  The class of passable games was recently introduced by Selinger as a class of
combinatorial games that are suitable for modelling monotone set coloring games
such as Hex. In a monotone set coloring game, the players alternately color the
cells of a board with their respective color, and the winner is determined by a
monotone function of the final position. It is easy to see that every monotone
set coloring game is a passable combinatorial game. Here we prove the converse:
every passable game is realizable, up to equivalence, as a monotone set
coloring game.
