h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Actually, you can just write out all the combinations. With three doors, there are only a few options. It makes it totally clear that you win more often when you change your mind.

We discussed this many year back on some un-edited entries, I recall it got quite heated, but dug out a simulation link

http://www.shodor.org/interactivate/activities/monty3/

I think the past converations have long been lost (or attached to deleted entries)

CHawke

found the previouis heated debate, in case anyone was interested, some on this entry

A309278 (mine, still in HTML I'm afraid)

and someone who says, despite the evidence that we were wrong on this entry

A221446

CHawke

Ok Stage1

First off you have three choices 1 prize odds 1 in three
Second off you have two choices 1 prize odds 1 in two. The only diffirence is that I have narrowed the odds it does not mean that the other doors are now more likely.

Stage 2

This proves against you I think!

Stage 3

The odds were 1 in 3 but now monty has opened his door there is now a 1 in two chance. Two doors 1 prize. If you make a decision now there is a 1 in two chance that you will be correct.

Stage 4

We are now standing in front of two closed doors so that is 1 in 2 no amount of waggling of the third door is going to change the fact that the prize is behind one of those doors. So using my basic maths skills and knowing that what ever monty has done in the past does not affect my current choice. There is no advantage or disadvantage to opening the other door at that stage there is still a 50/50 chance of getting the correct door.

Still not convinced.

After monty has opened his 48 doors how many are left? 2 and the prize is behind one of them. What are the odds that you are going to pick the correct one? Are they 1 in two again?

if you are not convinced try the simulation software on the above link, after a dozen or so goes the odds start to get as predicted. Or try the multiple run option which is linked to on the above linked page, try a few thousand and see the odds fall into the predicted paterns

CHawke

Try thinking in this way:

Basically, there are only two situations: either your initial choice is the door with a prize, or the one without. Let's assume that you ALWAYS change your mind, so the choice between two doors is purely mechanical.

The odds for the first case are 1 to 3 (three doors and you pick the right one). Then Monty opens a door, showing no prize. Now you change your mind and LOSE. Probability 1:3.

For the second case, the odds are 2 to 3 (three doors, you pick the wrong one). Monty opens a door (drum roll), no prize (crowd goes AAAH!). You change your mind and WIN. Probability 2:3.

So, if you systematically reconsider, you win in 2 cases out of 3. If you still won't believe, go to a nearby corridor with some mates and try it out.

Was skeptical. Thought I'd write it out before posting. Nice mindf**k I'll remember it for the future.

Think of it like this. There are 2 wrong doors and 1 right one.
So
1/3 you chose correctly
gives 1/6 he opens wrong1 and a 1/6 he opens wrong2
1/3 you chose wrong1
gives 1/3 he opens wrong2 (There is no chance of him openeing correct)
1/3 you chose wrong2
gives 1/3 he opens wrong1 (There is no chance of him openeing correct)

So at this point there is a 1/6 chance you have selected correctly and wrong1 is closed and a 1/6 chance you have selected correctly and wrong2 is closed.

Total chance of being correct 1/3

To check the working there is a 1/3 chance that you chose wrong1 and wrong2 is closed and a 1/3 chance you chose wrong2 and wrong1 is closed.

Total chance of being incorrect 2/3

Proabilities total one so the working should be correct. Unless there is a mistake somewhere.

Still common sense screams that it should be 1/2

The first time I read about this it was in a conversation attached to another post (can't remember where). I had to stare at the screen for half an hour before I could make my common sense stop disagreeing with the math. I probably should have just written it out like this. *sigh*