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Welcome! We're mathematicians and computer scientists studying commutative monoids arising as solutions of misere-play combinatorial games.

What to read first?

In November 2006, Aaron Siegel gave five two-hour lectures on misere games at the Weizmann Institute. There's no better introduction to our subject.

Misere Games and Misere Quotients (PDF, 34 pages)
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 misere quotient construction; a proof of the Guy-Smith-Plambeck Periodicity Theorem; and statements of some recent results and open problems in the subject.


Alternatively, dive into the nitty-gritty. Here are some books and papers on our subject that have been already published or are available in the arXiv as preprints:

  • 2013-Aug-31: Combinatorial Game Theory [Aaron N. Siegel]. AMS Graduate Studies in Mathematics, American Mathematical Society (July 14, 2013).
  • 2013-Oct-07: Partizan Kayles and Misere Invertibility [Rebecca Milley. Here are more papers by Milley and her collaborators.]
  • 2013-Jan-08: The Secrets of Notakto: Winning at X-only Tic-Tac-Toe [Thane Plambeck, Greg Whitehead]
  • 2012-Sep-04: Lattice games without rational strategies [Alex Fink]
  • 2011-Sep-16: Various papers of Ezra Miller (his Duke web site) and Alan Guo (his MIT web site), and their collaborators (eg, Mike Weimerskirch). You'll find some of them using this arXiv search link.
  • 2007-May-27: Misere quotients for impartial games [Thane Plambeck, Aaron Siegel]
  • Journal of Combinatorial Theory, Series A (May 2008) pages 593-622.
  • 2007-May-16: Misere quotients for impartial games: supplementary material [Thane Plambeck, Aaron Siegel]
  • 2007-Mar-04: The structure and classification of misere quotients [Aaron Siegel]
  • 2006-Mar-01: Advances in losing [Thane Plambeck]
  • 2005-Jan-20: Taming the wild in impartial combinatorial games [Thane Plambeck]
  • The previous papers all treat impartial misere games.

    For a canonical theory of partizan misere games, start here:

  • 2007-Mar-20: Misere canonical forms of partizan games [Aaron Siegel]
  • EmblemXXV


    There is considerable mystery surrounding the category of commutative monoids that arise as misere quotients of impartial combinatorial games. We're quite interested in finding a structural theory. Since the algebraic objects of interest are beyond by-hand calculation, it's good that excellent software for investigating misere quotient monoids is already available.

    Solutions archive

    As new solutions of misere games are discovered, we're archiving them here.

    The email list

    You're invited to join the misere games mailing list.

    The blog

    That's right—there's even a blog on misere games! It's called Advances in Losing. If you're interested in more (particularly the history) of this topic, go see!

    Related material

    Theses, presentations, web sites, preprints, research notes

    Books (combinatorial games)

    Books (commutative monoids)

    These pages were last modified by Thane Plambeck (tplambeck@gmail.com)
    Last updated 8:16am Pacific time, Tue 8 Oct 2013