The Monty Hall Paradox

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As this seems to be a mathematical paradox more than anything else, I suppose it belongs in this forum.

The premise is to play the Monty Hall gameshow game by choosing the door that the big prize conceals. But before that door is opened, another door will be opened revealing a booby prize and you must then decide on whether to stay with your original choice or choose the other unopened door. My rationale is that once the choice is down to two doors, you have a 50-50 chance of being right no matter which door you pick. Not so says those who analyze the probability of the big prize being behind the chosen door.

So try it a few times for yourself here:

PLAY THE GAME HERE

And then see if your experience matches the explanation of probability:

And Behind Door No. 1, a Fatal Flaw

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10 tries.

8 cars 2 goats

one stay. got a goat.

Switched the next seven tries, got one goat, six cars.

Joe(where do I get tickets to the show?)Nation

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So gut level, Joe, do you think the on line game was rigged to demonstrate "proof" for the theory of probability here? Or is the theory of probability the real deal?

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What do you mean rigged?

If the initial door chosen had the goat every time, how could it not be the proper choice to switch?

out of 10 tries of not switching, I got 1 car, 9 goats.

out of 10 tries of switching, 6 cars, 4 goats.

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What made this click for me is that Monty Hall always opens a losing door. If he opened a door randomly, it wouldn't make sense. But it's not completely random -- he always opens a losing door, never a winning door.

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Chai wrote:

What do you mean rigged?

If the initial door chosen had the goat every time, how could it not be the proper choice to switch?

out of 10 tries of not switching, I got 1 car, 9 goats.

out of 10 tries of switching, 6 cars, 4 goats.

By 'rigged', I mean do they have the game rigged to favor those switching rather than offering a truly random choice? And it would be rigged to support their conclusion that the law of probability says that switching will produce more wins than staying with your initial choice.

To me it seems that once the door that is opened--Soz is correct, that this will always be a losing door--you are down to two choices. One will have a car and one will have a goat. Why wouldn't the probability then be 50-50 between a win and a loss?

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It would be. Evens I mean.

But if it's rigged you get an argument going with all the elite and that results in PUBLICITY and that results in increased viewing figures and that results in bigger fees for screening the ads.

The opened door is an irrelevance. Once it's opened it's out of the game.

It is included to make the show last longer. Tossing up would cause a 20 second show. Useless eh?

It's a joke about how thick Americans are.

It's easy. Follow the money never mind your own inflated ego.

The monkeys are a snowstorm.

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Of course the game is rigged--Monty knows which door contains the car.

Look the player initially has a one out of three chance of choosing the car, and a two out of three chance of choosing the goat---Monty then shows one of the goats and the odds change (See conditional probability AKA Bayes Theorem)). The one out of three, suddenly change---now the unknown doors are a 50:50 chance, and the odds were that the players initial guess was the goat.

Try this

Initial chance--player picked car(1/3)--Monty shows goat (1/1)--player Switches-loses (1/3)*(1/1)=1/3
Initial Chance---player picked goat(2/3)---Monty shows goat (1/1)--player switches--wins (2/3)*(1/1)=2/3

Rap

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Well Spendi agrees and RipRap puts out the math theorum that, while I gut level believe is probably spot on accurate, makes me blink and wish I could understand. I still cannot understand why switching from your initial choice is likely to produce a better result than staying with it once the equation is reduced to two choices.

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rap is showing the odds in two different situations.

Once the goat is revealed it's history and that door might as well be at the North Pole.

Car or goat. 2 doors. Now. Nothing to go on except a wink from the continuity girl. Ads. Contestant ponders. Ads. Contestant decides.Ads. Car revealed. Latest model with all the extras. Tastefully lit. Ready to drive away.

Who chooses which car?

Love it. Saps wanted.

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Foxfyre wrote:

Well Spendi agrees and RipRap puts out the math theorum that, while I gut level believe is probably spot on accurate, makes me blink and wish I could understand. I still cannot understand why switching from your initial choice is likely to produce a better result than staying with it once the equation is reduced to two choices.

Well, keeping blinking, because the odds are 2 out of 3, not 1 out of 2.

there are 3 doors, period, that is always the denominator. It doesn't change to 2 just because monty picked a door.

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They said it did.

If the contestant can switch it means that his first choice is of no consequence. It is there to spin the time out.

Once the goat as been shown there are 2 choices. And the contestant has not yet chosen. 50-50. If a switcher beats the odds all the time somebody is winking.

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spendius wrote:

They said it did.

If the contestant can switch it means that his first choice is of no consequence. It is there to spin the time out.

Once the goat as been shown there are 2 choices. And the contestant has not yet chosen. 50-50. If a switcher beats the odds all the time somebody is winking.

You're wrong.

Pick a door: You have 1/3 chance of being right.

Eliminate a door: No effect on your initial choice; still 1/3 chance of being right.

Change doors: 2/3 chance of being right.

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They said you could switch after the goat appeared hopefully after having had a ****.

If I have that wrong I apologise and, of course, you are right DD. But if you can switch you haven't yet made a choice.

It costs a lot of money to advertise a car so the guy whose job it is to advertise cars has found some lesser advertisers willing to reduce his costs so you end up watching a dragged out advert for a car whilst complaining about how many adverts you have to put up with to see the main one.

The mathematics is to help you think you are watching a programme. It's not all that much different from Find the Lady on the racecourse car park.

It also advertises cars in general and thus foreshadows the destruction of the planet. According to Mr Gore I mean.

I have no view on that.

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spendius wrote:

I have no view on that.

Thank God for small favors... :wink:

RH

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Makes sense to me, but I had to think about it a bit. No matter which door he opens, the odds of your first pick being right are 1 in 3. You have a 2 in 3 chance of picking wrong, so when he opens the door to reveal the goat, there is a 2 in 3 chance that the other door is the right one.

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But if the car is there the show's over. That's a million to one. At least.

Cut!

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DrewDad wrote:

spendius wrote:
They said it did.

If the contestant can switch it means that his first choice is of no consequence. It is there to spin the time out.

Once the goat as been shown there are 2 choices. And the contestant has not yet chosen. 50-50. If a switcher beats the odds all the time somebody is winking.

You're wrong.

Pick a door: You have 1/3 chance of being right.

Eliminate a door: No effect on your initial choice; still 1/3 chance of being right.

Change doors: 2/3 chance of being right.

DD has it right.

Joe(the rest is blather)Nation

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spendius wrote:

But if the car is there the show's over. That's a million to one. At least.

Cut!

WTF are you talking about?

cars and other grand prizes where given away on that game show and every other game show all the time. That's why they do it at the end of each show you dip ****.

New day, new car. The more winners, the more viewers, the more sponsors, the more revenue.

Have you never watched a freaking game show before?

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Still doesn't make sense to me. Seems like once one choice is eliminated you are left with a choice of two doors. Behind one door is a car and behind the other is a goat. Whether you change your initial choice or decide to change your initial choice, how at that point are your odds any other than 50-50 of making the right choice?

(And surely even A2Kers don't have to fight over two fictitious goats and a fictitious car. Smile

)

By the way, when I stayed at the website through a series of picks, changing doors did net me the car more often.

When I exited and re-entered the website between each pick, the results were more even.

Coincidence? Fluke? Or by design?

When I get time I'll experiment some more with it.

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The Monty Hall Paradox

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