The deceptive number changing game, in the absence of symmetry

One player, Changer, in a two-person zero-sum game is given a random vector having independent identically distributed coordinates. He changes a limited number of coordinates and shows the resulting vector to Chooser who then chooses one of the coordinate positions. Changer then pays Chooser the number that was originally in that position. It is shown that if Changer is permitted to change at least half of the coordinates in the vector given to him, then he can show Chooser a vector that will not aid her in making a self-serving choice of a coordinate position.