Collecting Trading Cards (UMAP)

Author: Crista Arangala, J. Todd Lee, and Ellen Mir

We consider various questions related to trading card collecting. Specifically, we find how much one must spend to have a given probability of obtaining a complete collection of cards.

Table of Contents

1. INTRODUCTION

2. COLLECTING EQUALLY-LIKELY CARDS
2.1 Question 1. Expected Number of Cards for a Complete Collection

2.2 Question 2. Expected Number of Cards without a Repeat

2.3 Question 3. The Probability of a Complete Collection

2.4 Question 4. The Probability of a Complete Collection with No Duplicate Cards in a Pack

3. MULTIPLE CLASSES
3.1 Question 5. The Probability of a Complete Collection

3.2 Question 6. Expected Number of Cards Needed for a Complete Collection

4. FURTHER QUESTIONS

5. SOLUTIONS TO THE EXERCISES

REFERENCES

ABOUT THE AUTHORS