Variants of Monty Hall problem

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In summary, the conversation discusses variants of the Monty Hall problem and how to handle situations where Monty may or may not open a door. The main question is how to behave in different scenarios if Monty either wants or does not want the contestant to find the car, or if his intentions are unknown. The speaker also asks for ideas or suggestions in this situation.
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I have a couple of variants of the http://en.wikipedia.org/wiki/Monty_Hall_problem" that I have a hard time to figure out how to handle.

What if Monty doesn't have to open the door. All we know is that he is smart. How should we then behave if
1) he wants us to find the car?
2) he does not want us to find the car?
3) we don't know if he wants us to find the car or not, or maybe he doesn't have any intentions?

Do you have any ideas?
 
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  • #2
If he doesn't open a door after you made your selection, then it may not matter. Are you assuming he opens a door sometimes? Your question is vague.
 

1. What is the original Monty Hall problem?

The original Monty Hall problem is a probability puzzle named after the host of the game show "Let's Make a Deal". It involves a game show contestant choosing one of three doors, behind which are two goats and a car. The host then opens one of the remaining doors, revealing a goat. The contestant is then given the option to switch their choice to the other unopened door. The question is, does switching doors increase the contestant's chances of winning the car?

2. What is the variant where the host always opens a door with a goat behind it?

This variant is known as the "always switch" Monty Hall problem. In this version, the host will always open one of the remaining doors to reveal a goat. The contestant is then given the option to switch their choice to the other unopened door. The question remains the same - does switching doors increase the contestant's chances of winning the car?

3. What is the variant where the host randomly opens a door?

This variant is known as the "random door" Monty Hall problem. In this version, the host can randomly open one of the remaining doors, revealing either a goat or the car. The contestant is then given the option to switch their choice to the other unopened door. The question remains the same - does switching doors increase the contestant's chances of winning the car?

4. What is the variant where there are more than three doors?

This variant is known as the "multi-door" Monty Hall problem. In this version, there are more than three doors to choose from, but only one door has a prize behind it. The host will then open all but one of the remaining doors to reveal they are empty. The contestant is then given the option to switch their choice to the remaining unopened door. The question remains the same - does switching doors increase the contestant's chances of winning the prize?

5. Can the Monty Hall problem be applied to real-life scenarios?

Yes, the Monty Hall problem can be applied to real-life scenarios involving decision making and probability. For example, it can be used to explain the concept of conditional probability and how our initial assumptions can affect our decision-making process. It can also be used to demonstrate the benefits of gathering more information before making a decision, as switching doors in the Monty Hall problem is only advantageous if we have more information about the remaining doors.

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