2022/11/08 by Tipaluck Krityakierne, Krityakierne, Tipaluck, Thotsaporn Thanatipanonda +1
Business, Management and Accounting · Computer Science · #05A15 #Artificial Intelligence in Games #Combinatorics (math.CO) #Consumer Market Behavior and Pricing #FOS: Mathematics #Organizational Management and Leadership #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2211.04374
openalex publication_date 2022/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the classical coupon collector's problem, every box of breakfast cereal contains one coupon from a collection of n distinct coupons, each equally likely to appear. The goal is to find the expected number of boxes a player needs to purchase to complete the whole collection. In this work, we extend the classical problem to k players who compete with one another to be the first to collect the whole collection. We find the expected numbers of boxes required for the slowest and fastest players to finish the game. The odds of a particular player being the slowest or fastest player will also be touched upon. The solutions will be discussed from both the tractable algebraic techniques as well as the probability point of views.