1. A system for facilitating player interaction with virtual containers in an online game, the system comprising one or more physical processors configured by machine-readable instructions to: host the online game, wherein hosting the online games comprises managing player inventories of virtual items associated with individual players in the online game, the managed player inventories including a first player inventory associated with a first player of the online game; provide instances of virtual containers for player interaction in the online game, the instances of the virtual containers being associated with corresponding sets of potential items such that a first instance of a first virtual container is provided to the first player for interaction and is associated with a first set of potential items, wherein the individual potential items in the first set are associated with corresponding distribution probabilities for distribution to the first player inventory; receive from players activation requests for activating instances of virtual containers and responsive to such activation requests, determine which one or ones of the potential items will be distributed to the players as initial payouts in accordance with the distribution probabilities corresponding to the potential items associated with the requested instances of the virtual containers such that responsive to an activation request from the first player for activating the first instance of the first virtual container, one or more items in the first set of potential items are determined to be distributed to the first player inventory as an initial payout in accordance with the distribution probabilities corresponding to the individual potential items in the first set; responsive to the determination of the initial payout to be distributed to the first player inventory, effectuate presentation of a first offer and a second offer on a client computing platform associated with the first player, wherein the first offer specifies that the first player may accept the initial payout as an actual payout to be distributed to the first player inventory, and the second offer specifies that the first player may pay a first amount of consideration in exchange for having the one or more items in the initial payout redetermined such that the player may improve the actual payout, wherein the first amount of consideration includes value in addition to any value that the one or more items in the initial payout have; and receive an acceptance of the first or the second offer from the first player and determine the actual payout of the first instance of the first virtual container in accordance the offer accepted by the first player such that if the first player accepts the first offer, distribute the initial payout to the first player inventory as the actual payout, and if the first player accepts the second offer, redetermine, stochastically or quasi-stochastically, the one or more items in the initial payout and distribute the actual payout to the first player inventory based on an outcome of the redetermination.