Riddles

[Legion]

OK but since the host will always eliminate one of the 3 that is not yours and is wrong then possibility 2 and 3 should not count as 2 different situations since it makes no difference if which one is eliminated, since it will not be yours or the correct box.  

Think about it no matter which box you choose and not matter which box is correct your choice is always coming down to picking between one of two boxes not one of three boxes.

[The Jade Knight]

As much as you don't think they "should count" as two different situations, they are.  And you just agreed there were three possible outcomes with a 33% chance of each.

Yes, it always comes down to one of two boxes, but initially (and this is very, very important), it gets placed in one of three boxes.

So you do, indeed, have three potential scenarios, even though, in any of the three given scenarios, you have two choices.

Do you understand?


If I handed you two boxes, and said there was $50 in one, there would be two potential scenarios:
Either the $50 is in box a, or
the $50 is in box b.

However, because the situation we're given starts with three boxes, there are three different scenarios we're dealing with.


Again, I recommend you click on the link Ookla provided for verification of this.  If you can figure out another reason things stack the way they do, you're welcome to try a mathematically sound explanation.

[Legion]

I would agree with you completely if you where not given the choose to switch after the first box was removed.  But since 1 of the 3 boxes are taken away and you are given the choice to either switch to the other box or stay with your current box then it completely negates one of the situations.

OK Facts:
1) You pick 1 of three boxes
2) No matter which box is correct and which box you pick, a wrong boxes that is not yours will be eliminated.
3) The host will ALWAYS give you the chance to switch

This means that your first guess has no impact on whether you will win or lose, it is just like getting a buy round in a tournement.  So the only real choice you have in this situation is whether you stay with box 2 or switch to box 1....which is a 50% that yours is right. Now if the host never gave you that chance to switch then you would be right you would only have a 1 out of 3 chance of winning.

I will look at Ookla's link again, but I cannot till tonight.

[The Jade Knight]

This means that your first guess has no impact on whether you will win or lose, it is just like getting a buy round in a tournement.  So the only real choice you have in this situation is whether you stay with box 2 or switch to box 1....which is a 50% that yours is right. Now if the host never gave you that chance to switch then you would be right you would only have a 1 out of 3 chance of winning.

I will look at Ookla's link again, but I cannot till tonight.

Your first to comments above are correct, but your conclusion does not stem from them at all.  Also, WHICH box you guess initially has no impact on your chances of winning or losing, however, the fact that you get the guess makes an impact.
It is not just like getting a "buy" round.

You YOURSELF agreed that there were three possible outcomes of any given round.  I've explained how these fall <b>with percentages</i> so you can add up the math.


If you feel you were incorrect in your own statements, or would otherwise like to argue your point further, you're going to have to include some math that takes into account the situation, and logically provide an explanation that supports it.


In the face of everything I've provided you, "There are two boxes, therefore it must automatically be a 50% chance" does not cut it; there are three possibilities.  You agreed to this yourself.  Your "solution" only provides us with two.

[Firemeboy]

You can look at it another way.  If I gave you three boxes, and said you could either pick one box, or pick two boxes, in hopes to find the 'prize', what would you pick?  You would pick two, even though you knew that one of the boxes would be empty.  You would rather have two chances at winning than just one.

So, in the scenario, when you 'switch', you are in affect picking the other two boxes, even though you know one of them already is not the prize.  

[Legion]

I have been thinking about the scenarios you gave Jade and if you really think about it there are 4 scenarios not 3

You Pick box 2 in all of the scenarios
scenario 1
1) You pick B
2) C is eliminated
3) A is correct
4) You lose

scenario 2
1) You pick B
2) A is eliminated
3) C is correct
4) You lose

scenario 3
1) You pick B
2) C is eliminated
3) A is incorrect
4) You win

scenario 4
1) You pick B
2) A is eliminated
3) C is incorrect
4) You win

4 scenarios and you lose half of them using the game show rules.  Still need to re-look at Ookla's link but just thought of that.

[Legion]

You can look at it another way.  If I gave you three boxes, and said you could either pick one box, or pick two boxes, in hopes to find the 'prize', what would you pick?  You would pick two, even though you knew that one of the boxes would be empty.  You would rather have two chances at winning than just one.

So, in the scenario, when you 'switch', you are in affect picking the other two boxes, even though you know one of them already is not the prize.  

yeah that makes sence but at the time when you can switch you know that 50% of the 66% is wrong.  This leaves you with 50% of 66% which is 33%.  So really its 33% of the orignal against 33% of the orginal....once again is it better to switch to 2 of 3 boxes when you know exactly which one of the two is empty...no its not because it still comes down to a 50/50 chance.

Its like this you can pick box 1 and 3 against box 2, but the host tells you ahead of time that box 3 is not it....so which do you do, does it really matter if you pick box 1 and 3 or box 2......I do not see how it does

[The Jade Knight]

You Pick box 2 in all of the scenarios
scenario 1
1) You pick B
2) C is eliminated
3) A is correct
4) You lose

scenario 2
1) You pick B
2) A is eliminated
3) C is correct
4) You lose

scenario 3
1) You pick B
2) C is eliminated
3) A is incorrect
4) You win

scenario 4
1) You pick B
2) A is eliminated
3) C is incorrect
4) You win

So, remember this:  You agreed that there was a [33%] chance (equally), that the correct answer was in box A, B, and C, therefore:

Scenarios 3 and 4 BOTH fall under one scenario which has a [33%] chance of occuring (the correct answer being in box B), so Scenario 3 has a [16%] chance of occuring, and scenario 4 has a [16%] chance of occuring.

Once again, you are left with 66% verses 33%.

[The Holy Saint, Grand High Poobah, Master of Monkeys, Ehlers]

Will someone just call someone else a Nazi already?

[JP Dogberry]

e, you're a nazi.

[The Holy Saint, Grand High Poobah, Master of Monkeys, Ehlers]

That wasn't quite what I expected.

[Archon]

Don't worry, it's just the anarchist calling the Nazi black.

[Firemeboy]

It's easier to think of it in larger terms, again, assuming the host knows where the thing is, and always takes away all of the doors that are not correct.

If there are 10 doors, and you pick on at random, then 8 are removed, you will win 90 percent of the time if you switch.

[Firemeboy]

Since it's been more than 24 hours, again...  Here is another one.

You and two other very smart people were brought before the President.  He want's to see which of you is the smartest, so you can figure out how to lower gas prices.  

You are led blind-folded into a small room, and seated around a table.  The president describes the test.

"Upon each of your heads I have placed a hat. You are either wearing a blue hat or a white hat. You don't know which, but I will tell you this; at least one of you is wearing a blue hat. There may be only one blue hat and two white hats, there may be two blue hats and one white hat, or there may be three blue hats. But you may be certain that there are not three white hats."

The president explains that when the blindfolds are taken off, the first to correctly announce the color of his hat shall be his advisor.

With that, the president uncovers your eyes and you see that your two competitors are each wearing blue hats. You see from the look in their eyes that they are thinking, "What is the color of my hat?"

For hours nobody speaks, then finally you stand up and say, "The color of the hat I am wearing is..."

What color is your hat?  And how do you come to that conclusiong?

[Archon]

Blue, because he wants to give the same test to all three applicants.