A random number generator and a gaming machine employing such random number generator are set forth in accordance with preferred embodiments of the present invention. The random number generator disclosed employs a white noise source to clock a counting arrangement whose maximum count exceeds the largest random number desired. A variable counter, clocked at a fixed rate, is loaded with random numbers obtained from the counting arrangement and each time the variable counter is counted down to a threshold state a new random number is read from the counting arrangement. Random numbers obtained in this mamner are then checked to ascertain their propriety and those which are accepted are then subjected to pseudo-random number regenerative techniques to further randomize the same. The resulting random numbers are then employed within a digitally controlled and operated gaming machine to select winning condition, the probabilities to be displayed during periods when wagers are accepted and otherwise to vary initial conditions associated with the gaming event prior to the actual occurrence thereof. The gaming event is then visually displayed in accordance with the winning conditions selected and any successful wagers are paid.