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Without calculations, how can you visualize "that half the squares are white and half are black"?

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Please see the 2nd para. below alongside my red line. I can't "[i]magine rotating the chessboard 90 degrees clockwise." I can't visualize how "all the positions that had a white square now contain a black square, and vice versa".

Blitzstein. Introduction to Probability (2019 2 ed). Pages 9-10.

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