🎲 Chance ★★★★☆ +22 points #14

Three Doors

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Open — answers are being collected The solution goes up on 31 August. Send in your answer before then and it counts for full points — you will not be told whether it is right until the reveal.

A television game. There are three closed doors. Behind one of them is a car; behind each of the other two is a goat. You pick a door — say door 1 — but it stays shut.

The presenter knows where the car is. He opens one of the two doors you did not pick — always one with a goat behind it, always a door you did not choose — and shows you the goat.

The presenter never opens your door, and never opens the car.

Then he offers: stay with your door, or switch to the other closed one?

🎲Nearly everybody says it makes no difference — two doors left, so it must be fifty-fifty. That answer is wrong, and the reason is worth more than the puzzle.

Answer to type: if you play this game 300 times and always switch, how many cars do you win on average?

💡 I want a nudge

Forget the doors for a moment and ask a simpler question: how often is your very first pick the car? Switching wins in exactly the opposite cases.

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Previous puzzle: The Missing Thousand