The black box has the potential to turn Archie's genius against him.
The purpose of the black box is to keep Archie from creating an assignment that is too cruel or extreme. Every time Archie creates an assignment, he has to draw a marble from the black box. If he draws the wrong marble, Archie will have to carry out the assignment himself.
Up to this point in the story, Archie has "beaten the box" every time. If he draws the wrong marble now, Archie will be forced to participate in the fight that he has set up. Both Obie and Carter have become fed up with Archie at this point and would like to see him fail, at least once.
At the end of the book Obie attempts to outwit Archie by unexpectedly presenting him with the Vigils' box of marbles (which serves as a check on Archie's power)...
Forcing Archie to draw a marble from the black box before the fight is their way of removing Archie's advantage and potentially creating an opportunity for Archie to fail.