The Joy of Teaching Games

Last Wednesday was the second day we just spent playing games in class, and the first one where they had learned some of the theory (specifically, outcome classes). What a blast! I started putting up Amazons positions for them to find the outcome classes of partway through the class. They picked up on this challenge immediately, students flocking to the boards to post the class they had found, then either verifying or questioning the results of others. I had about twenty positions around the room and only a few of them remained unexplored by the end of the hour. The air is very charged, but the feeling is very positive. Students are working together to solve the problems, and this requires them to try out moves on physical boards, then confer with the people around them. Your opponent quickly becomes your best teammate as you collaborate to test all possible game tree paths. For some of the harder boards I put on the marker boards, groups had banded together to discuss their results as a bigger team. There was not an unengaged mind in the room!

As I've mentioned, this class is a first-year-experience seminar at Wittenberg (a WittSem) and has the dual purpose of helping integrate the students into college life. After teaching the math/compsci-elective version of the class last year, I thought games could make for a nice WittSem topic. I was further spurred on by David Wolfe, who told me he had once taught a freshman-introduction class all about playing Go. (I only just played my first game of Go last week, so I wasn't ready for that!)

These new students have actually been very patient. I promised them early on we would spend entire class periods playing games, and it took over two weeks of class before we covered outcome classes; giving them something to analyze while playing.

Also on the point of teaching, I happened across an old reddit post of Joshua Biedenweg's, prior to his teaching a CGT course at UCSB. Josh finished teaching his course right as I was prepping for mine over a year ago; I took some good advice from him and unfortunately ignored some better advice! (Josh, I'm using Toads and Frogs more this year! Pictoral Evidence:

)

Next on the class agenda is Game Sums, and soon it will be time for them to find actual game values! Woohoo!

Conclusion: Teaching CGT is awesome. If you have the opportunity, take it!

Game Description: Amazons

Amazons was first introduced to me by Dale Garraway, a visiting professor at Colby while I was an undergrad. It is a nice combinatorial game because it can be played on a common checkerboard using chess pieces (though if you use the queen piece as an amazon, you will need multiple sets of pieces) and something to mark destroyed squares. Each turn, a player chooses one of their amazons, then moves that amazon just as a queen piece in chess, but may not move onto or through a square either occupied by another amazon or which had been "destroyed". After moving, that queen shoots an "arrow" at another square which is a "queen move" away from their current location.

The next player then takes their turn, continuing until the current player does not have a move.

Amazons was invented in 1988 by Walter Zamkauskas. The rules are simple to learn and enjoys computer-based opponent championships. In 2005, Bob Hearn showed Amazons to be PSPACE-complete, thus it is unlikely that an efficient algorithm can evaluate all Amazons boards of general size.

The play tip that Dale and I learned was that sugar packets do a great job of marking destroyed squares.

Enjoy the winter break! I am planning on returning to a normal posting schedule on Monday, Jan. 11, 2010.