An enhanced gaming system through which a variety of games of chance and/or games of skill can be made available to players. The gaming system separates game outcomes from game themes and game payout/buy-in information, thereby enhancing game flexibility. The gaming system also allows different games of chance and/or games of skill to be available to different subsets of player units, and gives a gaming hall operator the ability to dynamically control the size and distribution of such subsets. An "apparently random" permutation production technique is disclosed for use in certain games and regulatory environments. A PKI-based architecture is also disclosed.