Quizmaster’s dilemma

Slighty off-topic, but fun: the Quizmaster’s Dilemma. I learned about this a long time ago, and it is a quite well known case in game theory. Tonight I tried to explain this to Robin, our housemate, but he is still not convinced. So let me tell you the dilemma and challenge you to give your answers in the comments below (and of course: do not cheat by looking it up first…)

Here we go: a candidate is about to win a prize in a quiz. He is presented with three curtains; one of them hides the prize, the other two are empty. The quizmaster asks the candidate to select a curtain and make his choice known. Before opening the curtain of choice, the quizmaster opens up one of the other curtains, one of which he knows that it is empty. He then asks the candidate if he wants to change to the other curtain. The dilemma is: does changing from curtain improve his chances of winning the prize or not?

Let me know what you think and why!

6 gedachtes over “Quizmaster’s dilemma

  1. I would say no. After the quizmaster has opened up one curtain, the fact that the quizmaster gives the candidate an opportunity to switch, improves the candidate’s chances of winning the price from ‘1 out of 3’ to ‘1 out of 2’. But this improvement is independent of the choice of the candidate. Changing from curtain will not increase this chance. So whether the candidate changes from curtain or not, his chance of winning the price remains 1 out of 2…

  2. Hi Frank, good to meet you here. I have altered the text a little bit to make an important clue a bit clearer… and with that I also mean to say that you answer is close but not sufficient 🙂

  3. No, there’s no reason to change to the other curtain – it’s 50/50 now – the quizmaster has only eliminated a third option – without doing this, the candidate’s changes would have been 33,33333333 percent. Right?

    PS I didn’t read any of the other comments – honestly! But I will do that now… of course. Just to check whether I’ve made a complete fool of myself. Again.

  4. Okay, no more candidates for the prize… here is the solution.

    The answer is that it is better to switch curtains – it will double the chances of winning from 33% to 66%! Sounds strange and completely counter-intuitive, but it is true and can be statistically proven. How can this be so?

    Read it in the next post…

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