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Chess on an Infinite Plane. Chess game with no boundaries (infinite board), and Guard, Chancellor, and Hawk. () [All Comments] [Add Comment or Rating]
V. Reinhart wrote on 2018-01-09 UTC

@Aurelian, that is a really interesting comment, and I love that idea. Like you say, an unbounded board can be populated with an infinite number of pieces in many ways. In addition to what you mention, and "on top" of the "normal" armies (near the kings), pawns can be populated for example on every 10th file and every 10th rank. So the density in half the plane is 1/10 x 1/10 = 1%. Similarly bishops and rooks can be populated with a density such as 0.1%, and queens populated on 0.05%.

So now you really have an "infinite" game with "infinitely many" pieces. But still - only one king of each color. As in the diagram, the White king starts on (5,1) and the Black king starts on (5,8).

This could have amazing and very interesting mathematical properties. Obviously, the strategy of the end-game cannot be "simplification" to just a few pieces! Players will need to learn to mate as other pieces slowly march inward, trying to replenish captured pieces.

Who is going to solve this type of game strategy? You said it best: "But we as cyborgs of the future will get there".  I agree with you 100%!!!