A lottery gaming system (10) utilizes one or more pools (24) of predetermined game play records (25). In response to a game play request, the gaming system allocates a number or set of game play records. A representation for each allocated game play record is then displayed to the player in some fashion that does not indicate the result of the respective game play record (25), and the requesting player is allowed to select one or more of the allocated game play records through the respective representations. The selected game play record or records (25) are assigned to the player and the player ultimately sees the result associated with each selected game play record. However, the allocated game play records that are not selected by the player, and thus remain unassigned, are collected or otherwise made available for use in response to another game play request.