A loopy game is a combinatorial game in which a sequence of moves can return to a previous position (Siegel 2009, p. 93). Such a cycle violates the termination condition for a Conway game, which applies even when successive options belong to the same player.
Loopy Game
See also
Conway Game, Short GameExplore with Wolfram|Alpha
References
Siegel, A. N. "Coping with Cycles." In Games of No Chance 3 (Ed. M. H. Albert and R. J. Nowakowski). Cambridge, England: Cambridge University Press, pp. 91-124, 2009. https://doi.org/10.1017/CBO9780511807251.004.Cite this as:
Weisstein, Eric W. "Loopy Game." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LoopyGame.html