Final Decision

[ccvi]

Originally posted by MANDO
Ok Raider179,
now imagine you have 1000000 doors with only one golden coin, the rest are goats. Initially you select door number 710567.

Suddenly, all the goats but one piss their doors, only your door and other remain clean. Would you change the door? If you dont change your door, and you win, you are really, really, really lucky.

And yes, at the end you have two doors, one good, one bad, 50%?

50%. Because there's nothing that preven'ts the possible goat behind the selected door to also releveal itself.
probability for selecting the correct one is 1/1000000
probability that, if 999999-1 random goats releval themseleves (because all goats are equal, and the one behind the selected door does not get any important parts cut off etc - that's not in the story) and the one that does not reveal itself is the one you selected is if it was a goat 999999/1000000 * 1/999999 = 1/1000000.

Both probabilities are equally low.

You need an external all-knowing intervention like a game-show master or a wizzard to get different results. Mechanical failures and goats both lack this part.

[Tilt]

Originally posted by MANDO
BlauK,
considering that the initially selected bomb may be training and lost, if we change always the lever, we'll get 50%, if we dont, 33%. Even in this case the answer is the same: TO CHANGE THE LEVER.

You seem to assume by changing the lever the odds are changed...........

Actually the odds were changed when he saw that the first bomb was a training bomb........

If he did not know if the first bomb was real or not (even after dropping) then the chance was still 33%.


According to your arguement changing the lever changes the odds...........but supposing he changed it and then changed it back again............. your logic would assume that the odds revert to 33%? if your logic assumes that it remains at 50% then it was 50% before the lever was moved also.

[dedalos]

Originally posted by MANDO
Raider179, the idea is that first time you were in front of a door, you have 2/3 chances of missing the correct door. So, it is more probable that the correct door is any of the other two.

If you dont agree this from the beginning, do not continue.

If a goat sounds in any other door but yours, then you take out that door from the group with 2/3 chances of having the correct door. Now you have your original door and another one. Your door has the same chances as the beginning 1/3. But the group with 2/3 now has a single door left (with 2/3). So, it is better for you to change your door.

Mando, with this logic it is bretter not to switch

[MANDO]

Originally posted by ccvi
You need an external all-knowing intervention like a game-show master or a wizzard to get different results. Mechanical failures and goats both lack this part.

Why do you need an external all-knowing intervention? He is just going to show you all except 1 bad and 1 good (the only good). You may force that kind of situations without external all knowing intervention.

Lets get back to the 2 goats and a golden doblon example, and lets change the preparation a bit.

1 - you force the goats to drink a lot of water and place them randomly, also place the doblon.
2 - the "player" selects initially a door and wait in front of the doors.
3 - As soon as a single goat pisses (clearly noticeable below the door because the floor behind the door is inclined) the player will take a final decision.

Should the player change his door when a goat in a different door pisses? Of course, the golden doblon is not going to piss.

[lasersailor184]

Exactly mando.  That changes the odds of finding the right door.  There is one less door to worry about.

[MANDO]

Originally posted by lasersailor184
Exactly mando.  That changes the odds of finding the right door.  There is one less door to worry about.

So, he should change or not?

[ccvi]

Originally posted by MANDO
Why do you need an external all-knowing intervention? He is just going to show you all except 1 bad and 1 good (the only good). You may force that kind of situations without external all knowing intervention.

He, who opens the doors, knows what's hidden where.

Originally posted by MANDO
Lets get back to the 2 goats and a golden doblon example, and lets change the preparation a bit.

1 - you force the goats to drink a lot of water and place them randomly, also place the doblon.
2 - the "player" selects initially a door and wait in front of the doors.
3 - As soon as a single goat pisses (clearly noticeable below the door because the floor behind the door is inclined) the player will take a final decision.

Should the player change his door when a goat in a different door pisses? Of course, the golden doblon is not going to piss. [/B]

a) 1/3: initial selection correct
b) 1/3: initial selection wrong, goat reveals behind the non-selected door
c) 1/3: initial selection wrong, goat reveals itself behind the selected door

In cases a and b (they look the same from the point of view of the player) switching will not improve the probability of winning. It's 1/2.
In case c switching will improve the probability of winning from 0 to 1/2.
Always switching results in the same probability of winning as only switching when required to (when the initial selection is revealed as false).

The pilot with the lost bomb was in case a or b. Switching does not help him.