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For a good 15-minute exercise for undergraduates, I like Heidi Burgiel's paper 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.