Winning Strategies for the Game of Chomp: A Practical Approach

Chomp 게임의 승리 전략: 실천적 고찰

  • Received : 2018.04.22
  • Accepted : 2018.06.18
  • Published : 2018.06.30


The rule of the game of Chomp is simple and the existence of a winning strategy can easily be proved. However, the existence tells us nothing about what strategies are winning in reality. Like in Chess or Baduk, many researchers studied the winning moves using computer programs, but no general patterns for the winning actions have not been found. In the paper, we aim to construct practical winning strategies based on backward induction. To do this we develop how to analyze Chomp and prove and find the winning strategies of the simple games of Chomp.


Supported by : Kongju National Univ.


  1. S. BADILLO-RIOS and V. MOJICA, Mathematical and Computational Analysis of Chomp, mimeo.
  2. A. BROUWER, G. HORVARATH, I. MOLINAR-SAKA, and C. SZABO, On Three-Rowed Chomp, Integers, 5, G07 (2005), 1-14.
  3. D. GALE, A Curious Nim-Type Game, American Mathematical Monthly, 81 (1974), 876-879.
  4. M. GARDNER, Sim, Chomp and Race Track: new games for the intellect (and not for Lady Luck), Mathematical Games, 228(1) (Jan. 1973), 108-115.
  5. M. GARDNER, A new miscellany of problems, and encores for Race Track, Sim, Chomp and elevators, Mathematical Games, 228(5) (May 1973), 102-107.
  6. E. FRIEDMAN and A. LANDSBERG, Nonlinear dynamics in combinatorial games: Renormalizing Chomp, CHAOS 17, 023117 (2007).
  7. F. SCHUH, Spel van delers, Nieuw Tijdschrift voor Wiskunde, 39 (1952), 299-304.
  8. X. SUN, Improvements on Chomp, Integers, 2, G01 (2002), 8.
  9. D. ZEILBERGER, Three-Rowed CHOMP, Advances in Applied Mathematics, 26 (2001), 168-179.
  10. U. SCHWALBE and P. WALKER, Zermelo and the Early History of Game Theory, Games and Economic Behavior, 34 (2001), 123-137.
  11. E. ZERMELO, Uber eine Anwendung der Mengenlehre auf die Theorie des Schachspiels, Proceedings of the Fifth International Congress of Mathematicians, Cambridge, 1912, Cambridge University Press, 1913, 501-504.