An inclination calculation apparatus within a game machine computes inclination of an input device having an acceleration sensor/detector capable of detecting acceleration in at least two axial directions. Programmed logic circuitry within the apparatus generates preliminary data which is representative of a current inclination and which is uniquely determined from acceleration data obtained from the acceleration sensor/detector. Programmed logic circuitry within the apparatus also regularly consecutively computes new/updated inclination vectors in real-time based on a previously computed inclination vector, a variable “effectiveness” valve and a current inclination vector, where the effectiveness value is a correction factor that represents the degree to which the direction of the previously computed inclination vector must be made closer to the direction of the current inclination vector to result in a direction for the new/updated inclination which more accurately reflects the actual inclination of the input device at the time the acceleration data is acquired.