The object of the invention is to provide a machine which, while completely autonomous, allows performing drawings in which the actual player can make certain that the drawing exclusively follows the laws of chance and that the result therefore is not pre-programmed according to a pre-established prize cycle. To that end, the machine is based on a physical drawing by means of at least one drum (2) containing balls (5), the machine having reading or identification means (8) for reading or identifying the resulting balls (5), such that, through a game interface and prior to the drawing, the player or players can place their bets. According to another one of the features of the machine, it has been envisaged that there can be multiple game interfaces, a main machine in which the drawing takes place, and a series of satellite machines (12) in which each player places their bets, being defined.