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Thank you Jeremy for your comments and rating and thank you Joe for your comments. It's very possible something similar has been tried before; I just haven't come across it. And one simple rule I considered adding along the lines of what Joe was saying is: in lieu of a turn, simply add 1 move to any piece. Call it 5hess+
And yes, there is no restriction on Pawn movement.
'...the only thing a chess piece values, moves.' I'll add captures, checks, pocketing / drops and mates to that....
An interesting idea. Likely excellent. Not necessarily suitable for games of maneuver with shortrange pieces, but an idea that might transpose well to Grand Chess, say. It also gives ideas for new pieces, say a Q-3, or an out-and-out time bomb, something that explodes and takes out the squares around it after 2 or 3 moves. Handicapping would also be easier here. Weak pieces could get more moves. You might design a 'Vampire' piece that would suck moves from a neighboring piece or three, but starting with just 1 or 2 moves. You might even have a 'life station' where you could fill up on moves. It certainly allows for trading of moves back and forth - allow a move and a trade per turn. Heck, allow 1 trade between neighbors and 1 move per side per turn in 6hess, and castling could give you a source of available moves, as a castled king with pawns should not need a lot of moves immediately, and that could be your 'filling station' spot. You get a real chess economy - one based on the only thing a chess piece values, moves.
Adrian, you designed an ingenious preset as a way of implementing the brilliant idea in this game, a transferable idea that I believe will open up new vistas for chess variants. Great ideas usually have predecessors, and this variant makes me hungry to learn more about this genre. Can anyone add some links to similar ideas? I believe David Howe may have a variant or two that uses something similar. Having played both versions, I'm prepared to rate this game excellent (both versions); it's simple and elegant. In the log for our game of 5hess, you mention that pawns in 5hess can travel more than five moves (a pawn in FIDE will travel a maximum of six moves during its lifespan). I'm glad you've finally posted these great games. Well done, Adrian!
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[Added note: Though 6hess was posted a little later than Multimove Chess, Adrian and I were playing it earlier, so it seems the two concepts - in fact different from one another - were possibly being developed around the same time.]