[lqdtsotf] Distance to disaster

How many much of an advantage could be gained from a given chess position if one player could make N moves in a row (opponent not responding, i.e., null moves)?

Graph the shape of the "advantage" as a function of N. (In zugswang the graph dips first.)  For both players to move.  This might be a measure of the criticality of the position.

Perhaps king capture is forbidden, but setting up checkmate is acceptable.