ABSTRACT
Most of the examples in Winning Ways have had only finitely many positions. But a game can have infinitely many positions and still satisfy the ending condition. More interesting are the games obtained by dropping the ending condition which was called as loopy games, since it's often possible to find oneself returning to the same position over and over again. Impartial games that need not end are handled by a similar generalization of the Smith theory. A play in a sum of several games defines plays in the individual components in an obvious way. The Inequality Rule amounts to a definition of inequalities between loopy games and must be shown to work. This chapter describes that every loopy game had stoppers for its onside and offside before Clive Bach, to whom some of the theory in this chapter is due, eventually found a game was called as the Carousel which has several disturbing features.
