A gaming machine 10 has a display 14 and a game controller arranged to control images displayed on the display 14 The game controller is arranged to play a game 16 wherein at least one random event is caused to be displayed on the display 14. If a predefined winning event occurs, the machine awards a prize. The display 14 displays a plurality of movable carriers 18. Each of at least certain of the carriers 18 carries a representation of at least one polyhedral element. Each polyhedral element has a plurality of faces which are visible at any one time with an indicium being carried on each face. Indicia on faces of the polyhedral elements which are visible at a rest condition of the carriers are taken into consideration in the determination of whether or not a winning event has occurred.