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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 contestants were asked to pick one of three doors. Behind one door was a big prize — behind the other two, smaller prizes… occasionally, goats. In its original form, the game wasn’t so rigid. Sometimes, Monty offered cash instead of letting the player switch, and sometimes, his actions were influenced by what made for better TV.
But in 1990, Marilyn vos Savant, in her “Ask Marilyn” column, simplified the scenario into a mathematical problem. Monty always reveals a goat and always offers the option to switch. The result? Switching is the better choice, doubling your chances of winning from ⅓ to ⅔.
This is where the controversy began. Professors, mathematicians, and skeptics flooded vos Savant with letters arguing she was wrong. Some outright refused to believe it even after the math was laid bare.
