Optimal card-collecting strategies for ‘Magic: The Gathering’

‘Magic: The Gathering’ is a fantasy-based card game which has been extremely popular in the USA and other countries. Players must collect special cards, to create ‘decks’ which are then compared with those of other players in contests. Since the cards are sold in random packs, and the cards themselves are divided into categories within these packs, the problem of optimal strategies for collecting is a variant of the coupon collector's problem. Dynamic programming is used here to determine the optimal policy for purchase.