said special short messages, and to store a p repaid amount which can be used to pay for wagers and to which winnings can be booked.