Misère Games and Misère Quotients

These notes are based on a short course offered at the Weizmann Institute of Science in Rehovot, Israel, in November 2006. The notes include an introduction to impartial games, starting from the beginning; the basic misère quotient construction; a proof of the Guy–Smith–Plambeck Periodicity Theorem; and statements of some recent results and open problems in the subject. First and foremost, I wish to thank the scribes for the course: Taub. I also wish to thank Professor Aviezri Fraenkel for inviting me to the Weizmann Institute and suggesting this course, and thereby making these notes possible. Finally, I wish to thank Thane Plambeck, for recognizing the importance of misère quotients and inventing this beautiful and fascinating theory.