How much does it cost to complete a sticker collection? A simulation study using R

TL;DR

This paper presents a simulation-based approach using R to estimate the cost and number of packages needed to complete a sticker album, exemplified by the Qatar 2022 World Cup album, highlighting computational methods in probability.

Contribution

It introduces a simulation algorithm for the coupon collector problem and applies it to a real-world sticker collection scenario with practical cost estimates.

Findings

Average of 950 packages needed to complete the album

Estimated cost of 3,800 reals for completing the album

Simulation code provided on GitHub

Abstract

This paper considers some computational issues related to the problem of the coupon collector behavior. In addition, we propose a simulation algorithm to find the solution to the problem, where we present as a numerical illustration an album of stickers related to the Qatar 2022 Official Football World Cup, which is being sold in Brazilian newsstands. In this case, the complete album has N = 670 stickers, which are sold in packages containing n = 5 stickers each. The simulation was based on a computational code written in R. For this application we obtained as a solution, an average number of 950 packages needed to complete the album, at an average cost of 3,800 reals (Brazilian currency), assuming that the collector does not exchange any of its repetitions with nobody. All computer code used in this article is provided on GitHub. The assumed simulation study could be useful for statistics teachers to motivate their students for lectures in computational statistics and fundamentals of probability.