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That's a great idea. I've seen the <a href=http://www.chessvariants.com/multiplayer.dir/4players.html>Four-Handed Chess Variants</a> on plus-shaped boards criticized for their wide-open spaces and slow action (the Cincinnati 4-way article makes this criticism, for example). But, as the setting for an epic tale, the vastness and slow opening would be part of the charm.
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I would consider Dessau (described in the Four-Handed Chess article) first. It has a plus-shaped board consisting of an 8x8 center to which four 3x8 rectangles have been appended, with the familiar Chess armies standing on the first two rows. The Ring would have to behave a little differently, since White needs to carry it sideways instead of forward. Instead of granting White the power to move one space straght or diagonally forward, it could be one space straight or diagonally toward Mordor.
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I don't think I like how some of White's pawns are so much closer to the final goal than others. Maybe the Ring can only be destroyed on the far half of Mordor's back rank.
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If I had more friends, I'd try it out. Thanks for the insight.