Common sense and intuition: Monty Hall Problem Case

*Note: Bold texts are links

We know the dangers of acting and making judgments based on common sense, intuition, or gut feel. We are aware that these modes of thinking can be the worst way to find a solution, especially when it comes to medical problems, relationships and interaction with people, and making ethical decisions. How many times have we heard doctors tell people not to self-medicate? How many times have we ruined someone else’s day when we answered them “akala ko kasi e” and “para kasing?” But we still do. We still do actions by the dictates of common sense and a priori notions. We still let intuition be the arbiter of our lives, of society. One way or the other, this is reflected on the country’s (PH) love for games of chance such as lotto, jueteng, and ending. 

And again, I will illustrate the failure of common sense and intuition not to proscribe its use; but to advise others to think further before letting the two have the say. To argue this stance, I make use of the Monty Hall Problem.

Here’s a simplified version of the MHP (Monty Hall Problem) lifted from the book The Curious Incident of the Dog in the Night-Time by Mark Haddon (2003):

“You are on a game show on television. On this game show, the idea is to win a car as a prize. The game show host shows you three doors. He says that there is a car behind one of the doors and there are goats behind the other two doors. He asks you to pick a door. You pick a door but the door is unopened. Then the game show hosts opens one o the doors you didn’t pick to show a goat (because he knows what is behind the doors). Then he says that you have one final chance to change your mind before the doors are opened and you get a car or a goat. So he asks you if you want to change your mind and pick the other unopened door instead. What would you do?”

Your common sense and intuition will probably say that sticking or changing your chosen door does not matter and it is just about caprice and sheer luck since there will be a 50-50 chance that you will end up with the door with the car behind it, since there are only two doors left. But is this right? Simple analysis and critical thinking says NO.

Look at this graphical representation showing all the possible outcomes: 

The image demonstrates that whatever door you pick, the probability that you will get a car when you change door is 2/3 while sticking is 1/3.  These fractions tell us that it is always better to change the door than to stick with it because it has the higher probability of going home with the car.

This problem shows the shortcomings and weakness of common sense and intuition. (There is a reason why physicists conduct experiments, right?) Believe it or not, a number of mathematicians and people with doctorate degrees have argued that the probability you will get a car is 50-50, only to be proven wrong – I bet they trusted their common sense and intuition this time. Have a look at the tip of the roster:

Scott Smith, Ph.D., University of Florida
Robert Sachs, Ph.D., George Mason University
W. Robert Smith, Ph.D., Georgia State University
Everett Harman, Ph. D., U.S. Army Research Institute
E. Ray Bobo, Ph.D., Georgetown University

There are situations where use of common sense is not enough and the urge of intuition not worth the shot. Fundamental assumptions that were commonly accepted without further inquiry and questioning. Everyday knowledge proliferated to next generations such as superstitions and spiritualism. It is time to move to science, reason and logic for explanations. It is high time for empiricism. You would think that the Monty Hall Problem is superficial a reason to show the necessity to choose science and logic over common sense and intuition, but what if what’s behind one of those doors is a cure to cancer, to AIDS and laws that enshrine human rights? What would you do?