Marilyn vos Savant and the Monty Hall Problem (2015)

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Yeah, this problem is special because it's so familiar. If you ask a riddle about two trains moving at different speeds, people will treat it like a math problem and just assume they won't get it. The Monty Hall problem really makes people upset when they don't get it.

> Imagine that you’re on a television game show and the host presents you with three closed doors. Behind one of them, sits a sparkling, brand-new Lincoln Continental; behind the other two, are smelly old goats. The host implores you to pick a door, and you select door #1. Then, the host, who is well-aware of what’s going on behind the scenes, opens door #3, revealing one of the goats.

> “Now,” he says, turning toward you, “do you want to keep door #1, or do you want to switch to door #2?”

There are some implied assumptions. You need to know that the car is randomly placed (or that your door choice was made at random), and that the host always has to show you an empty (ok, goat) door before offering you to switch.

Under those assumptions, the winning odds of the switching strategy equal the odds of your initial pick NOT being the car.

> You need to know that the car is randomly placed

You don't need to know this.

> and that the host always has to show you an empty (ok, goat) door before offering you to switch

You know this through the line, "Then, the host, who is well-aware of what’s going on behind the scenes." If you can't understand that a game show host won't spoil the game they're hosting, that's on you and a good opportunity to pick up common sense.