Abstract: Gaming machines or devices utilize the output of random number generators (RNGs) in the presentation of games, wherein one or more of the RNGs are each assigned to a single player. Each uniquely assigned RNG is used to determine the outcome of the games played only by the assigned player, such as a casino gaming machine or a game board devices accessed via a remote presentation device such as a phone or computer. An RNG may also be stopped or paused and then restarted, whereby a sequence of random data remains continuous or contiguous relative to a number of games played, such as by the single player to which the RNG is assigned. Multiple players may also time-share a gaming machine in a manner whereby the gaming machine acts as a unique device to each player.