262144 is correct. Unless you did strange things with blocking rules, I suspect 6 or more dimensional chess might be "boring" (first player always wins with some simple strategy), because it would be near-impossible to keep your king blocked. There is a lot if room up there
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Actually I think the opposite is true? I think it's probably not possible to win 6D chess (much to Donald's chagrin). For example, using the standard movement rules, a king can move to any of 728 different squares on its turn... it'll be very hard to cover so many!
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The bad news is we will never know. Web 2.0 couldn’t possibly render a board of that size.
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