To provide a game machine which has its running improved by not fixing but varying the game number till a ceiling is reached.

If a replay 0 is a display combination in a general game state, the game shifts to an RT (replay time) 1, and a replay 1, a replay 2 and a special replay then become a display combination so that the game state transits stepwise to an RT2 game state, an RT3 game state and an RT4 game state, which becomes a ceiling at a very high replay probability. For the RT1 game state, the RT2 game state and the RT3 game state, the internal winning probability of a normal replay become higher in the recited order. In the RT2 game state, the replay 0 may also be a display combination so that the game state returns back to the RT1 game state, or the replay 1 may also be a display combination in the RT3 game state so that the game state returns back to the RT2 game state.