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So I don’t understand. Bishop is just a Nightrider (repeats knight steps) or knight jumps OVER two squares to third one (by this it can reach all the squares in Tape chess)?
I like very much tape chess, especially the variant played on a circular shape tape. It's a pity that there's no Game Courier preset for Tape chess. So far I've played only with Zillions. I like simple and clear games, just as this one is.
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Since the Knight “moves” two squares and “jumps over” one, I'd go with the first interpretation: a Tape Chess Knight is a single‐leap TC Bishop. Iow they are Dabbabas/Dabbabariders
(per the page)
Since the ring basically is 1D (no ‘almost’ about it) and Möbius strips are a 2D idea (albeit realisable physically only bygoing into 2D/3D repectively) nothing special would happen; it'd be the same game