Systems, apparatuses, and methods are presented for operating a generalized progressive gaming system which offers a common progressive jackpot for a various games with different sets of winning hands and different denominations. The generalized progressive system represents a jackpot in terms of probability and adds a normalizing random event to a player's bet and the hand player receives. In order to win a jackpot the player must receive a qualified hand and a combined probability of these two events, namely a hand and a normalizing random event, must be smaller than a required value. Any qualified hand can win the jackpot. Handling of various denominations is proposed. Generalized progressive system apparatus is also provided that includes a display, a user interface, a processor and a server.