Abstract: A system whereby a plurality of players can play a plurality of different gaming machines. The performance of the plurality of players is recorded through multiple rounds of the game and awards are provided based upon the performance of a player over multiple rounds of the game. In the preferred embodiment, the plurality of gaming machines are video poker machines and the players play these machines in order to obtain the well-known winning combinations. The gaming machines provide signals to a central computer that records in files for each of the players the winning combinations received by the players and the number of rounds played by the players. The central computer also determines whether the player has received a set of winning combinations, e.g., all thirteen possible different four-of-a-kinds, within a pre-selected number of rounds.