Method of playing a multi-access feature game played along with a primary game. The method comprises: a) playing a primary game, b) initiating feature-game play process upon occurrence of a trigger outcome in the primary game, and c) allowing a player to play the feature game. The latter comprises: i) determining an access type associated with the triggering outcome among many types associated with distinct permissions, ii) providing a feature-game representation composed of a plurality of selectable objects having values and positions, the objects being displayed according to a state based on previous plays of the feature game, iii) receiving a player selection of an object according to a determined permission, iv) affecting the selection according to permission associated with the access type, and modifying selected object status accordingly, v) registering the status and position of all of the feature-game selectable objects, and vi) resuming the primary game.