How Does Adding a Fourth Door Affect the Monty Hall Problem?

In summary, the conversation revolves around a variant of the Monty Hall Riddle where a contestant must choose one of three doors in order to potentially win a car. The probability of the car being behind any door is 33.33%, but after one door is chosen, another door is added as an option. There are two solutions to this problem, depending on the host's attitude towards the contestants. The conversation also mentions the famous Marilyn vos Savant's handling of the problem and suggests testing the probability by generating random integers. Ultimately, the consensus is that switching choices is better in this scenario.
  • #1
cookiecrunch
2
0
Hello all,


I stumbled upon a basic probability type question from the movie 21 and was hoping someone could provide me with an explanation. The question is as follows:

If i have 3 doors and behind one of the doors is a car and behind the other 2 doors is nothing and i have to choose one of the doors. In this case it doesn't really matter which door i choose because the probability of a car being behind any door is equal that is 33.33%, so say i choose door 2. Now given that i chose door 2 what if another door was added and i had an option to either leave door 2 as my choice or pick another one the answer was to pick another one to account for variability and the fact that picking between door 1,3 and 4 will increase my chances of winning.. I don't understand how the probability of 1,3 and 4 is higher given that i picked door 2 and after which another door that is door 4 was added..


Any help will be greatly appreciated!


Thanks
 
Physics news on Phys.org
  • #2
This is a variant on the well-known and highly contentious Monty Hall Riddle. Probably easier if you read up on this first and then adapt it to your riddle.

Some very intelligent and highly respected people have weighed in on this - trouble is, different very intelligent and highly respected people have come to opposite conclusions!

Search PF for a host of posts on that very subject.
 
  • #3
This variant doesn't work, I think. You know that door 4 does not have the car. You have gained no new information.
 
  • #4
It has something to do with the host's atitude towards the contestants of the tv show I believe and there are two solutions as a result ("friendly host" and "tricky host").
 
  • #5
DaleSpam said:
This variant doesn't work, I think. You know that door 4 does not have the car. You have gained no new information.

Well, practically speaking, we don't know that for sure that the car is not behind door 4 just because the host made it an option...i mean he could simply be toying with your mind..i think most people would think that given the fact that he opened the door after "I" made my choice that the car is probably not behind that door.

Actually i just listened to the question part of the movie again and it turns out that the person first chooses door 1, the car is actually behind door 2 and only the host knows that..and he opens another door that is door 4 after i make my choice..and apparently the probability of switching my choice given that another door has opened for me to choose from is better...Does this help?
 
Last edited:
  • #6
DaveC426913: This is a variant on the well-known and highly contentious Monty Hall Riddle. Probably easier if you read up on this first and then adapt it to your riddle. Some very intelligent and highly respected people have weighed in on this - trouble is, different very intelligent and highly respected people have come to opposite conclusions!

Hold your horses! Didn't Marilyn vos Savant handle that problem? You can easily prove it to yourself: Let you computer generate pairs of random integers 1-3. The first integer represent your choice of door, the second the correct answer.

In the case, that you are correct, the two numbers match, and you will win. This will happen about 1/3 of the time. BUT IF YOU SWITCH, well the only number that now can be shown now with yours, if you were originally wrong, IS THE CORRECT ONE! This will be the case about 2/3 of the time.

Marilyn said that she suggested this type of tests to many people and no one failed to report that switching was better.

HOWEVER, there can be a question if we assume the announcer has some leeway in what he is going to do once you chose, but I don't see that as part of the original problem.
 
Last edited:

FAQ: How Does Adding a Fourth Door Affect the Monty Hall Problem?

1. What is the probability question from the movie 21?

The probability question from the movie 21 is, "What is the probability of drawing a card from a standard deck of cards and it being an ace?"

2. How does the probability question from the movie 21 relate to the plot?

The probability question from the movie 21 relates to the plot because the main character, Ben, uses his knowledge of probability to win at blackjack and make money.

3. What is the formula for calculating the probability in the movie 21?

The formula used in the movie 21 to calculate the probability is P = desired outcomes / total outcomes.

4. Is the probability question from the movie 21 realistic?

The probability question from the movie 21 is based on a real-life technique called card counting, but the specific scenario in the movie may not be entirely realistic.

5. Can anyone use the probability question from the movie 21 to win at blackjack?

While the concept of card counting can increase your chances of winning at blackjack, it is not a guaranteed method and is also considered illegal in many casinos. Additionally, the specific technique used in the movie may not be effective in real life.

Back
Top