Man there’s something about the monty hall problem that just messes with human reasoning. I get it now and it’s really not even complicated at all but when you first learn about it you tend to overthink it. Now I don’t even understand how I was ever confused.
I think the problem is that people forget Monty Hall has information that the contestant does not. The naive assumption is that he’s just picking a door and you’re just picking a door. The unsophisticated viewer never really stops to think about why Monty Hall never points to a door and reveals a prize by mistake.
One way I’ve had success explaining it is to expand the problem to more than three doors. Assume 100 doors. Monty Hall then says “Open 98 doors” and fails to reveal a prize behind any of them. Now its a bit more clear that he knows something you don’t.
The thing you’re getting by switching is the benefit of the information provided by the person who revealed an empty door.
Before a door is open, you have a 1/3 chance of selecting correctly.
After you select a door, the host picks from the other two doors. This provides extra information you didn’t have during your initial selection. The host points to a door they know is a dud and asks for it to open. So now you’re left with the question “Did I pick the correct door on the first go? Or did the host skip the door that had the prize?” There’s a 1/3 chance you picked the right door initially and a 2/3 chance the host had to avoid the prize-door.
It literally doesn’t matter whether you stick with your door or switch.
Takes mathematical model and shoves it in the trash
No! I won’t listen! It doesn’t matter, I tell you!!!
Man there’s something about the monty hall problem that just messes with human reasoning. I get it now and it’s really not even complicated at all but when you first learn about it you tend to overthink it. Now I don’t even understand how I was ever confused.
I think the problem is that people forget Monty Hall has information that the contestant does not. The naive assumption is that he’s just picking a door and you’re just picking a door. The unsophisticated viewer never really stops to think about why Monty Hall never points to a door and reveals a prize by mistake.
One way I’ve had success explaining it is to expand the problem to more than three doors. Assume 100 doors. Monty Hall then says “Open 98 doors” and fails to reveal a prize behind any of them. Now its a bit more clear that he knows something you don’t.
Maybe? I don’t think that was my issue. I think I was overthinking it and using the second “choice” as an event with separate odds.
The thing you’re getting by switching is the benefit of the information provided by the person who revealed an empty door.
Before a door is open, you have a 1/3 chance of selecting correctly.
After you select a door, the host picks from the other two doors. This provides extra information you didn’t have during your initial selection. The host points to a door they know is a dud and asks for it to open. So now you’re left with the question “Did I pick the correct door on the first go? Or did the host skip the door that had the prize?” There’s a 1/3 chance you picked the right door initially and a 2/3 chance the host had to avoid the prize-door.
Are you being facetious, or do you want a non-mathematical explanation?