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Comment by officehero | Hacker News Reader

Extending these types of examples to 100 doors with 99 goats of which Monty opens 98 makes it even easier.

Especially if you walk through what that would look like. You choose door #14. Monty then goes from door to door, opening every single one except door #67. What's special about door #67? Either you picked the door with the car behind it at 1/100 probability, and Monty picked it at random, leaving it closed. Or, with 99/100 probability, Monty is skipping opening that door because it's got the car behind it...

Never thought of it this way, but extending to 100 doors will definitely be my go-to explanation/walkthrough in the future! Thanks for the insight.

I've tried that with people with limited success, though it could be that I've explained it badly.

When you put the games in terms of "you and a friend playing the game simultaneously", most people get it.

You and a friend are playing the game simultaneously; you both decide ahead of time to: a. always pick the same initial door b. no matter what Monty does, you ALWAYS switch, your friend NEVER does.

The possible outcomes before the reveal are: * Monty wins, because he shows you the car. We agree ahead of time that this never happens.

Now, since you know one of you is going to win, since Monty didn't, who has the better chance? Your friend started with a 1/3 chance, and he hasn't switched; does his chance suddenly change because Monty opened a door? Most people (not all!) will agree that it has not.

Since one of you MUST win, and friend has 1/3 chance, what's left?

Woah. That's such a concise way of immediately making the concept clear.

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