Mathematics 116    Brown

January 3, 2006

 

As a warm-up to the use of mathematical thinking in social situations, we will look at a deceptively simple gambling example.  If gambling is something that you yourself would never do, I hope that you can participate in the discussion and analysis of this example without compromising your own ethical principles. Perhaps you could think of the example as a metaphor for competition for scarce resources.

 

It costs you a certain fixed and unchanging fee to play a game, and you can keep playing as many games as you please.

 

A.  You begin a game by paying the dealer the fee. 

 

B.  The dealer has three screens that you cannot see behind.  After the dealer receives the fee from you, he decides randomly on one of the screens and places  $3.00  behind it.  He does not disclose to you which screen the money is behind.

 

C.  Next, you temporarily choose a screen and point to it.

 

D.  There are two other screens besides the one that you pointed to, and the money cannot be hidden behind both of them.  The dealer removes one of the other two screens that is not hiding the money.

 

E.  Two screens now remain, the one you pointed to and one other, and the money is behind one of the two.  You now get to make your final choice of screens, which can be either to stay with the screen that you originally chose or to switch to the other remaining screen.

 

F.  The game now ends as the dealer removes your final choice of screen.  If the money is behind it, you get the money.  Otherwise, you get nothing.

 

(a)Would you be willing to play if the fee were $1.75 per game?  Why or why not?

 

(b)  If the fee were $2.00?