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

All passable games are realizable as monotone set coloring games