1. A game control method carried out by a game control device connected to a plurality of communication terminals used by each of a plurality of users who play a game so as to be capable of communicating therewith, the game control device having a storage unit for storing group information indicative of a group consisting of a plurality of users who play the game and game piece information indicative of a plurality of game pieces constituting one item, the method comprising the steps of: giving a game piece to each of the plurality of users in accordance with an operation of the user to a communication terminal used by the user; storing obtained game piece information indicative of the game piece given to each of the plurality of users in the storage unit; determining whether all of the plurality of game pieces necessary to constitute the one item indicated by the game piece information are given to a plurality of users constituting a group indicated by the group information based on the obtained game piece information stored in the storage unit; and giving a reward to a plurality of users constituting a group indicated by the group information in a case where it is determined that all of the plurality of game pieces are given, wherein the storage unit further stores level information indicative of a level of each of the plurality of users which varies in accordance with the play of the game of each of the plurality of users, and at the step of giving a game piece, each of the game pieces indicated by the game piece information is given to users at levels in different ranges with different probabilities based on the level information.