In any two player game both players start and play in the same universe. A third and fourth player would be playing against players one and two in the other universe.

Now see how each player has access to hyperspace and how two of the four hyperspaces align with the Parallel Universe.

Even more interesting is the fact that each player starts with access to only two of the four spaces in the center of the board.

Another note is the fact that each hyperspace aligns with one of the four singularities in the center.

Master Diagram