3 ms·

I agree that "Monty knowing the answer" isn't the "whole reason" MH is confusing. IMO, people are confusing MH with a case where the door is opened randomly be

I agree that "Monty knowing the answer" isn't the "whole reason" MH is confusing. IMO, people are confusing MH with a case where the door is opened randomly before your choice. Let's say Monty shows you three doors, then knowingly opens a wrong door (B) before you choose. Do you want A or C? It's a coin toss, of course. But suppose you pick door A first and THEN he knowingly opens a wrong door you didn't choose (B). Now the odds of winning are 2/3rds if you switch. But it feels the same as in the previous case. ("How could choosing a door first affect the odds?! It couldn't possibly change anything!!") The answer is that your choice of a door constrains Monty. Suppose you choose a door secretly before Monty opens a door. Suppose you choose A, and Monty opens door A, revealing a goat. Well, uh, you can't pick that any more, now, can you? You're forced to choose between B and C, a toss up. But if you publicly pick door A then Monty can't/won't open A; he has to open one of the other doors. Since you probably chose the wrong door to begin with, and he always opens a wrong door, the other remaining closed door probably has the car.

officehero 6y ago
Extending these types of examples to 100 doors with 99 goats of which Monty opens 98 makes it even easier.
- henrikschroder 6y ago
  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...
- shandor 6y ago
  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.
  - michaelcampbell 6y ago
    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?
- Vinnl 6y ago
  Woah. That's such a concise way of immediately making the concept clear.

officehero 6y ago

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

henrikschroder 6y ago
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...
shandor 6y ago
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.
- michaelcampbell 6y ago
  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?
Vinnl 6y ago
Woah. That's such a concise way of immediately making the concept clear.