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I think I could recommend Gary Gifford's Time Travel chess as an excellent
example of 'what if' chess. Every one of us has wanted to make different
moves in the same game, and this variant lets us do that. Given the
criterion of a simple, unique change that's easy to understand and shows
something of the extent of chess variants, I think this game of Gary's
just might fit.

As for placement games, they have their good points. Modern FIDE chess is a
speed game, with every piece pre-placed so that 1 move can bring it into
contact with the other side. As a wargame, it narrows conflict down to the
one decisive point of the war, starting just before the 'moment of
truth'. This eliminates many aspects of warfare, some of them important
but dreary, like logistics, some of them important but slow, like the
marching and counter-marching before the battle as the armies jockey for
position. Even the deployment of the troops is taken care of in FIDE before
the game starts. 

Big Board Chess brings the deployment back. That's an interesting touch
and provides a different experience, as the players now have 2 games to
play, deployment and combat. That's something I've looked at in some of
my own games, although not necessarily successfully, goChess being a good
example of a less than successful game. In those successful games, what I
do is offer pieces that are very short range compared to the board size.
Chieftain is the obvious one. The pieces need a few turns to come into
contact, and since the games are multi-movers, you can re-arrange a
significant portion of your army in a few turns. 

This advance to contact feature is obvious in the large multi-move
chieftain variants, but it also operates, although much less obviously, in
the game to be evaluated here, Great Shatranj. I think you would find some
evidence of the need to deploy and advance to battle in any game which,
like shatranj, allows the possibility of totally separate battles occurring
at the same time in 2 different board areas. Slower pieces add a more
strategic character to the game, as you must decide in advance what to send
to each area of the board before knowing what the enemy will have available
to oppose you when you get there. It's a chess game of a different flavor.