Correct, at least to the extent as presented.
(An oversimplified and, in real life, worse than useless problem)
(The original fuferah from Marilyn Vos Savant actually included the shell
game)
(This example does not have that context in it, leading to the Forum's
oversimplified analysis)
(Possibly why the original trigger for this discussion left it off)
{{Not this list correspondent (Eldon: well written) nor the first in thread
in all likelihood}}
A more compleat discussion of the full problem is available on request
from the response I sent to MvS from the first times on her column
she sold the shell game as a Monty Hall problem
where she proved she is also a fair games master
above and beyond merely reporting her reputed genius IQ
whether she is a genius mathematician or not.
She is also quite often wrong
As in her response to the kvetch-ion: ABCDEHIKMOTUVWXY
Which was: Symmetric characters.
My comment was: Zounds, Not So. _Bilaterally_
symmetric characters.
(also, as presented here, _capital_only_).
And, like any good knife salesman, when caught at it, wrong: she does
not ever admit it:
She just keeps selling knives.
And everyone else gets cut by it.
Now that the discussion has died down, a few simplified comments:
0) On an infinite trials basis, "it is obvious": no doubt. But also wrong
(for most any real life problem).
But: that's the math of an infinite trial, and
doing the simple combinatorics shows this.
1) A contestant actually enters a Monty Hall show
a) She/he is lucky enough to be called on stage (whee).
b) She/he gets to choose, and chooses (actually, really)
the first time, the door with the good prize behind it
(the car, not the goat)
c) She/he reads the genius mathematicians on J Forum
d) She/he believes them, and in the.
e) She/he chooses again.
f) She/he loss the car. And gets the goat.
g) And, on the REAL Monty Hall show, does not get to choose again.
h) And she/he never gets on the REAL Monty Hall show again.
i) And feels like a goat.
So: the combinatorics says:
All you genius mathematicians just co$t
one third of the contestants
the car
As one recent correspondent just quietly remarked on the sideline:
A lot of mathematicians a lot smarter than [[any/all of]] you
get fooled by this.
2) First dilettante-ic response is likely to be:
'But you just admitted we got 2/3s to WIN the car; overall, that's a
better chance of winning!'
Nope, I didn't. _You_ folks (tacitly) asserted that.
And, in the world of mathematics, "it is obvious".
No doubt: the math says so.
a) But 1/3 on the average would have lost.
b) And on a single trial basis, you might do the R values and find the
real PDF here,
then answer the kvetch-ions below:
i) How likely is it that 2/3s would have lost?
ii) How likely is it that 2/3s would have won?
Those are the more revealing real world statistics for people who
would take
a genius level mathematician's mathematical advice
(or equivalent programmer's programming advice:
witness the Denver Airport ongoing fiasco)
or MvS's advice as if it were the truth
or in any sense adequate for advice in real life:
If you do,
you will GET the goat
and you will BE the goat
much more than a third of the time.
And those who lost would be justified in noting being taken to the
cleaners.
(The modern American way of business: witness Worldcom, Enron,
Parmalat,
and the other 200,000 cases of ti ongoing in accounting fraud not
resolved or reported)
c) In the REAL Monty Hall game, he actually is NOT offering on a
'uniform' distribution.
He rally offer a second choice to those who have the goat
much more often than those who have the car.
So: the problem as presented here is incorrect. And is not a Monty
Hall game.
d) Note I avoided the term 'fair choice' (I used 'uniform distribution')
Because the term is actually a loaded shell games usage in the
middle of
a Monty Hall game: phraseology used to hide and "spin" the reality
in mid flight
to distract and confuse
Much like Washinton style political spin rhetoric.
Which has lead to such successes as Katrina, Worldcom, Enron, and
Parmalat:
Where the games players walk away with the money
While someone else's children die from the flood or the
next bullet in Iraq or elsewhere.
3) The original MvS columns had the shell game reference in the discussion
thread.
But: any street smart child will know you cannot win by choosing in a
shell game.
Ever: first, send, third, or final choice.
Nor win at a knife seller in the Mall: loss leader, front runner,
paid fan (from Sinatra to American Idol: studdard and clay
notwithstanding)
or other shill notwithstanding.
Here the recursive echo beginning?
You have to solve the full eigenstate to even come close to
getting it right.
If you think otherwise, I know of a bridge salesman in NYC
before, during, or after 9/11: she/he will keep selling the
bridge.
And: people will lose in the buying of it Just as they lose in
listening to that sales pitch.
4) Now, in modern politics, the games theory becomes concerned with herd
control
in order to maximize the ca$h crop.
So the intelligent grafter in office will want to have a pacific herd
at quietus
And will tend to resent anyone commenting on the shell games being sold
as if they were Monty Hall game choices
And will try to cull any member of the herd FROM the herd
in order to maintain a proper profit margin.
