Mathematics Problem Of the Week
Spring 2005
POW 5: Four Boxes Game
Four Boxes Game: Four boxes are placed in front of you. One
box contains $100; one contains $50; one contains $20 and one contains nothing.
In each round of the game, you may open as many boxes as you wish and keep the
money. However, if you open the empty box, the round ends and you win no money
for that round. Assuming that you will play many rounds of this game using the
same strategy, what is the best strategy for playing this game?
Hint: By “best” strategy, one means the
strategy resulting in the highest expected average winnings. For example, a possible strategy would be to
always open just one box. After playing
many rounds using this strategy, one expects to have won $100 in about ¼ of the
rounds, $50 in about ¼ of the rounds, $20 in about ¼ of the rounds and $0 in
about ¼ of the rounds. Therefore, the
expected average winnings for this strategy would be 100(¼) + 50(¼) + 20(¼) +
0(¼) = $42.50 per round. You should be
able to do much better than this!
Solutions should be
submitted to Dr. Maegan Bos’ mailbox in the Math office or sent via e-mail to mbos@stlawu.edu
Presentation counts! The
prize-winning entry will be selected from all correct submissions, based on the
clarity, creativity and elegance of the solution.
Look for the SLU POW on
the Web at http://it.stlawu.edu/~math/activities/