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Message
re: Marilyn vos Savant and the history of the Montel Hall question
Posted on 2/24/15 at 9:14 am to CockHolliday
Posted on 2/24/15 at 9:14 am to CockHolliday
already read the 100 door example. The link even had it.
I dont think it matters at all. In the end you are still left with 2 doors. 1 has a car. 1 has a goat. It could be the initial door you chose, it could be the other door.
I dont think it matters at all. In the end you are still left with 2 doors. 1 has a car. 1 has a goat. It could be the initial door you chose, it could be the other door.
Posted on 2/24/15 at 9:16 am to bbap
Your opinion would hold if the other 98 doors were randomly opened, with no prior knowledge of which door held the car...but in the case of the game show, the host always knows which door has the car. It's his job to fool you into thinking you made the right choice initially.
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?
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?
This post was edited on 2/24/15 at 9:18 am
Posted on 2/24/15 at 9:18 am to CockHolliday
quote:
It's his job to fool you into thinking you made the right choice initially.
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.
Posted on 2/24/15 at 9:18 am to CockHolliday
Ok, statisticians, riddle me this.
1) This scenario recurs a hundred times, and I switch a hundred times.
2) Then we do it another hundred times, except this time I don't switch.
Are you really telling me that I win the car more times by switching? I just don't buy that. And if you aren't, then what difference does it make in real life?
1) This scenario recurs a hundred times, and I switch a hundred times.
2) Then we do it another hundred times, except this time I don't switch.
Are you really telling me that I win the car more times by switching? I just don't buy that. And if you aren't, then what difference does it make in real life?
Posted on 2/24/15 at 9:19 am to CockHolliday
quote:
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?
ok. it took me a second but im finally on board when looking at it from this angle. carry one.
Posted on 2/24/15 at 9:20 am to JudgeHolden
quote:
Ok, statisticians, riddle me this.
1) This scenario recurs a hundred times, and I switch a hundred times.
2) Then we do it another hundred times, except this time I don't switch.
Are you really telling me that I win the car more times by switching? I just don't buy that. And if you aren't, then what difference does it make in real life?
Absolutely.
Posted on 2/24/15 at 9:21 am to bbap
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
I think I'd still be arguing the 50/50 opinion if I didn't consider the expanded model
Posted on 2/24/15 at 9:24 am to bbap
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.
Posted on 2/24/15 at 9:32 am to bbap
quote:
took me a second but im finally on board when looking at it from this angle. carry one.
Ok, but which one? Door 1 or 2?
This post was edited on 2/24/15 at 9:40 am
Posted on 2/24/15 at 9:47 am to bbap
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.
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.
This post was edited on 2/24/15 at 9:52 am
Posted on 2/24/15 at 9:50 am to slackster
Wouldn't picking door #1 twice also be 2/3?
Posted on 2/24/15 at 9:52 am to bbap
quote:
dont think his psychology should be factored into the answer at all. This isnt the princess brid
Posted on 2/24/15 at 9:55 am to RedHawk
quote:
Wouldn't picking door #1 twice also be 2/3?
No. That is the same 1/3 you had to begin with.
The problem is the 2-phase part that some people aren't getting. You're making the choice to switch from the very beginning - you're HOPING to get a goat - if you get a goat (2/3) you win the car (on the switch) - if you get the car (1/3) - you really lose the car, which you should be okay with, because you're going with your 2/3.
You have no information to make the switch - you're just playing the percentages from the beginning. If you had more information, it wouldn't work.
Posted on 2/24/15 at 9:59 am to slackster
quote:
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.
I finally understand. That was broken down perfectly.
Posted on 2/24/15 at 10:05 am to Ace Midnight
quote:
You have no information to make the switch - you're just playing the percentages from the beginning. If you had more information, it wouldn't work.
this is the key -- you are playing percentages from the beginning.
Posted on 2/24/15 at 9:19 pm to CockHolliday
quote:
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.
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.
This post was edited on 2/24/15 at 9:22 pm
Posted on 2/24/15 at 10:30 pm to Big Scrub TX
Enjoyable read. I remembered the hullabaloo about the problem.
Posted on 2/24/15 at 10:47 pm to Big Scrub TX
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.
Yet, people STILL insist it's 50/50. Bless their hearts.
This post was edited on 2/24/15 at 10:49 pm
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