Comments by "" (@PunmasterSTP) on "The Rook's Romp: A Game Theory Puzzle" video.
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@Gametheory101 That would be really cool, and I'm not sure if this would work, but I thought of something. You could represent the third dimension with a color. That's the tl;dr anyway; keep reading if you want more details.
For instance, say that we have a chess "rectangular prism" with one slice being the 6 by 12 board shown in the video. Then consider there to be 4 "slices" stacked vertically, for a total of 4*6*12 = 288 "cells". The rook starts off in the top, front, left corner, and the king is in the bottom, back, right corner. You could take a top-down view of the arena, exactly like what is shown in the video. Then you color the entire board a certain color corresponding to the level (kind of like color-coded levels in a parking garage, or the complex in The Andromeda Strain). Anytime one of the players moves the rook downwards, the color of the entire board changes. Or maybe you could show several different views of the arena at the same time.
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