Win 1 Million Dollars: Pick the Right Door

  • Context: High School 
  • Thread starter Thread starter KingNothing
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Discussion Overview

The discussion revolves around the game show scenario known as the Monty Hall problem, where a contestant must decide whether to switch their initial choice of door after one non-winning door is revealed by the host. The conversation explores the implications of switching versus staying with the original choice, examining the probabilities involved and the reasoning behind them.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants argue that switching doors increases the probability of winning from 1/3 to 2/3, citing the information gained when the host reveals a goat behind one of the doors.
  • Others contend that the initial probabilities remain unchanged after the host opens a door, asserting that the prize is equally likely to be behind either of the remaining doors.
  • One participant expresses skepticism about the validity of the switching strategy, comparing it to philosophical paradoxes and questioning the reliance on "commonsense" reasoning.
  • Another participant suggests that the problem can be understood differently by considering a scenario where two doors are picked at once, which they argue leads to a clearer understanding of the probabilities involved.
  • There are claims that the reasoning of those who support switching is flawed, with some participants emphasizing the importance of logical proof over intuitive reasoning.

Areas of Agreement / Disagreement

Participants do not reach a consensus; there are multiple competing views regarding the effectiveness of switching doors and the interpretation of the probabilities involved. The discussion remains unresolved with ongoing debate about the reasoning behind each position.

Contextual Notes

Some participants highlight the potential for confusion regarding the role of the host's actions in providing information about the location of the prize, indicating that assumptions about the problem may vary among participants.

  • #31
the door on the RIGHT!
 
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  • #32
When I first encountered this problem, I did't seem right to me that switching would help. Many posters before me gave other excellent ways of looking at the problem that might convince one that switching is good. I will propose another way of looking at the problem here that doesn't rely much on the probability of it all, but on intuition.

Consider these two games:

Game 1: You get to pick one of the curtains, the host doesn't reveal anything to you, and you are given the option to switch.

Game 2: This is the original game. You pick one curtain, the host reveals an empty curtain, and you are given the option to switch.

What happens if you don't switch in either of the two games? Your intuition should tell you here that your chances of winning will be the same in both games.

Now what happens if you do switch? Which game will you win more in if you play the game a considerable amount of times? (Note that in Game 1, your chances of winning will not change whether you switch or not).

Before I leave, I would like to propose a variation of the original game. Suppose a contestant picks one of the three curtains and leaves. The host lifts one of the 'bad' curtains leaving two curtains (one of them being the one the contestant picked). In comes another contestant (who doesn't know what has happened) and is asked to picked a curtain. The probability that this contestant will choose the winning curtain is 1/2 right? Now what if the contestant chose the the same curtain as previous one. Would his/her chances of winning increase by switching? What if before choosing one of the two curtains, the current contestant was told the whole story of what happened. Will this information allow the current contestant to choose a curtain that will increase his chances of winning?

e(ho0n3
 
  • #33
I think you've forgiot to mentiomn the fact that there are 3 curtains:

Game 1: the probability remains 1/3 whether or or not you decide to change.

Game 2: the proabbilty increases to 2/3 if you change curtains

In your final paragraph, the proabilty of choosing the correct curtain is indeed 1/2 if he doesn't have any prior knowledge, BUT this will increase to 2/3 if he chooses the curtain that the last player DIDN'T pick
 

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