Riddle Me This

**galwayhoop** · 19/09/2007, 1:02 PM

Originally Posted by Schumi

Say at the start you pick box A. If the prize is in box A, the host shows you an empty box and you'd be better off sticking with box A. .

makes sence

Originally Posted by Schumi

If the prize is in box B, the host shows you the empty box C and you'd be better off changing to box B. .

still makes sence

Originally Posted by Schumi

If the prize is in box C, the host shows you the empty box B and you'd be better off changing to box C. .

what you on about willis. there are only 2 boxes remaining and therefore it can't be in box c (we are assuming that is the empty at the start).

Originally Posted by Schumi

Therefore, two thirds of the time, you will win by changing your box.

you will not because in your example you kept moving the bl0ody prize!

assume all along that the prize is in box A. The host eliminates box C (empty).
if you orininally chose Box A and you change then you lose.
if you originally chose box B and you change then you win.
so you are right half of the time.

you move from a 33.33% chance to a 50% chance automatically when the empty box is removed. half of the time you are right to move and half you are not. you gain no actual advantage from moving. you are mixing up you theoretical odds when there were 3 boxes with the actual odds of there being 2 boxes - one with and one without.

Originally Posted by the 12 th man

The reason why you should change.

http://math.ucsd.edu/~crypto/Monty/monty.html

i didn't and i won too!

**Schumi** · 19/09/2007, 1:11 PM

Originally Posted by galwayhoop

what you on about willis. there are only 2 boxes remaining and therefore it can't be in box c (we are assuming that is the empty at the start).

You've misunderstood. The three scenarios listed cover all the outcomes after you've chosen box A. If the prize is in box B, the host opens box C and vice versa so if the prize is in either of these, the box you can change to holds the prize.

you move from a 33.33% chance to a 50% chance automatically when the empty box is removed.

This is the fundamental misconception that people have in this riddle. This is not true. We're all agreed that you have a 33.33% chance of picking the right box at the start. The host then opens an empty box. There is guaranteed to be an empty box for him to open so showing you that doesn't change the probability that the prize is in your box. The opening of the box is not a random choice, he'll never show you the prize in a box.

I did the website 6 times, changed 3 times and won twice, didn't change 3 times and won once.

**galwayhoop** · 19/09/2007, 1:18 PM

Originally Posted by Schumi

This is the fundamental misconception that people have in this riddle. This is not true. We're all agreed that you have a 33.33% chance of picking the right box at the start. The host then opens an empty box. There is guaranteed to be an empty box for him to open so showing you that doesn't change the probability that the prize is in your box. The opening of the box is not a random choice, he'll never show you the prize in a box.

this was not stated in the riddle. we were going on the assumption that there was an equal chance. and by that token then your odds are the same if you switch or if you don't. however from that quiz show on the link i get your drift. going on the assumption that the 3 boxes are random (like say on deal or no deal) then there is no advantage to switching.

**Schumi** · 19/09/2007, 1:21 PM

Originally Posted by galwayhoop

going on the assumption that the 3 boxes are random (like say on deal or no deal) then there is no advantage to switching.

Agreed, it would be a shorter gameshow then though!

**Aberdonian Stu** · 19/09/2007, 2:25 PM

Incidentally the problem Schumi explained is called The Monty Hall paradox in honour of the game show host who's show inspired it.

**John83** · 19/09/2007, 3:12 PM

Originally Posted by galwayhoop

you will not because in your example you kept moving the bl0ody prize!

assume all along that the prize is in box A. The host eliminates box C (empty).
if you orininally chose Box A and you change then you lose.
if you originally chose box B and you change then you win.
so you are right half of the time.

you move from a 33.33% chance to a 50% chance automatically when the empty box is removed. half of the time you are right to move and half you are not. you gain no actual advantage from moving. you are mixing up you theoretical odds when there were 3 boxes with the actual odds of there being 2 boxes - one with and one without.

Three possible places for the prize, three possible selections:

Prize is in:

Code:

you pick  \ prize   A                     B                 C
A                   Don't change          Change            Change
B                   Change                Don't Change      Change
C                   Change                Change            Don't change

6 times in 9, the right choice is to change.

**Bluebeard** · 19/09/2007, 3:35 PM

This is all rather like Blaise Pascals simple grid of why to believe in God - life isn't mathematical odds - either it is or isn't the box you picked. Odds may be in your favour, but in a one off situation, odds don't actually matter a damn when it comes down to it - it either is or it isn't.

**John83** · 19/09/2007, 3:36 PM

Originally Posted by Bluebeard

This is all rather like Blaise Pascals simple grid of why to believe in God - life isn't mathematical odds - either it is or isn't the box you picked. Odds may be in your favour, but in a one off situation, odds don't actually matter a damn when it comes down to it - it either is or it isn't.

I hope you don't gamble.

**Bluebeard** · 19/09/2007, 3:38 PM

Originally Posted by John83

I hope you don't gamble.

Compulsively.

I also no longer have the vast fortune I inheirited from my dear Grandfather.

Got the lend of €20? I swear I'll get it back to you after the 3.15 tomorrow.

**galwayhoop** · 19/09/2007, 3:59 PM

Originally Posted by John83

6 times in 9, the right choice is to change.

if the box opened first is done so because the host knows that it doesn't contain the prize then yes but if all choices are random then there is no difference.

hence if it is a random choice between the 3 boxes, where no-one including the 'host' knows what is inside then there is no advantage to changing, if however the 'host' knows all along where the prize is then you should change.

**Seano** · 19/09/2007, 4:10 PM

Name ten parts of the body with 3 letters in the name, no slang words , so bum or gut won't do.

**Schumi** · 19/09/2007, 4:17 PM

8 for a start

eye
ear
gum
arm
leg
toe
lip
jaw

**DmanDmythDledge** · 19/09/2007, 4:19 PM

Originally Posted by Seano

Name ten parts of the body with 3 letters in the name, no slang words , so bum or gut won't do.

Any ten. They all have 3 letters in them.

**Seano** · 19/09/2007, 4:24 PM

Originally Posted by DmanDmythDledge

Any ten. They all have 3 letters in them.

True..... but no

Schumi is nearly there

**osarusan** · 19/09/2007, 4:39 PM

Originally Posted by Schumi

8 for a start

eye
ear
gum
arm
leg
toe
lip
jaw

fat..
rib...

What do i win?

**TonyD** · 19/09/2007, 9:03 PM

Hip is the missing one I think.

**John83** · 20/09/2007, 10:52 AM

Originally Posted by galwayhoop

if the box opened first is done so because the host knows that it doesn't contain the prize then yes but if all choices are random then there is no difference.

hence if it is a random choice between the 3 boxes, where no-one including the 'host' knows what is inside then there is no advantage to changing, if however the 'host' knows all along where the prize is then you should change.

Eh, the point is that the host knows.

Regardless, even if he opened one of the other two at random, either it would contain the prize, or we're back in exactly the situation we would be in if he did know.