A portable electronic device and an entertainment system that can give a user a sense of familiarity by generating a proper character using an identification number and by displaying it, for example, on a display means include an identification-number holding section which holds a proper identification number through a bus, which is connected to an interface to connect to a game-machine main body having a program-execution function. Input operation is performed by a player at an input-operation section. At an operation-information generation section, an operation information is generated in response to the input operation at the input-operation section. The RAM provides for use for operation information stores the operation information received from the operation-information generation section. A character-information generation section generates proper character information in accordance with the operation information and gene information when the latter is received through the game-machine main body. The gene information determines the character-transmission factor of the character corresponding to the proper identification number.