Abstract: There are few results pertaining to John Conway's game of PHUTBALL or Philosophers Football. The problem of deciding whether a given position has a winning jump has been shown to be NP-complete and for the 1-dimensional case, only a partial strategy has been found. I consider a restricted version of PHUTBALL called DIRECTIONAL PHUTBALL, in which, as the name suggests, each player may only jump in a specified direction. The goal of this paper is to determine a partial order for the 2 x n case.