re: Marilyn vos Savant and the history of the Montel Hall question

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It's his job to fool you into thinking you made the right choice initially.

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I'm leaving the game show hosts psychology out of it since he could be using reverse/reverse/reverse psychology.


I dont think his psychology should be factored into the answer at all. This isnt the princess bride.

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Another way to look at it: 98 doors will always be opened to reveal goats. It will always come down to your initial door and the last remaining closed door. If you played the game 100 different times, do you really feel that you would have picked the winning door initially 50 of those times?

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ok. it took me a second but im finally on board when looking at it from this angle. carry one.

bbap, it took me more than a second

I think I'd still be arguing the 50/50 opinion if I didn't consider the expanded model

Everytime we go over this on this board I feel that "Ahhh now I get it", just for it to pop up at a later date and me just not believing switching doors or not makes a difference. Maybe my brain just isn't wired for this stuff. Business Statistics kicked my burnt arse.

Bbap, I assume you aren't trolling, so I'll continue.

Regardless of the number of doors, as long as Month knows which door holds the car, you should switch. If you don't switch, you're basically saying that it doesn't matter that Month has opened other doors. You're saying that this new knowledge is irrelevant. However, that is obviously not true and is the flaw in your logic.

Most people think of the events in reverse. They look at it as either one door or the other, thus a 50% chance, but that ignores the things we've learned while getting to the two doors.

ETA: I see that you've seen the light.

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dont think his psychology should be factored into the answer at all. This isnt the princess brid

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I like to break it down much further than 3 doors. Imagine 100 doors - 99 goats and 1 car - Door #37. You choose Door #42. Monty opens the other 98 doors leaving you with your choice and #37. Basically, if you stay, you're saying the other 98 doors being opened were irrelevant, because you stayed with your original choice. If you switch, your effectively giving yourself the chance to see 99 doors get opened, hence your chance of winning is 99% if you switch, and only 1% if you stay.

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I finally understand. That was broken down perfectly.

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As a few posters (myself included) have suggested, try using MANY more doors (100, 1000 etc) and then remove every door with a goat except for your initial choice and the last remaining door. The more doors you add, the more clear it becomes that you do not have a 50/50 chance by staying with your initial pick every time.

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Exactly. Monty knows the correct answer, and he's opening all the wrong doors for you. That is information you should use.

Say you're playing the lottery, and you pick six numbers. The cashier (who knows the winning numbers) then prints up a gazillion tickets, scratches off all of them except for one to show they are all losers.

I bet you switch.

What I love about this is that ANYONE can prove out for themselves that switching wins 2/3 of the time by using nothing more than three pieces of paper to represent the three doors and following the rules of the problem and playing the game themselves. No math involved, just play the game.

Yet, people STILL insist it's 50/50. Bless their hearts.