Dear Allstatters,

 

Thank you very much for all the responses I have received so far.  They have
been fascinating and include one that must qualify for the longest reply
ever on ALLSTAT.  What I will do with these replies is create a PDF file
with all of them and put a link to that on my website.  However, before I do
that, I want to clarify my query a little as your responses showed I hadn't
fully specified the rules of the game.

 

The reason why I put the query out is that I use the Monty Hall problem as
an ice-breaker in my training courses.  It is a great way of getting people
to realise that statistical thinking is essential since normal human
intuition fails in this problem.  However, I do like to then make the Monty
Hall problem real by translating it into a context that people are likely to
experience in real-life.  My example wasn't the prisoners & king which I
used in my previous email but a competitive tender involving 3 companies A,
B, C who bidding for a contract with client X (could equally be 3 people
applying for a job).

 

The rules of this game are.  You are working for company A and to begin with
all 3 companies tendering can be regarded as equally likely to win.  You
decide you want to change the odds by bribing someone who works for X (call
him P) to find out what the person (call her Q) in X who will be making the
decision, is currently thinking about B and C.  We will suppose that P and Q
are quite friendly with each other and are having a chat when P casually
says "I know a bit about company A since I've worked them in the past but I
don't know much about B & C.  What are your impressions so far of B & C?".
Let's now imagine two responses that Q could give:

 

1.       "Definitely not choosing B!  Can't tell you yet which of A & C I
will be choosing but I have made my mind up."

2.       "Definitely not choosing B!  However, I haven't decided whether C
is better than A."

 

Both statements contain different information but it is now up to P to
convey the information back to you.  In this scenario, it seems to me that
if you are the salesman for A, if you hear P relay statement 1 correctly
then you should conclude that the Monty Hall problem applies i.e. you are
playing a stick strategy and you now know that C has a 2/3 chance of
winning.  Therefore you have wasted your money bribing P and you should now
resign from A and go and work for C.  But if you hear statement 2 from P,
does the Monty Hall rationale still apply?  Finally what if P provides you
with incomplete information and only says "It's not going to be B" and
leaves out the second sentence from Q?  What conclusions can you as the
salesman for A make?

 

Regards

 

Nigel Marriott

Chartered Statistician

 <http://www.marriott-stats.com/> www.marriott-stats.com

 

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