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The Chess Variant Pages

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Joe Joyce wrote on 2007-05-26 UTC
I would respectfully disagree that the board is infinite. By the rules, there can be at most 16 pairs of pieces, each in its own 8x8 playing area. If I'm doing the numbers right, that's 1024 squares maximum that can be used, although it is true that these 16 areas can be totally disconnected. 

Well, that seems reasonable, but let's re-think this. Assume the pair of pieces are diagonally separated by 6 empty squares. The opponent piece can move anywhere up to 7 squares away from the friendly one, giving a 15x15 square centered around the friendly piece. That gives 15x15 squares x16 pairs, or 3600 squares max potential board squares. If we don't know who's turn it is, that 15x15 square is duplicated over every piece, friendly and enemy. Doubling 3600 gives 7200, but there's overlap - 64 squares per pair, if I understand this correctly - subtracting 1024 squares from the total, leaving 6176 squares as the maximum potential size of the 'infinite' board. I think the 'actual' maximum size would be 3200, given that we know who moves next. That would occupy about a third of a 100x100 board.

This of course ignores any concept of chess strategy.

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