Title text:
The draw-by-repetition rule does a good job of keeping players from sliding a tile back and forth repeatedly, but the tiles definitely introduce some weird en passant and castling edge cases.
Transcript:
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Source: https://xkcd.com/3139/
no, because it hasn't reached the 8th rank.
So even if it does not move, this pawn could get promoted by some future tile-slide... come to think of it, I guess two pawns could get promoted in the same turn via a tile-slide.
That does seem to be the case, yes. Although I expect your opponent wouldn't let you pull that off so easily.
A surprise, to be sure, but a welcome one