A gaming machine has a display which displays a symbols in an array format of n rows and m columns of symbol positions. A game control controls images displayed on the display and is arranged to pay a prize when a predetermined combination of symbols is displayed in a predetermined arrangement of symbol positions including one and only one symbol position in each column of the array. The number of said predetermined arrangements in the gaming machine for any one game is a value which is the product k.sub.1 . . . .times. . . . k.sub.i . . . .times. . . . k.sub.m, where k.sub.i represents a number of symbol positions which have been selected by the player in an i.sup.th column of the n rows by m columns of symbol positions on the display (0<i.ltoreq.m and k.sub.i .ltoreq.n). At least one symbol position is selected from each column, and the number of predetermined arrangements represents the number of possible combinations of the selected symbol positions which have one symbol position in each column of the display means.