The Monty Hall Problem: Trust the Math, Not Your Gut

Imagine you are on a game show facing three closed doors. Behind one is a brand-new sports car 🚗; behind the other two are goats 🐐. You pick a door... let's say Door 1.

The host, Monty Hall, who knows what is behind every door, steps in. Instead of opening your door, he opens Door 3 to reveal a goat. He then turns to you and asks: "Do you want to stay with Door 1, or switch to Door 2?"

Your brain is probably screaming: "It's 50/50! There are two doors left, one car, one goat. It doesn't matter!"

But your brain is lying to you! Dun dun DUN! You should always switch.

Here is the secret: When you made your very first choice out of the three doors, you had a 2/3 chance of picking a goat. The odds were heavily stacked against you.

If you initially picked a goat (which happens 66% of the time), Monty has to reveal the only other goat left. This means the remaining closed door contains the car! Therefore, switching doors wins the car every single time your first pick was a goat.

By switching, you aren't flipping a coin between two doors; you are betting on the fact that your first guess was probably wrong. Switching flips your odds from a 1/3 chance of winning to a massive 2/3 chance of winning.

Don't believe it? Play the simulation above! Play it 10 or 20 times. Try sticking to a "Stay" strategy, then try a "Switch" strategy. Watch the statistics tracker update in real-time and prove that sometimes, reality is deeply counter-intuitive.