Envelopes

There are 13 envelopes, and each one is either red or blue.  There are 5 of one color, each containing $100, and 8 of the other color that are empty.  You don’t know which color is the winning color other than it is the one with the smaller number of envelopes.

At the start of the game, one of the thirteen envelopes appears on your computer screen and stays there for 15 seconds.  During that time interval, you have two options.

(1)   You can pick the envelope and see what’s inside, which ends the game, or

(2)   You can pass on the envelope.  If you pass, the envelope disappears forever and brings up one of the remaining envelopes for you to choose or let pass.

  • How should you play the game to maximize your chance of getting the $100?
  • How would the winning strategy change if the amount of money in each winning envelope decreases by $5 each time you pass on an envelope?

Suppose there are  winning envelopes and  empty envelopes.  How should you adjust your strategy given different numbers of winning and empty envelopes?