Abstract: A system is adaptable to any game where a player sequentially receives a number of elements having identifying characteristics, with certain combinations of elements defined to be winning combinations. After all or part of an initial set of elements is obtained, the system offers the player an award to stop play prior to receiving a final set of elements. The amount of the offer is preferably based, at least in part, upon the probabilities of obtaining a winning combination using the initial set of elements received by the player. In accepting the "stop play" offer, the play of the game may cease, with the player forfeiting the right to win an award based on the final winning combinations, or, in an alternate embodiment, play can continue with an award, if any, based upon a modified pay schedule.