A gaming machine uses a time-based method for generating game results having nonuniform probability. The gaming machine employs an addressable memory in cooperation with a counter and a clock. The clock generates a very fast series of pulses, and includes a digital-to-analog converter. The counter holds a number representing one of the possible reel stop positions and counts the clock's pulses, so that with each pulse, the value of the counter advances by one. To vary the odds that a particular reel stop position will be selected, the clock's pulses do not come at even intervals. Rather, the clock is responsive to a digital input signal to control how long it will allow a particular number to remain in the counter before the next clock pulse. The binary numbers which are used to control the clock are stored in memory. The memory accepts as input the current value of the counter. Thus, when the counter is incremented, the memory provides the binary number associated with the new counter value. By selecting appropriate binary numbers for each possible counter value, the relative amounts of time which the counter holds each value (and, therefore, the probability of selection) can be varied.