I am interested in the two player games where there is perfect information, the players move alternately, there are no random factors like die, and the last player to move determines the winner. Moreover, the games tend to break up into components and the players only get to play in one component on a turn. This includes games such as Nim and Amazons and the theory has been useful in Dots-&-Boxes, Go and Chess. The full theory was expounded in Winning Ways by Berlekamp Conway and Guy and On Numbers and Games by Conway---shamless plug--- also see Lessons in Play by Albert, Nowakowski and Wolfe. Games which are not immediately covered by this theory are the maker-maker and maker breaker games such as Tic-Tac-Toe and Hex.

For an introduction to a general theory of these games see the recent book Combinatorial games: tic-tac-toe theory by József Beck.


Current Topics of Interest:

  1. •Option closed games 

  2. •All-small games 

  3. •Loopy subtraction games

  4. •Hexadecimal games

  5. •Misere games

  6. •Enriched environments

  7. •Specific games: Phutball, Clobber and Snort

  8. •Scoring Games

Useful Links for budding Combinatorial Game Theorists

  1. •Combinatorial Game Suite, a java-based program for calculating values of games, including misere quotients and loopy games.

  2. •R. K. Guy, R. J. Nowakowski, Unsolved Problems in Combinatorial Game Theory, Games of No Chance 3, Cambridge University Press, 2009.

  3. •R. J. Nowakowski, History of Combinatorial Game Theory, Proceedings of the Board Game Studies Colloquium XI, Lisbon, 2008. 

  4. •MSRI publications, Games of No Chance, More Games of No Chance, and coming soon Games of No Chance 3, particularly the survey articles.

  5. •A. S. Fraenkel's bibliography of combinatorial game theory literature.

  6. •David Eppstein's games page

  7. •Thane Plambeck's misere games page

  8. •University of Alberta’s Games group


Publications---last 6 years

Articles

  1. • Richard J. Nowakowski, Gabriel Renault, Emily Lamoureux, Stephanie Mellon
    & Timothy Miller, The game of TIMBER!, Journal of Combinatorial Mathematics and Combinatorial Computing 85 (2013) 213-225.

  2. •Rebecca Milley, Richard J. Nowakowski, Paul Ottaway, The misere monoid of one-handed alternating games,  Integers (2012) 12b Article A1.

  3. •Przemyslaw Gordinowicz, Richard J. Nowakowski, Pawel Pralat, POLISH---or---Let's play the cleaning game, Theoretical Computer Science, 463 (2012) 123–132.

  4. •N. A. McKay, R. J. Nowakowski, Outcomes of Partizan Euclid, Integers (2012) 12b Article A9.

  5. •T. Cazenave, R. J. Nowakowski, retrograde Analysis of Woodpush, In Games of No Chance 4, to appear 2013.

  6. •Michael Albert, R.J. Nowakowski, Lattices of Games, Order, 16 (2011) 1-10.

  7. •R.J. Nowakowski , Paul Ottaway, Option-closed games, Contributions to Discrete Mathematics, 6 (2011) 142-153.

  8. •Eric Duchene, Aviezri S. Fraenkel, R. J. Nowakowski, Michel Rigo, Extensions and restrictions of Wythoff’s game preserving its P positions, to appear in J. Comb. Th. Ser A 117 (2010) 545-567.

  9. •J. P. Grossman, R. J. Nowakowski, A new pattern in hexadecimal games, to appear in Games of No Chance 4.

  10. •A. Fink, R. J. Nowakowski, A. N. Siegel, D. Wolfe, Toppling Conjectures, to Games of No Chance 4.

  11. •N. A. McKay, R. J. Nowakowski and A. A. Siegel, The Gods play MAZE, Proceedings of the

  12. •Recreational Mathematics Colloquium 1, Evora, 2009

  13. •Eric Duchene, A.S. Fraenkel, Sylvain Gravier, R. J. Nowakowski, Another bridge between Nim and Wythoff, Australas. J. of Combin. 44 (2009) 43-56.

  14. •G. A. Mesdal*, Partizan SPLITTLES, Games of No Chance 3, pp. 457-461, Cambridge University Press, 2009.

  15. •R. K. Guy, R. J. Nowakowski, Unsolved Problems in Combinatorial Game Theory, Games of No Chance 3, Cambridge University Press, 2009.

