For a good 15-minute exercise for undergraduates, I like [Heidi Burgiel's paper][1] on how even a perfect Tetris player must eventually lose with probability one. I've given it as a talk before with almost no boardwork, and that was only to prove more rigorously some ideas that are pretty intuitive: that the best way to stack Ss and Zs vertically is by putting like-on-like, which I think most undergrads are happy to believe with just a little hand-waving.

  [1]: http://www.geom.uiuc.edu/java/tetris/tetris.ps