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Re: [Phys-l] Never Trust a Theoretician! - Monty Hall Revisited.



Memo from Uber-BeanCounter:
To: Monty Hall.

With immediate effect, arrange all doors to be empty as the default scenario.
Set one prize behind the chosen door once in ten trials for the optimal return on media investment.

Sincerely
UBC

On 11/24/2011 6:26 AM, Philip Keller wrote:
Memo
> From network bean-counters
To Monty Hall

We see that you have been giving away cars about 1/3 of the time. In an effort to reduce costs please start revealing a wrong door and offering the player a chance to switch. Do this almost every time they have guessed correctly on their initial guess and only occasionally when their guess was wrong. This will save us money because there are many websites that claim that switching is always better. Hopefully our contestants will have read those.

Paul Nord<Paul.Nord@valpo.edu> wrote:


The answer is 2/3 probability if you switch.

Imagine the game this way:
You: Monty, I would like to choose both doors #2 AND #3. I want you to give me the best prize that's behind either of those doors.
Monty: I'm sorry but you have to pick just one door.
You: I could play by your rules. But let me tell you ahead of time that I'm going to choose door #1. And then you will show me that either door 2 or 3 is a non-winner. At that time I will switch my choice to the the other door -- the best of doors #2 and #3.

Or extend the game to 100 doors with only one prize. You choose a door and Monty can always reveal 98 non-winning doors. (Better yet, picture playing Minesweeper on a 10x10 grid with one mine. You pick a square. I show you 98 squares with no mine.) The odds of winning by not switching are 1/100. But when you switch you get the best choice of all of the other 99 doors - 99/100.

Paul


On Nov 23, 2011, at 10:12 PM, brian whatcott wrote:

I seem to recall quite a protracted discussion here on the merits of the
Monty Hall Paradox.
This concluded that in the three door variant - with the empty door
revealed, I seem to
recall that if you stuck, you rated a one in three chance of winning:
but if you swapped
your door choice after the third empty door was opened, your chances
rose to one in two.

But tonight I saw a Mythbusters experiment, nicely done *, that made the
relative chances
one in three for sticking, and TWO in three for swapping doors.

Bah humbug!

Brian W
* Discovery Channel (HD) 9-10 pm CST. Wed Nov 23rd 2011