An apparatus for implementing a game having a deterministic component and a non-deterministic component wherein a player uses the game through at least one player interface unit. Each player interface unit generates a player record indicating player-initiated events. A random number generator provides a series of pseudo-random numbers and a rules library stores indexed rules for one or more games. An interface registry stores mapping records where the mapping records are used to associate the player-initiated events to pre-selected rules in the rules library. A control means is coupled to the player interface to receive the output of the player interface unit, coupled to the interface registry, the rules library, and the random number generator. The control means processes the player record and returns an output record to the player interface unit where the output record is determined by executing the game's rules with reference to the pseudo-random numbers and predefined combinatorial algorithms for selecting sets of the pseudo-random numbers. In various embodiments, random numbers may be generated for use in a particular game or set of games, but not for use in all games.