The Monty Hall Paradox explained, for once, in English

Quote: MathExtremist

If the monkey chooses randomly (and happens not to show you a car), switching or not doesn't matter. But if the monkey acts like Monty -- that is, it will always show you the goat because it knows where the car is and, under the rules, can't show it to you -- then you should always switch.

Not saying you're wrong so dont jump on me. I have read on other forums from a few math 'experts' that say you ARE suppose to switch doors. The question was geared around NO HUMAN interaction.


Ken

The way I have read this in the past (not saying I'm right)........human interaction and lets say non-human interaction, are or could be (?) two different answers??

Ken

The species of the host doesn't matter, only the behavior. Wikipedia has a good article on this, and near the bottom is a table that compares different host behaviors. If the host acts randomly (as a monkey is presumably going to do) then switching doesn't matter.

http://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_behaviors

Let me explain this problem that is as simple as it gets. Let us assume that there were 100 doors instead of just three. Behind 99 doors are goats, and behind one door is the car. Pick a number between 1-100. I randomly choose the car to be behind door number 25. You choose x. I will open all doors except door 25 and door x. Let us assume that x does not equal 25. Now I will give you the choice of having door x or door 25. Although there are only two doors left it is not a 50/50 proposition. 99% chance it is behind door 25 and only 1 % chance it is behind door x.

The key is that i know where the prize is and only open the doors without the prize. Hope this helps.

Quote: AceCrAAckers

99% chance it is behind door 25 and only 1 % chance it is behind door x.

The key is that i know where the prize is and only open the doors without the prize. Hope this helps.

Most people understand it immediately if you make it 1000 doors.
What they get hung up on is the size of the sample, 3 doors. When
you greatly increase the sample, a child can understand it.

wow, I just noticed the prior unappreciated-genius-in-residence of this website could not get the monty hall paradox!! That does surprise me as whatever else you wanted to think about mkl654321 he was at least fairly smart, and very good at chess.

You're all forgetting three very important points:

1 - Monty Hall knew where the car was hidden.

2 - He did not always open a door and give the option to choose.

3 - He wanted want to avoid giving away the car.

As such, it was very rare for him to give you the option to switch, unless you already had selected the car.

A discussion of this was initiated here:
http://wizardofvegas.com/forum/off-topic/general/4396-the-monty-hall-paradox-interview-with-monty-hall/
It includes a link to an article which includes an interview with Monty Hall himself.

Quote: odiousgambit

wow, I just noticed the prior unappreciated-genius-in-residence of this website could not get the monty hall paradox!! That does surprise me as whatever else you wanted to think about mkl654321 he was at least fairly smart, and very good at chess.

Its called an adult asking a question and then getting feedback. The only thing that DOES surprise me are foul comments and I did mention, I have read contradicting answers from other boards.

Ken

Quote: DJTeddyBear

You're all forgetting three very important points:

1 - Monty Hall knew where the car was hidden.

2 - He did not always open a door and give the option to choose.

3 - He wanted want to avoid giving away the car.

As such, it was very rare for him to give you the option to switch, unless you already had selected the car.

A discussion of this was initiated here:
http://wizardofvegas.com/forum/off-topic/general/4396-the-monty-hall-paradox-interview-with-monty-hall/
It includes a link to an article which includes an interview with Monty Hall himself.

Thank you for the reply. I am mainly interested in the answer with NO human interaction, which I guess I got.

Ken

Quote: mrjjj

Quote: DJTeddyBear

http://wizardofvegas.com/forum/off-topic/general/4396-the-monty-hall-paradox-interview-with-monty-hall/
It includes a link to an article which includes an interview with Monty Hall himself.

Thank you for the reply. I am mainly interested in the answer with NO human interaction, which I guess I got.

That's fine, but remember one thing:

It's difficult / impossible to set up this problem without human interaction.

FYI: In the interview, Monty agrees with the math, but also explains why the math is meaningless.