A plurality of electronic gaming machines (10) are connected to a network (11), to which a feature jackpot controller (12) and display means (13) are also connected. Each of the electronic gaming machines (10) are provided with a network interface arranged to provide a signal onto the network (11) on each occurrence of an operation of a respective machine and the jackpot controller (12) is arranged to receive each of the machine operation signals and to increment the value of a random jackpot prize on the occurrence of each of these operation signals. Prior to each game, the gaming machine (10) selects a random number from a range of numbers and during each game, the machine allocates the first n numbers in the range, where n is the number of credits bet by the player in that game. At the end of the game, the randomly selected number is compared with the numbers allocated to the player and if a match occurs the particular machine is switched into a feature game mode in which a jackpot game is played for all or part of the incremental jackpot prize.