Wednesday, January 30, 2013

CGT Upcoming Events and a Wittenberg Games & Topology Talk

I added a section in the sidebar for upcoming CGT events.  Here's some info about 2013 events:

At Dalhousie University in Halifax, Nova Scotia (Canada), the CMS will hold their summer meeting June 4 - 7Richard Nowakowski and Paul Ottaway are organizing a special session on CGT as part of the meeting.  There will be more information coming about that.

I missed Games-at-Dal 2012, but if there is enough interest, the 2013 incarnation will take place the weekend following the CMS meeting. 

Also, if the pattern of odd-numbered years continues, Integers 2013 will take place this fall.  I saw dates for October 24-27, but that is from a second-hand source. 

Lots happening this year! 

Our department was lucky enough to host a talk about games (not by me).  On Monday, we had Lynne Yengülalp from the University of Dayton speak about infinite-turn topological games.  The starting position of the game is a topological space.  For both players, a move consists of choosing a non-empty, open (not strictly proper) subset of the previous position.

Even though the move options are the same, the game is strictly partisan: the two players, NOT-EMPTY and EMPTY, have different goals.  If the result of the infinitely-long game is the empty set, then the EMPTY player wins.  Otherwise, the NOT-EMPTY player wins.  This is a bit unintuitive at first, but if you consider the infinite sequence of open sets chosen in accordance with each player's strategy, then it can be the case that the infinite intersection is empty.

Lynne showed an even more unintuitive result for the real line where the NON-EMPTY player loses if they always choose the "biggest" set they can: namely the last position.  Instead, they win if each time they choose any proper open set contained within a closed subset of the last move. 

I don't know much about infinite games, but I'm pretty sure this is still combinatorial.  Either way, it's an excellent application of topology to games!

Wednesday, January 23, 2013

A Games Class, take Three!

Ahhh, a new year and a new semester!

There's plenty to talk about, but I'd like to begin with a success relevant to teaching.  I am teaching yet another CGT class.  Previously I've taught a Math/CS elective and a first-year seminar to college undergraduates.  This time I am teaching an honors seminar and so far things are going quite well.  I changed my teaching strategy a bit. We'll see how it pans out. 

We're in the third week and so far I haven't touched the book at all.  We've done nothing in class but play games and take notice of a few interesting aspects that come up.  I give them some challenges and let them puzzle through things.  I ask lots of questions and have been very pleased with the answers and ideas they're coming up with.

My goal is to instill motivation.  These are undergraduates, many with a non-math/cs/science background.  They are probably taking this class because it sounds fun (and it is worth Math credit).  Not only will I keep the class fun, by the end, I want them to be constantly asking me: "When are we going to learn how to play this game well?"

Or, even better: "When are we going to learn how to play sums of XXXX and YYYY well?"

The point is that while I can expect them to be motivated to play games and learn new games, I also want them to get a glimpse of how the more advanced material will become relevant to game play.  Perhaps then they'll be dive in to learning that as well.

I've rarely talked about hot games here, which is regrettable.  If you want to use CGT to play games well, determining the temperature of your summands is a vital aspect.  If you want to make the correct play on the sum of a Domineering game and a Clobber game, which of the two should you evaluate first?

We have seen just a few values, but today we'll actually delve into game trees and the "set notation" for positions.  Very soon we'll hit the fundamental theorem and take off from there.