Even Math Professors Fail in This Simple Game – Why ?

Even Math Professors Fail in This Simple Game – Why ?

The title is a funny disparaging statement and people say that because it is sensational and to add to that, the experiment explaining person actually works with a professor to prove this point.

The truth is it knocks off even highly trained mathematicians and statisticians, and yes even mathematics and statistics professors because some times we trust our intuition or do not listen extremely carefully.

Most of the times our intuition works, but not always. Of course, never undermine the power of careful listening.  It is better said than followed.

You will love this little video and see why you should also rely on mathematics (am i excited to say, rely on probability and statistics).  This is called ‘Monty Hall Problem’.

Ok, here is the interesting thing for real world application.  Where do you think you can use this as an application in real life.

I am collecting some examples.  My immediate example is the following:

If government regulations change and hence associated uncertainty distribution changes (specifically because at least one of the options available to you has been removed) then you should also change your strategy (move away from the existing strategy) what seems to be an equally likely situation!

For application to cognitive dissonance in free choice paradigm for explaining how human beings are not tricked into false choices in preferences, see, http://www.nytimes.com/2008/04/08/science/08tier.html?_r=0, and as an extension claiming the whole collection of psychological tests.

It becomes complicated because in many real life situations not all events are equally likely.  But then there is a way to figure out the likelihood of success.

No BIG data or power data are required here; this is just a human folly. You need a good mathematician or statistician to help you resolve such issues and remember when in doubt you just at least do simulation so that one does not have to be put in an embarrassing situation of being totally incorrect.

I love to hear your examples.

At least people will see the higher order intelligence why Mitt Romney is allowed to change his mind or if allowed to change why he would prefer that (popularly called flipping)!

updated 22Jul12:

Here is a snippet from  Wikipedia (ref: below).

“After the Monty Hall problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine claiming that vos Savant was wrong (Tierney 1991). Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy.”

Here is the simulation applet to experience yourself

Here is an excellent summary by Wikipedia

Here is NY Times’s sensational story

More Details on Monty Hall Problem

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