🚪🚪🐐 Lessons in Decision Making from the Monty Hall Problem

A journey into three intuitions: Common, Bayesian and Causal

Generated using Gemini Imagen 3

The Monty Hall Problem is a well-known brain teaser from which we can learn important lessons in decision making that are useful in general and in particular for data scientists.

If you are not familiar with this problem, prepare to be perplexed 🤯. If you are, I hope to shine light on aspects that you might not have considered 💡.

I introduce the problem and solve with three types of intuitions:

• Common — The heart of this post focuses on applying our common sense to solve this problem. We’ll explore why it fails us 😕 and what we can do to intuitively overcome this to make the solution crystal clear 🤓. We’ll do this by using visuals 🎨 , qualitative arguments and some basic probabilities (not too deep, I promise).
• Bayesian — We will briefly discuss the importance of belief propagation.
• Causal — We will use a Graph Model to visualise conditions required to use the Monty Hall problem in real world settings.
  🚨Spoiler alert 🚨 I haven’t been convinced that there are any, but the thought process is very useful.

I summarise by discussing lessons learnt for better data decision making.