39 The Monty Hall Problem: A Surprising Game-Show Connection to Christianity

The Monty Hall Problem is a decades-old puzzle with an unexpected application to Christianity.

Suppose you’re on a game show with three doors. Behind one door is a valuable prize, but there’s nothing behind the other two. You get to pick a door and keep whatever is behind it, and you choose door #1. Monty Hall, the game show host, opens door #2 to show you that there’s nothing there and gives you the chance to change to #3. Do you switch?

Most people think there’s no benefit to switching, but this is wrong. To see why, imagine not three doors but three hundred. There’s still just one prize, with the remaining doors having nothing.

So you pick a door—say number 274. There’s a 1 in 300 chance you’re right. This must be emphasized: you’re almost certainly wrong. Then the host opens 298 of the remaining doors: 1, 2, 3, and so on. He skips door 59 and your door, 274. Every open door shows nothing.

Should you switch? Of course you should—your first pick is still almost surely wrong. The probabilities are 1/300 for your pick, #274, and 299/300 for #59.

Another way to look at the problem: do you want to stick with your original pick, or do you want all the other doors? Switching is equivalent to choosing all the other doors, because, thanks to the open doors, you know the only door within that set that could be the winner.

You may have already anticipated the connection with choosing a religion. For most people, they adopted their religion as if they were picking a door in this game show. In the game show, you don’t weigh evidence before selecting your door, you pick it randomly. And most people adopt the dominant religion of their upbringing, which was also assigned at random.

Let’s imagine a similar game, the Game of Religion. You have picked your religion out of the three hundred choices—religion #274, let’s say. The host flings open door after door and we see nothing behind each one. Hinduism, Sikhism, Jainism, Buddhism, plus religions you have never heard of—all nothing, showing that these are manmade religions. As you suspected, they were just amalgams of legend, myth, tradition, and wishful thinking.

Here’s where the analogy between the two games fails. First, the host opens all the other doors. Only the believer’s pick, door #274, is still closed. Second, there was never a promise that any door held a true religion! Since the believer likely came to his beliefs randomly, why imagine his choice is any truer than the others?

Every believer plays the Game of Religion, and almost every believer believes their religion is the one true religion, with nothing behind all the hundreds of other doors. But maybe there’s nothing behind every door. And given the lesson from the three-hundred-door Monty Hall game, that the door you randomly picked at first is almost certainly wrong, why imagine yours is the only religion that’s not mythology?

Image credit: Poussin jean (CC BY-SA 2.5) via Wikimedia