The famous Monty Hall problem has been analyzed in great detail, but those new to it still get the answer wrong, even some professional mathematicians. I’ve had several arguments about it, but I’ve found only one way to convince people of the correct answer: offer to bet. Here’s a version of the Monty Hall problem: You’re on a game show. There are three doors. You’re told there is a car behind one door and a goat behind each of the other two doors. You’re asked to pick the door you think has the car. After you choose, the game show host, Monty Hall, opens one of the other doors to reveal a goat. Monty then asks you if you want to stick with your door or whether you want to switch to the other unopened door. Should you switch? To make things more precise, here’s some additional information: before the game began, Monty intended to open a door you didn’t pick to show a goat (no matter what door you chose), and he intended to offer you a chance to switch. It’s well known tha...