Undercut is a wonderful way to introduce the mathematics of games. When you
first play the game, ask for two volunteers to play. Bring them to the front
of the class and place them at opposite ends of the blackboard or whatever you
have in the front of your room. For each play of the game, each player will
write on the board his or her choice of number and what the accumulated point
total is. Give them each a piece of cardboard which they can use to shield
what they write down. To start the name, you say "1,2,3, write" and they write
their number down. The players then compare their selections and write down
how many points each would receive. You keep repeating the process until one
player wins.
After playing a couple of games, ask the class if there is a best way to
play this game. Have them write a brief paragraph about how they would
play. Compare these. Once the class has come up with the best way of
playing, hold a class tournament. Figuring who plays who is a great exercise
and would be very appropriate at this time of year when interest in
tournaments is very high because of the NCAA basketball tournament.
If you want some help with this send me
some e-mail, and I'll send you some notes on how you can do this. Ask
your class why the terms, "sweet 16" and "final 4" are used. I found the
class tournament to be a really
exciting event. Don't be afraid to play yourself (and to lose, the students
will love it). Next, I would have the students test their strategies by
playing Computer Undercut and to see how they do. If the students get really
interested in the game, have them check out some of the given references.
-- Jonathan Choate
