Antirandomizing the Wrong Game

We study a variant of the tenure game introduced by J. Spencer (Theor. Comput. Sci. 131 (1994), 415-429). In this version, chips are not removed from the game, but moved down to the lowest level instead. Though the rules of both versions dier only slightly, it seems impossible to convert an upper bound strategy into a lower bound one using the antirandomization approach of Spencer (which was very eective for the original game and several others)