Decision making and card collecting

^** D.K.Smith{at}exeter.ac.uk Collecting a set of different, yet similar, items is a popularhobby. The "coupon collector's problem" is concerned with thenumber of items which must be obtained, one at a time, in orderto complete the set, assuming that the collector is samplingfrom an infinite population where each item has a known probabilityof being found. In recent years, manufacturers have chosen toproduce the items in sealed packets which contain more thanone item, and possibly items from more than one set. This paperconsiders the problem of collecting items in packets, and thedecision problem faced by a collector who is offered the chanceto buy several packets at a discount. Dynamic programming isused to determine when it is worthwhile to purchase in bulk,for various sets and packets, as a function of the discountrate. Finally, mention is made of the other player in the transaction,the card manufacturer, who is also a decision-maker.