1. A player interactive gaming system comprising: a selected number of elements each having identifying characteristics, wherein certain combinations of said elements are defined to be winning combinations; an element assigning system, having access to said selected number of elements and receiving player input signals, which assigns and displays to said player a plurality of said elements; a stop play award system responsive to the identifying characteristics of at least one element assigned to said player for establishing a stop play award prior to said player being assigned a final one of said elements wherein the value of said stop play award is based at least in part on the probability that said at least one element will, in combination with another of said selected number of elements, comprise one or more of said winning combinations; a final award system responsive to the identifying characteristics of the at least one element and the assignment of the final one of said elements for establishing a final award; and an award distribution system responsive to the stop play award system, the final award system and player input signals, for distributing to said player the winning final award when the elements assigned to the player include said final one of said elements and when the combination of elements assigned to the player includes at least one of said winning combinations and for distributing to the player the stop play award when said distribution system receives a player input signal indicating said player has accepted said stop play award.