I looked at these online and they seemed pretty loser. One guy had a game with 64 pieces per side. Arrgh! As if a chess game wasn't long enough already.
I'd try a chess or checkers game with a 3x3x8 board. The 18 pieces per side fill the back two ranks on either end. A wall of nine pawns, nine other pieces behind them. That's not too far from trad chess. Better yet leave one of the cubes in the back rank empty. Then you have eight major pieces, just like trad chess. Or have a 2x4x8 board, in some ways that's more traditional. 64 cubes instead of 64 squares.
In trad chess one bishop is for only the white squares and the other for black. In 2D chess that falls out of the movement rules. In 3D chess this will also work with the rule that pieces in 2D moved between squares that shared only a vertex can in 3D move between cubes that share edges but not to cubes that share only a vertex. Rooks can still only move to cubes with which their cube shares a face.
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| R | Q | . |
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| k | K | B |
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| B | k | R |
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The back rank can be 3x3 or 2x4
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| R | Q | K | R |
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| B | k | k | B |
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Ha! I say that beats Fischer random. For a while anyway.
When I was a kid I had a 4x4x4 Tic Tac Toe board. That was pretty cool. 64 squares.