Imagine this.  There are three upside-down cups in front of you.  A ball is under one cup.  I ask you to guess which one has the ball under it.  What chance do you have of picking the cup with the ball?

33.3% right?  Simple and intuitive but keep reading.

Here is a wrinkle.  You select a cup then I lift one of the two you didn’t pick and reveal an empty one. Then I give you a choice

• Option 1: Stick with your first guess.
• Option 2: Change your mind to the other cup.

Is it better to change your mind and switch cups, or does it even matter?  Another way to ask, do your odds increase if you change your mind or is there an equal chance the ball is under either of the two remaining cups?  Think about that before continuing.

Here is a video from Khan Academy explaining the problem and which option is superior.

Want to try it for yourself? Here are a couple of simulations to try.  You may need to update your version of Java to use them:

• “Three Door Problem” Simulation – At the University of Illinois Office for Mathematics, Science & Technology website
• “Monty Hall Dilemma” Simulation – At Cut-the-knot.org

If you are interested in a deeper understanding of this type of thing then look into Bayes’ Theorem

So why bring it up?  We tend to resist changing our mind once we’ve made a decision even after we are presented with new and relevant information.  It feels safer to stay the course.  Salespeople learn it is easier to present a prospective customer with a “new decision” rather than persuading them to change their mind.  Changing our mind feels uncomfortable because it seems inconsistent.  It requires we accept that we were initially wrong.  But we would be better served if we try to remain flexible and revisit a decision when we have new information.