So You Think You're Smart? Take 4
Ah, yes. Time for another puzzler.
An evil magician has enslaved your true love. You, of course, come riding to the rescue. "Forsooth, evil magician," you say. "Release my true love."
"Yeah, well maybe not," he replies (evil magicians being predominately male and all). "But I'll tell you what. Are you feeling lucky?"
"Luck?" you say. "What need have I of luck when I am filled with virtue?"
"OK, Virtuous One. Here's the deal: you see these three cups that magically appeared in front of you? Well, one of them is poisonous, the other two are samples from my private stock of excellent wines. Pick the right one and your true love will go free."
Alas, there's no telltale smell or any other distinguishing characteristics. Drawing on your inner integrity, you bravely choose one and start to drink it.
"Not so fast, Skippy," the evil magician says. "I like your spunkiness. I'm gonna do you a favor." And with that, he picks up one of the glasses and drinks it down. "There, you now know that one of these drinks was non-poisonous. And, if you want, I'll even let you switch glasses now that you know that the glass I just drank was non-poisonous."
And now, it's up to you. Should you tell him...
A. "Thou fool and wretched fiend. What availeth it me if I switch unless by some trickery thou hast changed glasses?!" (Which he didn't do -- I know because I was watching).
B. "Hah! Thou didst not know, but that thou gavest me key information. I shall switch my choice to the other cup."
C. "Hah! Knowing thy wickedness, and that thou must surely attempt to mislead me, I shall surely stay with my original choice!"
Similar example was given i believe in the "21" movie by Kevin Spacey. But even without that the answer is same by simple Theory of Probability :)
The odds that it is the other glass is now 2/3.
However, in this case, it is life or death. The experiment will only be performed once. So it, is in my thinking, truly still down to chance. There are two glasses left, and by sticking with your glass, you are just as likely to have chose correctly as not. 50/50.
Again, if you were to repeat the experiment over and over again, then you would always be better off changing your answer after one poison glass is revealed. So I am guessing the answer you are looking for is B, but in this case, I believe that that answer is incorrect.
Perhaps there is a statistician in the room that can explain it in a way where it applies to a single experiment, because I don;t see how it would. But since I am not a statistician, I could very well be wrong.
turn of phrases and all. Here's why: First of all, you state that you had already begun drinking from one of the cups. It it were
poison, you would surely be dead already. Additionally, if you were already drinking from the poisoned galss the evil magician would not have stopped you, but
allowed you continue on in your follow and meet your certain fate. The only motive the evil magician would have for stopping you would be in an attempt
to change your mind since you were about to outwit him. Since he drank from one of the glasses, he has eliminated that one
from your equation, and that leaves the glass on the table being the one obviously with the poison. That, and
something about a land war in Asia...
In the classic version, there is one "good" choice, but in this case there is one "bad" choice, so the probabilities are reversed. Therefore, there is a 2/3 chance that the original choice is safe, and only a 1/3 chance of prevailing by switching.
That all said, the behavior of the magician is a key factor, and this probability would only hold true if he is bound to follow a certain set of rules, most notably that he must offer the choice to switch regardless of whether the initial choice was poisoned or not.
As this is an "evil" magician, there would be no logical reason for him to offer an opportunity to switch if the poisoned glass was chosen, so this would lead me to conclude that the glass I chose was safe, and that the remaining glass contains the poison.
In other words, what Brad and Ed said. And if all else fails, I have of course spent the last few years building up an immunity to iocane powder.
Wow. I didn't even notice the reversal. I was hung up on the Monty Hall stuff and did not even realize that I was mixing it up in my head. Good catch, very clever.
I too now agree that The Princess Bride is the answer to all of life's mysteries. I should just stick to trying to find rhymes for the things people say.
Inconceivable!
@jason dean ... statistics can never say with certainty the outcome of a single experiment; it only describes chance over a set. Even if the odds are 99:1, you can just as easily pick the 1 in any given trial. And I didn't see the reversal either ... damn damn damn.
Or, perhaps the magician realizes that "your true love" is not the a girl, but yourself and therefore by drinking the poison (again the magician's "right" one), he will be releasing "your true love" (ie, your death).