> >Monty opens one of the other doors. That does nothing
> > to change your
> > door's chances; it is still 2:1 that your door does not hide
> > the Big Deal.
>
> What Monty has done is REMOVE the other door's chance of
> being the correct
> one.  That leaves 2 doors with a chance of being the correct
> one.  Each
> remaining door has one chance.  The door you did not pick

I'm not really sure how do handle these responses. Let's try the simple
approach:

You're wrong. Period. Not negotiable.



Perhaps another approach:

I'll bet you USD50,000 that the "switch is better" choice is correct. That's
USD50,000 for each poster who insists that the odds of the original door
being the winner are 1:1 after a non-chosen non-winning door is opened, and
is willing to put his/her money where his/her mouth is. No limit on the
number of participants; if 200 of you insist on keeping your original door,
that's ten million USD on the line.

We'll perform a simulation to determine which strategy works best. The exact
mechanics, rules, and verification methods for the simulation will be worked
out to our mutual satisfaction before the test, but it will essentially be
done by generating a list of random evenly-distributed "winning" values from
[1,2,3] of appropriate length (say 10,000 or so), picking a random
equally-distributed "selection" value from [1,2,3] for each item in the
list, discarding one non-winning value, then switching the selection to the
remaining value and comparing it to the winning value.

If the resulting selection is the "winning" value less than 58% of the time,
I owe you 50 grand.

Any takers?


OK, maybe those numbers are a little large. Here's another option:

We'll do the same test as above, but change the payoff rules: for each
"loss", I owe you USD1. For each "win", you owe me the dollar. Count up the
"wins" and "losses"; the actual payment will be the difference between the
two.


Steve Dirickson   WestWin Consulting
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