Three doors

Originally posted by doodinthemood
But only if he was required to open a door would that be the case. By opening a door, he signals that he wants you to think like that and switch. By showing that, it's obvious that he knows you have the correct door.
You should stick.

"You pick one. The host doesn't open that door, but he does open one of the other doors"

That was the question. He always opens a door.

it doesn't say "always" it says he does on that particular time you're on the gameshow.

Originally posted by doodinthemood
it doesn't say "always" it says he does on that particular time you're on the gameshow.

I think it's safer to assume that's how it always works than it is to assume motives on the part of the host.

After all, most quiz show hosts want the player to win. It makes the show more popular.

Originally posted by doodinthemood
But only if he was required to open a door would that be the case. By opening a door, he signals that he wants you to think like that and switch. By showing that, it's obvious that he knows you have the correct door.
You should stick.

If you enter into that kind of assumptions then no reasoning is possible. What if the host wears brown pants more often when the door on the left is the right one, what if there are no correct doors, what if, what if.

The only assumption that is needed is that the game show host simply follows the rules of the show as neutrally as possible.

If there is a probability that he opens the door and a probability that he doesn't is irrelevant at that point as that particular event has already been revealed. The game show host DID open the door on that show. That he does so or not on other shows is irrelevant.

If a player won every time, the show would go bankrupt. Why do shows take lawsuits on those who win fraudulently if by winning they help the show?
No, it is fair to say that the host, while appearing friendly, would rather you didn't win.

However, to assume that something happens every time when that hasn't been said, and more importantly, he didn't say he would do beforehand, is a poor assumption.

Originally posted by doodinthemood
However, to assume that something happens every time when that hasn't been said, and more importantly, he didn't say he would do beforehand, is a poor assumption.

There is no need for the assumption that it happens every time, I explained that in my previous posts.

Edit - And prizes are usually trinkets compared to the receipts from advertising and the production costs of each show.

there is the need for that assumption. As if he doesn't do it every time, one must ask why he's done it now, and the only logical answer would be that he wishes you to switch.
If he does do it every time, then the probability of getting the correct door with switching is 2/3.

Originally posted by doodinthemood
there is the need for that assumption. As if he doesn't do it every time, one must ask why he's done it now, and the only logical answer would be that he wishes you to switch.
If he does do it every time, then the probability of getting the correct door with switching is 2/3.

No, he can simply do it randomly.

It's ridiculous to enter considerations about possible motives for the host when none are provided. Since there is nothing said regarding any possible ulterior motives, it is reckless to assume he has any.

Edit: If you do, then by a similar reasoning no problem would have a unique solution.

To assume that whether or not he opens the door is random seems wilder than to assume meaning. One would naturally assume actions are more often calculated than fatalistically arrived at, especially for a gameshow host.

Originally posted by doodinthemood
If a player won every time, the show would go bankrupt. Why do shows take lawsuits on those who win fraudulently if by winning they help the show?

Because their credibility rests on the fairness of the game, and the popularity rests on the credibility. The average quiz show, especially on a major channel, could easily afford contestants to win every time. They'd still probably be paying the host more than they give out in prizes. A quiz show that nobody ever won would be a complete failure.

You're not allowing a sensible assumption - that the rules will be the same every week, but you're replacing it with an assumption that will never be true.

Take the gameshow who wants to be a millionaire. They could very easily have easier questions so that the million is won each time, but don't, because that would be very counter-productive. The host is never trying to get you to win, or aid you towards that. "Ok, we have 5 envelopes, one contains some money. Feel free to pick one.....ok, you've gone for envelope 3, before you open that, let me show you envelope 1 is empty and you can switch......oKaaaay, envelope 5, I may remind you that envelope 2 is empty, do you want to switch? envelope 4, open it up. It's the money!" That scenario seems unlikely for a reason. It's just an exaggerated version of what the host is doing. It is the fairer assumption that the host does not want you to win.

Originally posted by doodinthemood
Take the gameshow who wants to be a millionaire. They could very easily have easier questions so that the million is won each time, but don't, because that would be very counter-productive. The host is never trying to get you to win, or aid you towards that. "Ok, we have 5 envelopes, one contains some money. Feel free to pick one.....ok, you've gone fo ...[text shortened]... hat the host is doing. It is the fairer assumption that the host does not want you to win.

No, it is not. You need to assume an ulterior motive for the gameshow host, instead of assuming that the host only follows the set of pre-established rules.

Your view requires an assumption that is not justified by the problem itself. Shows need to have a balance between winning and losing. You can't justify any ulterior motive that pushes the host to want the contestant to lose without even further assumptions.

It's simpler and more in relation to the puzzle to assume that the host simply follows mechanically the established rules of the show.

Originally posted by doodinthemood
Take the gameshow who wants to be a millionaire...It is the fairer assumption that the host does not want you to win.

Do you ever get the impression that Chris Tarrant doesn't want the contestant to win? He's not allowed to help them, but he seems genuinely happy when they do well.

What if the host opens the first door and the prize IS behind it? What is the probability that the producer will shoot the host on the spot?

Seriously though, If the prize is not behind the first door it must be behind one of the other two. Therefore, you have a 50/50 chance of picking the correct prize either way. What was the ? I'll take Cokies answer then.

Originally posted by mtthw
Do you ever get the impression that Chris Tarrant doesn't want the contestant to win? He's not allowed to help them, but he seems genuinely happy when they do well.

Because if they clearly indicate that they don't want you to win, it makes them seem horrible. (With exceptions of this being a personality quirk, take weakest link). Just like in carnival scams, the scammer has to act like they're on your side to make you feel comfortable when you lose hideously.

edit: I've just thought, as the two given logical answers both rely on assumptions, and both give opposite conclusions, can it not be said that maybe the likelihood is 50/50 after all? Think about it.