The invention is directed to methods and gaming units for conducting a multi-player wagering game, such as a Bingo game, in which at least one of the players may win the occurrence of the wagering game by matching a predetermined game-winning pattern of game indicia on a game array having a unique combination of game indicia based on matching the game indicia on the game array to game indicia randomly selected for the occurrence of the wagering game. The game-winning pattern or patterns for an occurrence of the wagering game may be determined for each occurrence based on the total number of game arrays enrolled in the occurrence of the wagering game. The game-winning patterns may be determined so that a desired statistical distribution of the number of randomly selected game indicia required for a player to match a game-winning pattern may be achieved regardless of the total number of game arrays enrolled by the players.