A new method of playing a lottery or other game of chance is described in which a Player who purchased a ticket for a first lottery may subsequently purchase a “Milligan,” a chance to win a subset of prizes at a subsequent lottery but at a reduced cost. Similar to a mulligan in golf, the “Milligan” affords the Player a second opportunity to play. While giving the Player the benefit of an additional, discounted chance to a win, this new method of play also provides Lottery Operators additional revenue at a lower payout risk. Ticket Retailers benefit from the new method of play because it may incentivize players to return to Ticket Retailers to purchase the “Milligan.” Another new method of playing a lottery or other game of chance is described in which a Player may purchase a ticket for a lottery for a chance to win a subset of prizes but at a reduced cost is also provided.