The Monty Hall Paradox--eggheads explain?

Quite Irate

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Does that actually work in lab testing with humans? Does changing actually result in more wins?
Yes. Works with computing programs, works with real life experiments. Rob's explanation game has a handful of permutations. Like all probability-related mathematics, you're going to end up using the properties of large numbers to truly demonstrate the odds. Example - 1000 coin flips will be (overwhelmingly) likely to return results closer to 50/50 than, say, 10 coin flips.
 

rob_just_rob

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Does that actually work in lab testing with humans? Does changing actually result in more wins?

I don't know about lab testing, but mathematically, you are much more likely to pick one winner out of 2 choices than you are to pick one winner out of 10 choices. You are 16% more likely to pick one winner out of 2 choices than 1 winner out of 3.
 

jason_els

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Fascinating!

Yes. Works with computing programs, works with real life experiments. Rob's explanation game has a handful of permutations. Like all probability-related mathematics, you're going to end up using the properties of large numbers to truly demonstrate the odds. Example - 1000 coin flips will be (overwhelmingly) likely to return results closer to 50/50 than, say, 10 coin flips.
 

Mem

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I like to think of it as a situation in Deal or no Deal. If you have 2 suitcases left one is the first one you picked and one other to reveal, your best bet is to quit. Chances are that you did not pick the Million Dollar suitcase to begin with out of the 25 other ones.
 

jason_els

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No I didn't. I remember when Marilyn vos Savant addressed this problem and she caught a ton of flack for saying switching was the right choice. Everybody but everybody was attempting to prove her wrong, even math professors. Since then I've always paid attention to this question.

I'll try the simulators! Thanks!

jason: I saw that you quoted the wiki page. Did you check out the simulators in the external links section?
Monty Hall problem - Wikipedia, the free encyclopedia
 

Mem

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I wish I had a brain for this kind of thing. I feel so stupid.

Here it is in a nutshell (no pun intended)

You have to pick from three curtains, you pick number 1.

They show you that the booby prize is in number 3.

You can either stick with # 1 or # 2.

(The car) can be in either one, but your best bet is to switch and pick #2.

Why, because the odds that you chose #1 correctly (when there were three) are against you.

You may still win or lose, but if you repeat the process over and over you would always come out ahead if you change your mind.

Anyway that is how I interpret it, if it is not I am stupid too.
 

jason_els

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The thing is, the car hasn't moved. Switching doesn't make it any more behind door number one than door number two if you switch!

If it does, then either humans and computers have an inherent tendency to choose incorrectly (even though there is no known foreknowledge), or else switching changes the reality of the outcome.

Here it is in a nutshell (no pun intended)

You have to pick from three curtains, you pick number 1.

They show you that the booby prize is in number 3.

You can either stick with # 1 or # 2.

(The car) can be in either one, but your best bet is to switch and pick #2.

Why, because the odds that you chose #1 correctly (when there were three) are against you.

You may still win or lose, but if you repeat the process over and over you would always come out ahead if you change your mind.

Anyway that is how I interpret it, if it is not I am stupid too.
 

rob_just_rob

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The thing is, the car hasn't moved. Switching doesn't make it any more behind door number one than door number two if you switch!

Correct.

Don't think of it as switching. Think of it as 2 separate games. Of course you'll play the one with 2 choices, as opposed to the one with 3 choices, if you know only 1 is correct. And of course you if someone told you one of the 2 choices is 67% likely to be wrong, you'd go with the other one.
 

Gillette

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The thing is, the car hasn't moved. Switching doesn't make it any more behind door number one than door number two if you switch!

If it does, then either humans and computers have an inherent tendency to choose incorrectly (even though there is no known foreknowledge), or else switching changes the reality of the outcome.

Finally some sense!

If the chance of it being 50/50 after one of the false prizes has been revealed, then now the probability is equal that the original choice is correct as incorrect.
 

Mem

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The thing is, the car hasn't moved. Switching doesn't make it any more behind door number one than door number two if you switch!

If it does, then either humans and computers have an inherent tendency to choose incorrectly (even though there is no known foreknowledge), or else switching changes the reality of the outcome.

No the car does not move.

When you were guessing out of 3 doors, you had a 33&#37; chance of getting it right. Now that you have 2 doors remaining you have a 50% chance of getting it right.

The reason you should switch is because when you guessed door number 1 you had a 66% chance you were probably wrong.

It does not mean that you will win if you do switch it just means that the odds are with you if you do switch.

If you do switch and lose you will kick yourself in the ass.

I understand it, but it is hard to explain in easy terms.

I think, but I may be stupid too.
 

jason_els

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Still, if the car is placed behind a random door then it's just a question of picking the right door. Switching doesn't make your choice of the remaining doors any more informed about the two remaining doors. Apparently, changing is the key to greater success even though the choice of doors was random as well. That shouldn't happen. If people truly choose doors randomly and stick with them, then switching shouldn't make a difference yet it does.

No the car does not move.

When you were guessing out of 3 doors, you had a 33% chance of getting it right. Now that you have 2 doors remaining you have a 50% chance of getting it right.

The reason you should switch is because when you guessed door number 1 you had a 66% chance you were probably wrong.

It does not mean that you will win if you do switch it just means that the odds are with you if you do switch.

If you do switch and lose you will kick yourself in the ass.

I understand it, but it is hard to explain in easy terms.

I think, but I may be stupid too.
 

rob_just_rob

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Still, if the car is placed behind a random door then it's just a question of picking the right door. Switching doesn't make your choice of the remaining doors any more informed about the two remaining doors. Apparently, changing is the key to greater success even though the choice of doors was random as well. That shouldn't happen. If people truly choose doors randomly and stick with them, then switching shouldn't make a difference yet it does.

Try this rationalization:

Taking away one option (e.g. revealing 1 goat) doesn't change the fact that your first choice had only a 33% chance of being correct, and is STILL only 33% likely to be correct.
 

Guy-jin

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The thing is, the car hasn't moved. Switching doesn't make it any more behind door number one than door number two if you switch!

If it does, then either humans and computers have an inherent tendency to choose incorrectly (even though there is no known foreknowledge), or else switching changes the reality of the outcome.

It's not about where the car is, nor is it about a tendency to choose incorrectly. It's about probability.

The point you may be forgetting about is that the car does have to be behind one of two of the doors, and is never behind the third door. Meaning, the door that's eliminated by Monty is never the car.

And that's how the game is won by switching. Because you have to wait until after Monty has increased your odds by getting rid of one of the doors that isn't the car and letting you choose again.

If you stick by your original choice, you're still playing as if you had a one in three chance, and you're not upping your chance of winning at all.

Ever play craps? :tongue:
 

Mem

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Still, if the car is placed behind a random door then it's just a question of picking the right door. Switching doesn't make your choice of the remaining doors any more informed about the two remaining doors. Apparently, changing is the key to greater success even though the choice of doors was random as well. That shouldn't happen. If people truly choose doors randomly and stick with them, then switching shouldn't make a difference yet it does.

The door you originally picked has a 66&#37; of being the wrong door. Once there are two doors left, the odds that you picked the right door from the beginning goes down. Therefore switching will increase the odds of winning on average, and in the long run, but not every time.