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I can tell you from personal experience that a planar-type piece is even
more powerful in 4D chess than in 3D. I would also recommend a smaller
board than 8x8x8x8. The problem with any planar-type piece is that it's
so powerful that you have to clog the board up with lesser pieces to
prevent instant checkmates. The more powerful the strong pieces, the more
plentiful the weak pieces is a really easy and very bad trap to fall into,
if you want a game that can be played by humans. And simple leapers work
fine in 4D. I used a knight that no longer has the leaping ability, and it
kicks butt, for my version of hyperchess. In 2D, you can add a lot of
pieces; the complications are in piece interaction. By the time you get to
4D, the board provides a good bit of the complication, so the pieces should
be simple, to balance. In hyperchess (does this need a new name - am I
infringing - how does Hyperchess 4D sound - that's what I thought). In
H4D only the standard 8 pieces and 8 pawns per side are used, on a 4x4x4x4
board, giving a starting piece density of 12.5%. And the movement rules are
basically simple translations from 2 to 4D. I would argue that good
movement rules and piece densities are very board-dependent. Ok, guess
I'm saying geometry-dependent, both the topology and the exact
measurements (as I'm finding out in a variant that mixes 2D-moving and
4D-moving pieces; ie: some pieces treat the board as 2D, some as 4D, and
some may choose.)
Is there a more appropriate forum for this discussion? Guess I'm too new
to know.                               Joe