And will prefer genius (l)evel folks to train the herd for them
All in the name of civilization, ethics, God, or the Objective
Go(o)d of Gaia or the Universe.
In Ye Goode Olde Dayes (still ongoing for most of the world's people)
this normally means being culled with physically and
emotionally detrimental methods:
violence (physical) , economic deprivation, blacklisting,
ostracization.
In Ye Goode Newe Peacefulle Tymes (still ongoing throughout all
history)
this normally means being culled with physically and
emotionally detrimental methods:
violence (emotional, social) , economic deprivation,
blacklisting, ostracization.
With Ye Goode Olde Finale Solutione (still ongoing throughout all
history AND now)
... as a final solution for any group or individual who does
not yield to
the demand for silence when the shell game is applied.
5) Otherwise, the current crop of controlling con(wo)men
..might have to earn a living.
7) To make method '4)' useful and sustainable in the net economy
The current herd handlers have to keep training a new crop of genius
level mathematicians
to sell the current instantiation of the shell game
as a Monty Hall problem (witness US EY2000/2004 vote counting
frauds)
or else the herd may accept the current advertising and sales spin
tactics.
In order to do that, all that has to be done is to stroke the ego
of the current genius level programmer group
And train any others i the method of hiding when caught with their hands
in the cookie jar
of being paid ongoing for doing this to the rest of the herd (shame on
you)
so the natural animal (l)evel reaction of culling anyone pointing
out
..where the meat came from
can be initiated and carried out
...by those same genius level folks
... in covert support of the actual top predators in the chain
...
Witness the Kurds over the last 50 years, the Turks pogrom against the
Armenians,
and so many more modern examples
including the modern hidden in plain site Western (and other),
Israeli (transfer policy),
Arab (and all other), Christian (And Muslim and other)
business, economic, and religious practices
...still ongoing ...
8) And if any one encountering a real world Monty Hall game, or other,
thinks that the trials are independent:
feel free to go to Las Vegas ... with your own money ...
$) By the way, all of this was solved in full generality
a) by games theory of mathematics of the 1500s CE onward
b) in European games parlors by 500s CE onward
Western European advanced thinkers being a bit slower than the
rest of the world
c) by street urchins playing shell and marble games by 500 BCE onwards
d) by adult humans playing the game of survival against each other by
5000 BCE onward
e) by feral pack tactics of top predators from about 500 million BCE
onward
So, none of this reasoning is accreditable (where correct) to me.
*) Vastly oversimplified: this is only a first rondo (musical reference:
see "Godel, Escher,Bach").
((I wonder how method '4)' will be applied [this time] here)):
explicitly,
with proper angst ('your comments are (in)appropriate') as if disrespect
were involved,
topical exclusion ('the topic is not correct for the Form' (or similar)
by ostratic*** vote (internal disenfranchisement)
or externally triggered event
(as in previous viral attacks penetrating the J Forum:
ignored by the genius level mathematicians herein
even when patiently pointed out over a five year period
by indivduals being ostracized by the method)
All notwithstanding
Cheers.
*** ostratic: ostrakon-ic, ostracization-al, ostracism-ic, ostrakic:
used in the propagation or cause of ostracism.
On 9/8/06, Eldon Eller <[EMAIL PROTECTED]> wrote:
This is not a simulation or even a program, but a way to reason about
the Monty Hall problem that I find easy to understand.
Suppose that you have chosen a door and somehow discover that there is a
goat behind your chosen door. If you wait until Monty shows you the
other goat, you will know certainly that the car is behind the other
unopened door, so you switch and win the car.
Even if you do not know that there is a goat behind your chosen door,
you know that two times out of three there will be a goat behind your
chosen door, and if you switch doors, you will win the car two times out
of three.
My son informs me that the British mathematician Hardy is behind the
"yes, it is obvious" anecdote. According to him, Hardy was giving a
lecture and said, "It is simple to show that . . . . ," whereupon he
stopped, left the room for ~20 minutes, returned, and said, "Yes, it is
simple to show that . . . ."
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
--
--
Roy A. Crabtree
UNC '76 gaa.lifer#11086
Room 207 Studio Plus
123 East McCullough Drive
Charlotte, NC 28262-3306
336-340-1304 (office/home/cell/vmail)
704-510-0108x7404 (voicemail residence)
[EMAIL PROTECTED]
[EMAIL PROTECTED]
[EMAIL PROTECTED]
http://www.authorsden.com/royacrabtree
http://skyscraper.fortunecity.com/activex/720/resume/full.doc
--
(c) RAC/IP, ARE,PRO,PAST
(Copyright) Roy Andrew Crabtree/In Perpetuity
All Rights/Reserved Explicitly
Public Reuse Only
Profits Always Safe Traded
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
