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So, lots of pieces, large board to give those subtle gradations of
positional value, multi-move turns with a mechanism to spread each turn's
moves across the gameboard, scalable... what games are examples of this
[besides Gas Hogs ;-) ]? 

Go is, I believe, still an example of a game that humans play better than
computers. The weak spot in the idea that computers can play any game
better than humans, with the right algorithm, is the algorithm. I would
guess that idea is not proved, and suspect it may not be able to be proved
[Godel is the mystic name I invoke here, for the obvious reason]. But that
is speculation. What is, to the best of my knowledge, true, is that
computers don't play all games equally well now. [Otherwise, we wouldn't
need generals or CEOs, except on gameboards.] So, by providing
'difficult' games for computers, we may encourage better AIs in the
future. :-D 'Gaming has always driven computer design' is to a
considerable extent, a truism. So let's maybe help it along in a slightly
different way, by providing games that need new algorithms.

[Edit] I see Ji is ahead of me. One point he made I only thought of is the amount of time a computer needs to come up with a good move. I lose to Zillions because I tend to attempt to match its speed. While I am beginning to look at 2 possible initial moves, it's already 11 plies down. I'd like a game where a 2 minutes per move time limit was an equal handicap to both me and the computer.