Collectibles
A local supermarket chain started to give away small plastic collectible Disney figurines. At first, they were a fun surprise to provide my kids. Then, when I got them a box with spaces for all of the 24 characters, it became a source of pain and want. “When are you going to the supermarket next time?” my older daughter will ask. She wants to know when I’ll get more of the figurines to potentially make up the set.
As the collection grows, so does the frustration over getting duplicate or triplicate figurines. When researching this, I started to wonder how many of these surprise packs of figurines I’d need to obtain in order to close off this saga. This is when I remembered it was some type of probability problem.
Can ChatGPT help with this problem? First, it made me aware that this problem is called the “Coupon Collector’s Problem”. The more you collect, the lower the probability that any individual surprise pack will not be a duplicate.
Assuming that all the toys were equally and randomly distributed, I asked the system to provide the probably that my daughter would complete her set (she has 14 of 24) with 10 new surprise figurines. Very low. OK, how many would I need to purchase to have 95% certainty that she’ll collect all them? It turns out it’s another 50.
But how did we get to that figure? ChatGPT wouldn’t comply in giving me all the figures. It said that the calculation was too resource intensive and that I should use a statistics calculator for it.
OK smarty pants, which one? OK smarty pants… how?
A few minutes later I had loaded up Google Colab and for the first time since university, was running a Monte Carlo simulation. The service had provided me with editable code that I could use to run the simulation and change variables.
What’s exciting about this capability is that it brings complex science, programming, and statistics to a schlub like me to use everyday. From using it, I can begin to understand it better and scratch the itch of curiosities rather than just let the questions rot. This will enhance humanity, not cause it to atrophy in skills.
