Simulating the Coupon Collector Problem

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

A statement of the coupon collector problem: suppose each box of cereal contains a coupon chosen at random from possible coupons. Let be the number of boxes of cereal that need to be purchased in order to get a complete set of all coupons. What is the expected value (or waiting time) of ? The answer is given by the formula .


This Demonstration illustrates this result for the following natural sets of "coupons": the digits , the four suits of a playing card deck, the 13 cards in a single suit and the six sides of a standard die. It generates a random sequence of coupons from the selected set until a complete set of coupons has been collected. The total number of coupons that have been collected is then compared with the expected value.


Contributed by: Yikai Teng (May 2019)
Based on an undergraduate research project at the Illinois Geometry Lab by Raymond Harpster, Tianli Li, Yikai Teng and directed by A. J. Hildebrand.
Open content licensed under CC BY-NC-SA




[1] B. Dawkins, "Siobhan's Problem: The Coupon Collector Revisited," The American Statistician, 45(1), 1991 pp. 76–82. doi:10.1080/00031305.1991.10475772.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.