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Re: [Phys-l] Monty Hall Revisited.



On 11/25/2011 12:10 PM, chuck britton wrote:
What _*I*_ got out of this MythBuster segment was the VERY strong
psychological tendency to STICK with your initial choice.

Twenty 'randomly' chosen 'contestants' all chose to Stick rather than SWAP.

I guess these California folks aren't as 'hip' to the vos Savant
column as I might have suspected.

Yes, the twenty-to-zero score was interesting.

As previously discussed at length, the right strategy is sensitive
to the details of the rules. Possibilities include
-- host always offers a switch
-- host offers a switch only if it helps
-- host offers a switch only if it hurts
-- anything in between

If you haven't been told the rules, *or* if you don't trust the
guy who told you the rules, then standing pat is in fact the
optimal (minimax) strategy.

One could generalize this to say:
As a rule, if somebody you don't trust is trying to
manipulate you, you should resist. [1]

Rule [1] may be something that people learn, even though it
doesn't appear on the state-imposed syllabus or standardized
tests. Indeed it could be an instinct acquired by evolution
over the course of many millennia.

It was interesting to see a twenty-to-zero score. It was also
interesting that none of the contestants could articulate a
rational explanation for their strategy. I suspect that in most
cases, they had no clue about the concept of "minimax" or other
game theory concepts. At the same time, it is possible that
they understood rule [1] and knew they were being manipulated,
but were too polite to call it manipulation, so they made up
a polite cover story.

It was depressing to see that the mythbuster guys assumed
from the get-go that the host was obliged to offer a
switch, always. This is certainly not the only version
of the game that needs to be considered.

=====================

As you know, I am rather fond of checking the primary data,
at least spot-checking it every so often.

I did some spot checking of Let's Make A Deal episodes from
the 60s and 70s, as found on YouTube. I found *no* examples
where there was a prize behind one of the three doors and
nothing behind the others. I found *no* examples where
Monty showed a non-winning door and offered a switch.

I am beginning to suspect that there are multiple layers
of urban legends piled atop urban legends here.

Can anybody point to actual data about an actual game show
where contestants were shown a non-winning door and offered
a switch? Please let us know!

=====================

I reckon it would be a Good Thing if people actually had
some training in game theory.

An informative yet easy-to-read book on the subject is:
William Poundstone
_Prisoner's Dilemma_
http://www.amazon.com/dp/038541580X

This leads me to wonder, in which class would it be appropriate
to discuss this?
-- Physical Education? (since it has to do with games and teamwork)
-- History? (history books seem to greatly emphasize wars, and
warfare involves lots of strategy)
-- Mathematics? (game theory is quite mathematical, and it
would make math class a lot more relevant to the real world)
-- Home Economics? (home-ec is supposed to teach how to live
in the real world, and knowing how to avoid being manipulated
is certainly relevant to that)
++ All of the above?

I would have hoped that "all of the above" would be the right answer,
... but instead what we have is "none of the above". I would have
hoped that the prisoner's dilemma and the concept of minimax would
be introduced in 7th grade (if not before) and reinforced again and
again in PE, history, math, home-ec, and other classes ... but
instead we get none of that.

It galls me when something artificial -- such as compartmentalization
of subject matter -- stands in the way of doing the right thing.

Modern game theory has been around for 60 years or more. Maybe
in another 100 years it will make its way into the curriculum.

Of course before anybody can understand game theory, they need
to understand some basic notions of probability, and all-too-often
students nowadays don't even learn that. Sigh.