Wait, shouldn’t the number go up since the job became available?

True, but that doesn’t affect the win conditions of the game. All this really means is that the game cannot end in a draw and that players can effectively skip their turn at any point.

EDIT: because you still drop tokens in from the top, a vertical and a horizontally infinite properties would lead to very different strategies. For example, in a vertically Infinite board, a player could not effectively skip their turn as previously described.