  16. •R. J. Nowakowski, History of Combinatorial Game Theory, Proceedings of the Board Game Studies Colloquium XI, Lisbon, 2008. 

  17. •G. A. Mesdal*, P. Ottaway, Simplification of Partizan Games in misere play, INTEGERS 7(2007) G6.

  18. •R. J. Nowakowski, A. A. Siegel, Partizan Geography on K_n x K_2, Combinatorial Number Theory, de Gruyter (2007), 389-401.  

Submitted

  1. •Alda Carvalho, Carlos Pereira dos Santos, Cátia Dias, Francisco Coelho, Joao Pedro Neto, Richard J. Nowakowski, Sandra Vinagre, On Lattices from Combinatorial Game Theory: Modularity and a Representation Theorem: Finite Case.

  2. •Alda Carvalho, Carlos Pereira dos Santos, Cátia Dias, Francisco Coelho, Joao Pedro Neto, Richard J. Nowakowski, Sandra Vinagre, On Lattices from Combinatorial Game Theory:  Infinite Case

  3. •Neil A. McKay, Rebecca Milley, Richard J. Nowakowski, Hackenbush Sprigs

Books and Proceedings

  1. •M. Albert, R. J. Nowakowski, D. Wolfe, Lessons in Play, AK Peters, 2007.

  2. •M. Albert, R. J. Nowakowski,, Editors, Games of No Chance 3, MSRI Publications 56, Cambridge University Press, 2009.

  3. •R. J. Nowakowski,, Editor, More Games of No Chance, MSRI Publications 42,  Cambridge University Press 2002.

  4. •RJN, Editor, Games of No Chance, MSRI Publications 29, Cambridge University Press, 1996.

  5. •E. D. Demaine, R. Fleischer, A. S. Fraenkel and R. J. Nowakowski, Appendix B: Open problems at the 2002 Dagstuhl Seminar on Algorithmic Combinatorial Game Theory,  J. Theoret. Comp. Sci., 313, (2004), 539-543. 

  6. •R. K. Guy, R. J. Nowakowski, Unsolved Problems in Combinatorial Game Theory, More Games of No Chance, Cambridge University Press, 2002, 457-473. 

  7. •Editor (with R. Fleischer) Special Edition, J. Theoret. Comp. Sci., 313, (2004), Proceedings of the Dagstuhl Seminar on Algorithmic Combinatorial Game Theory.


Students and Theses supervised

Graduates

  1. •Neil McKay       2013-expected  PhD topic: All-small games

  2. •Svenja Huntmann 2013 M.Sc.  (co-supervisor) topic: Simplicial Complexes of Placement Games.

  3. •Catia Dias          2013    Ph.D. Portugal, co-supervisor) Lattices related to Conway’s Construction.

  4. •Rebecca Milley  2013    Ph.D. Restricted Universes of Partizan Misere Universes

  5. •Angela Siegel     2011  Ph.D. topic: On the Structure of Games and their Posets

  6. •Carlos Santos     2010   PhD  (Portugal, co-supervisor) topic: nim-dimension

  7. •Meghan Allen    2009    Ph.D. An Investigation of Partizan Misere Games

  8. •Paul Ottaway     2009    Ph.D.  Combinatorial Games with Restricted Options under Normal and Misere Play

  9. •Neil McKay       2007    M.Sc. All-small games and Uptimals

  10. •Meghan Allen    2006    M.Sc. Impartial misere combinatorial games

  11. •Stewart Fraser    2006    M.Sc. Partisan misere games

  12. •Angela Siegel     2005    MSc.  Finite Excluded Subtraction Sets and Infinite Modular Nim

  13. •Paul Ottaway      2003    M.Sc.  Analysis of three new combinatorial games

  14. •Sarah McCurdy  2003    M.Sc. Cutthroat and Cherries

  15. •Todd Grimm      1998    M.Sc.  Describing the Play: Some Combinatorial Games.

Honours

  1. •Ethan MacCauley 2012    Halls and Walls

  2. •Ann Loosen         2007    Directions for Phutball

  3. •Sable McKeil       2004    Mancala and some variants

  4. •Amy Goldlist       2003    Constrained Geography

  5. •Sarah McCurdy   2002    The Lattice of Games born on day n

  6. •Megan Dewar     1999  The Ins and Outs of Geography