If You Still Don’t Understand the Monty Hall Paradox, You Never Will

You are presented with three doors and know that behind one of the doors is a new car, while the other two reveal a goat. The host of this game, Monty Hall, instructs you to pick a door. You pick Door 1.

Next, Monty opens Door 2, revealing one of the goats. He offers you the option to switch to Door 3 or remain with your chosen door. What should you do?

The vast majority of people choose to stay for purely psychological reasons. Those who attempt a logical response conclude it doesn’t matter — it’s a 50:50 choice. After all, there are exactly two doors, and we have no information about which has a car behind it… or do we?

In fact, the optimal strategy is to switch, doubling your odds of winning!

This is the Monty Hall paradox. Despite being a solved problem — its solution widely accepted and mathematically proven — it remains a source of confusion, disbelief, and even outrage.

The typical explanations tend only to confuse the skeptic further. Here, I’m going to explain why that is. Think of it as meta-explainer.

The history, in case you wanted to know

The Monty Hall paradox is named after the host of Let’s Make a Deal, a game show from the 1960s where…