Option-closed games

We consider the class of combinatorial games with the property that each player's move eliminates some options but does not add any new options for that player. While the canonical form can be complicated, we show that the reduced canonical form of a position is either a number or a switch. Moreover, for a given position, the difference between the two canonical forms is bounded by $cgdoubledowncgstar$ and $cgdoubleupcgstar$.