To enhance a thrill, and to increase interest of a game player by providing a maximum score control means for variably controlling an obtainable maximum score to a prescribed variable score value in a combinational game machine for imparting an obtained score according to a combination within a prescribed maximum score.

Then a game ball entering a first actuating ball entering means 21 passes through an actuating area 34, a passing gate is validated by generating a special game state by actuating a guiding increasing means 42. This continues until the game ball passes again through the actuating area 34 or games of a prescribed frequency finish. Afterwards, when the game ball passes through the passing gate, a second actuating ball entering means 22 is opened. When the game ball enters the second actuating ball entering means 22, the score increasing part 46 of an account settle processing means 43 operates to doubly increase a winning score in a range of a maximum score. Thus, since a difference is made in the score even when the same winning generator is realized, a game player can get a thrill by an expectant feeling and an anxious feeling.